CN110097579B - Multi-scale vehicle tracking method and device based on pavement texture context information - Google Patents

Multi-scale vehicle tracking method and device based on pavement texture context information Download PDF

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CN110097579B
CN110097579B CN201910514897.2A CN201910514897A CN110097579B CN 110097579 B CN110097579 B CN 110097579B CN 201910514897 A CN201910514897 A CN 201910514897A CN 110097579 B CN110097579 B CN 110097579B
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孔斌
赵富强
杨静
王灿
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Hefei Institutes of Physical Science of CAS
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Abstract

The invention relates to a multi-scale vehicle tracking method based on contextual information of pavement texture, which comprises the following steps: s1, acquiring the central position of the target vehicle for the linear space road texture condition, and S2, acquiring the central position of the target vehicle in the dual space for the nonlinear space road texture condition; s3, obtaining the central position of the target vehicle, and combining the central position with the optimal scale of the image of the current frame to obtain a more accurate position of the target vehicle; the invention also discloses a multi-scale vehicle tracking device based on the contextual information of the road texture. The invention combines the road texture area at the bottom of the target vehicle, the relative position of the target vehicle and the road surface can not change greatly in the moving process of the target vehicle, the road texture is more stable, the target vehicle can be accurately positioned by combining the road texture information, namely according to the relative relation between the target vehicle and the road surface area, and the target frame is prevented from drifting.

Description

Multi-scale vehicle tracking method and device based on pavement texture context information
Technical Field
The invention relates to the field of computer vision, in particular to a multi-scale vehicle tracking method and device based on road texture context information.
Background
Machine Learning (ML) is a multi-domain cross subject, and relates to multi-domain subjects such as probability theory, statistics, approximation theory, convex analysis, algorithm complexity theory and the like, and target tracking belongs to important application in the field of Machine Learning.
The invention patent with publication number "CN 108776974B" (application date 2018.05.24) discloses "a real-time target tracking method suitable for public traffic scenes, which comprises the following steps: step 1, acquiring an initial position P (i) of a tracked target on the current ith frame by a detector; step 2, training a relevant filtering tracker by using P (i); step 3, acquiring an image of the target in the (i +1) th frame; step 4, carrying out correlation calculation by using a correlation filter and the (i +1) th frame to obtain a target prediction position P' (i + 1); and 5, evaluating the scale change rate, and judging whether the target predicted value needs to be corrected or not according to a threshold value. And 6, correcting the predicted value by using Kalman filtering to obtain the position P (i +1) of the target in the (i +1) th frame. According to the method, the size change rate is evaluated, the tracking accuracy and the real-time performance are improved, meanwhile, the target predicted value is corrected through Kalman filtering, and the influence of scale change is minimized. "
However, the method only utilizes the target area to realize tracking, and in a traffic scene, when a target vehicle is shielded, the tracking accuracy is low, the average overlapping rate of the output result rectangular frame and the real target rectangular frame is low, and thus the target cannot be effectively tracked.
The existing tracking method only singly utilizes the characteristics of the target vehicle, when the target vehicle is shielded or motion-blurred, the frame selection area formed around the target vehicle to be positioned may deviate, so that the accuracy of predicting the position of the target vehicle is low.
Disclosure of Invention
The technical problem to be solved by the present invention is to provide a multi-scale vehicle tracking method and device based on the contextual information of the road texture, so as to solve the problem of low accuracy of the position of the target vehicle in the background art.
In order to solve the above problems, the present invention provides the following technical solutions:
a multi-scale vehicle tracking method based on contextual road texture information comprises the following steps:
s1, acquiring the central position of the target vehicle under the condition of linear space road texture;
s2, for the condition of the nonlinear space road texture, acquiring the central position of the target vehicle in the dual space;
and S3, obtaining the central position of the target vehicle, and combining the central position with the optimal scale of the image of the current frame to obtain a more accurate position of the target vehicle.
As a further scheme of the invention: the step S1 includes:
processing a plurality of background areas of the target vehicle by using a least square method to obtain a ridge regression formula, and performing cyclic shift merging simplification on ridge regression formula parts corresponding to the plurality of background areas; calculating the simplified ridge regression formula to obtain a first weight parameter matrix in the frequency domain
Figure GDA0003068994030000021
Using a first weight parameter matrix
Figure GDA0003068994030000022
Obtaining a first response matrix R, and carrying out Fourier transform on the first response matrix R to obtain the first response matrix in the frequency domain
Figure GDA0003068994030000023
Calculating to obtain a first response matrix in the frequency domain
Figure GDA0003068994030000024
The index corresponding to the maximum response value, namely the center position of the corresponding target vehicle;
wherein, the plurality of background areas comprise road surface texture areas.
As a further scheme of the invention: the step S1 further includes:
the obtained ridge regression formula is shown as the formula (1):
Figure GDA0003068994030000025
wherein, it is called
Figure GDA0003068994030000026
Represents a two-norm, A0A feature matrix representing samples after cyclic shift of the target vehicle; a. the1A feature matrix representing samples after cyclic displacement of a road surface area under a target vehicle; a. theiA feature matrix representing samples after cyclic shift of a background area of a left area or an upper end area or a right area of the target vehicle;
λ1representing the proportion of the information of the texture area of the road surface in the training process; lambda [ alpha ]2Represents A in the training processiProportion of corresponding noise area, lambda3Representing a regularization parameter and controlling the complexity of the first weight parameter matrix; y is0A two-dimensional Gaussian matrix label representing a target vehicle; w represents a first weight parameter matrix needing regression; k is a radical of1Representing the number of background areas around the target vehicle;
the formula (1) is divided into the following parts: the first part is
Figure GDA0003068994030000031
Representing training the target area as a positive sample; the second part is
Figure GDA0003068994030000032
The road area under the target is used as a positive sample for training, and the parameter lambda is1Controlling the degree of contribution to the loss; the third part is
Figure GDA0003068994030000033
Representing the sum of the noise training with the left, upper and right regions of the target vehicle as the parameter lambda2Controlling the degree of contribution to the loss; the fourth part is
Figure GDA0003068994030000034
Represents the complexity of the control weight parameter through training by regularization, which is represented by a parameter lambda3Controlling the degree of contribution to the loss;
then, combining the areas corresponding to the formula (1) to obtain a simplified formula (2):
Figure GDA0003068994030000035
wherein B and
Figure GDA0003068994030000036
is represented by formula (3):
Figure GDA0003068994030000037
b is a cyclic matrix, and B is a cyclic matrix,
Figure GDA0003068994030000038
a label matrix, which represents label values corresponding to samples in the sample space of each part;
by making
Figure GDA0003068994030000039
Obtaining a first weight parameter matrix w as formula (4):
Figure GDA00030689940300000310
wherein, BTWhich is the transpose of B, I denotes the identity matrix,
Figure GDA0003068994030000041
expressing that equation (2) derives w to be equal to zero;
fourier transformation is respectively carried out on two sides of the formula (4) to obtain a first weight parameter matrix in the frequency domain
Figure GDA0003068994030000042
The following were used:
Figure GDA0003068994030000043
wherein, aiA vector formed by a first row of a sample characteristic matrix in a sample space corresponding to the i-th area; an indication of a dot product operation;
Figure GDA0003068994030000044
is a vector aiAfter fourier transform processing, in the frequency domain;
Figure GDA0003068994030000045
to represent
Figure GDA0003068994030000046
The first response matrix in the frequency domain
Figure GDA0003068994030000047
The acquisition method comprises the following steps:
respectively expanding outwards by taking the position of the target vehicle in the previous frame as the center by taking the width N times and the height N times of the target vehicle, and taking the expanded region as a search region;
according to the property of the cyclic matrix, in the search area, cyclic shift is carried out in the horizontal direction and the vertical direction by taking pixels as units, a sample to be detected is obtained by each cyclic shift, the sample to be detected forms a sample space to be detected, and a sample characteristic matrix formed by characteristic values of the sample space to be detected uses Z1Representing, sample feature matrix Z1Performing matrix operation with the first weight parameter matrix w to obtain a first response matrix R, as shown in formula (6)
R＝Z1w (6)
And performing fourier transform on the first response matrix R to obtain equation (7), where equation (7) is as follows:
Figure GDA0003068994030000048
wherein the content of the first and second substances,
Figure GDA0003068994030000049
representing a sample feature matrix Z1The form in the frequency domain after fourier transform;
Figure GDA00030689940300000410
representing the form of the first weight parameter matrix w in the frequency domain after fourier transformation,
Figure GDA00030689940300000411
representing the form of the response matrix R in the frequency domain after Fourier transform processing to obtain
Figure GDA00030689940300000412
Namely, a first response matrix R is obtained, and the center position of the target vehicle is determined.
As a further scheme of the invention: the step S2 includes: by kernel function
Figure GDA0003068994030000051
Mapping the samples in the nonlinear sample space to a linearly separable dual space, and combining the eigenvectors of all the samples in the dual space to obtain a dual space weight parameter matrix wDualTraining a dual spatial weight parameter matrix wDualObtaining a second weight parameter matrix in the frequency domain
Figure GDA0003068994030000052
Solving a second response matrix in the frequency domain
Figure GDA0003068994030000053
And the index corresponding to the maximum response value is the center position of the target vehicle.
As a further scheme of the invention:
the step S2 further includes:
several regions of the target vehicle pass through the kernel function in dual space
Figure GDA00030689940300000511
After mapping, the corresponding sample space is as shown in equation (8):
Figure GDA0003068994030000054
wherein i represents an integer of zero or more and less than the number of target vehicle regions, aimFeature vector, A, of the m-th sample representing the i-th regioniRepresenting a feature matrix formed by samples of the ith area;
Figure GDA0003068994030000055
is a feature matrix AiA representation mapped into a linearly separable dual space,
Figure GDA0003068994030000056
mapping the circulant matrix B to a representation in a linearly separable dual space;
Figure GDA0003068994030000057
mapping the feature vector of the mth sample of the ith area to a representation form in a linearly separable dual space;
calculating a dual spatial weight parameter matrix w using equation (9)DualThe formula (9) is as follows:
Figure GDA0003068994030000058
wherein the content of the first and second substances,
Figure GDA0003068994030000059
to represent
Figure GDA00030689940300000510
A denotes a second weight parameter matrix, aiRepresenting the ith column vector in the second weight parameter matrix, biA feature vector representing the ith sample,
Figure GDA0003068994030000061
representing the characteristic direction of the ith sampleThe quantities are mapped to eigenvectors in a high-dimensional linear space, and 5m represents the dimension of the second weight parameter matrix;
obtaining a second weight parameter matrix in the frequency domain
Figure GDA0003068994030000062
The method comprises the following steps:
solving the second weight parameter matrix α loss function J (α) in conjunction with the loss function J (α) is shown in equation (10):
Figure GDA0003068994030000063
order to
Figure GDA0003068994030000064
Solving to obtain a second weight parameter matrix alpha, as shown in formula (11)
Figure GDA0003068994030000065
Wherein the content of the first and second substances,
Figure GDA0003068994030000066
K2is a matrix; by selecting kernel functions
Figure GDA0003068994030000067
So that the matrix K2The medium elements are changed in sequence, and the guarantee matrix K2Still a circulant matrix;
then will be
Figure GDA0003068994030000068
Substituted type
Figure GDA0003068994030000069
Obtaining a frequency domain representation of a second weight parameter matrix alpha in dual space
Figure GDA00030689940300000610
The formula is shown in formula (12):
Figure GDA00030689940300000611
wherein, Deltaij＝diag(mij+λ3),{(i,j)∈{(0,0)}}
Δij＝λ1diag(mij+λ3),{(i,j)∈{(1,1)}}
Δij＝λ2diag(mij+λ3),{(i,j)∈{(2,2),(3,3),(4,4)}}
Figure GDA00030689940300000612
Figure GDA0003068994030000071
Figure GDA0003068994030000072
Figure GDA0003068994030000073
diag(mij) The diagonal matrix corresponding to the ith row and the jth column of the block diagonal matrix is shown as formula (13)
Figure GDA0003068994030000074
Wherein, ai0A 0 th sample feature vector representing an ith region; a isj0A 0 th sample feature vector representing a jth region; a isjmAn m-th sample feature vector representing a j-th region;
Figure GDA0003068994030000075
m number representing i number of areaA kernel function between the sample feature vector and the mth sample feature vector of the jth region;
Figure GDA0003068994030000076
representing a kernel function between the m-th sample feature vector of the i-th region and the m-th sample feature vector of the j-th region,
finally solving a second response matrix in the frequency domain
Figure GDA0003068994030000077
Obtaining a second response matrix in the frequency domain
Figure GDA0003068994030000078
The maximum response value is the center position of the target vehicle.
As a further scheme of the invention: solving a second response matrix in the frequency domain
Figure GDA0003068994030000079
The calculation formula is as (14):
Figure GDA00030689940300000710
Z2represents: taking the position of the target vehicle in the previous frame as a center, respectively expanding outwards by N times of the width and the height of the target vehicle, taking the area after the outward expansion as a search area, in the search area, taking pixels as units, and circularly shifting transversely and longitudinally to obtain a sample space to be detected, wherein a sample characteristic matrix of the sample space uses Z2Represents;
Figure GDA0003068994030000081
is Z2Representation in the frequency domain after fourier transform;
Figure GDA0003068994030000082
and representing the parameter weight vector corresponding to the ith area in a frequency domain after Fourier transform.
AsThe further scheme of the invention is as follows: the step S3 includes: extracting different scale images of a plurality of target vehicles as training samples, training the scale sequence of the training samples by a least square method to obtain loss functions J (H), and processing the loss functions J (H) by Fourier transform to obtain J (H)*) To J (H)*) Calculating to obtain a third weight parameter matrix H in the frequency domain; then obtaining a scale response matrix RsCalculating a scale response matrix RsAnd the scale corresponding to the index corresponding to the medium maximum value is the optimal image scale of the current frame, so that the more accurate target vehicle position is obtained.
As a further scheme of the invention:
the step S3 further includes:
let the size of the image of the target vehicle in the current frame be W × H1Extracting a plurality of images with different scales as training samples and recording the training samples as S, wherein the scale sequence of the training samples is shown as the formula (15):
Figure GDA0003068994030000083
wherein b represents a scale factor; w represents the width of the rectangular frame area of the target vehicle; h1Representing the height of the target vehicle rectangular frame area; s represents the number of samples in the sample space;
Figure GDA0003068994030000084
is a rounded-down symbol;
the loss function obtained by calculating equation (15) by the least square method is shown in equation (16):
Figure GDA0003068994030000085
wherein y' represents a label vector generated by a one-dimensional Gaussian function, h represents a scale estimation weight parameter matrix, and f represents a sample set characteristic matrix extracted at different scales;
fourier transform is carried out on J (h) to obtainTo J (H)*) As shown in equation (17):
Figure GDA0003068994030000091
wherein, YiThe value of the ith element of the vector corresponding to the label vector y' in the frequency domain through Fourier transform; h*Performing Fourier transform on the scale estimation weight parameter matrix h to represent a conjugate transpose in a frequency domain; fiA representation form of Fourier transform of an ith sample feature vector in a sample feature matrix f in a frequency domain; sigma is a summation symbol, and the value of N is the same as that of S;
solving for J (H)*) The function obtains a third weight parameter matrix H, and a scale response matrix R is calculated by using a formula (19)sThe scale corresponding to the index corresponding to the medium maximum value is the optimal scale of the current frame, and equation (19) is as follows:
Rs＝F·H (19)
f is a representation form of a sample characteristic matrix F in a frequency domain after Fourier transformation;
Figure GDA0003068994030000092
is composed of
Figure GDA0003068994030000093
The conjugate transpose of (1); rsA scale response matrix R representing a calculated target vehiclesThe scale response matrix RsAnd the scale corresponding to the index corresponding to the medium maximum value is the optimal scale of the current frame, so that the more accurate position of the target vehicle is obtained.
As a further scheme of the invention: the solution J (H)*) The method of the function is as follows:
order to
Figure GDA0003068994030000094
And solving to obtain a third weight parameter matrix H in the frequency domain, as shown in formula (18):
Figure GDA0003068994030000095
as a further scheme of the invention: a multi-scale vehicle tracking device based on contextual road texture information, comprising:
the first acquisition module is used for acquiring the central position of a target vehicle under the condition of linear space road texture;
the second acquisition module is used for acquiring a central position dual space module of the target vehicle in a dual space under the condition of the road texture in the nonlinear space;
and the scale module is used for obtaining the central position of the target vehicle and combining the central position with the optimal scale of the image of the current frame to obtain a more accurate position of the target vehicle.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the method, the relative position of the target vehicle and the road surface is not changed greatly in the moving process of the target vehicle by combining the road surface texture area at the bottom of the target vehicle, and the road surface texture is stable in the moving process, so that the target vehicle is accurately positioned according to the relative relation between the target vehicle and the road surface area by combining the road surface texture information, the target frame is prevented from drifting, the average overlapping rate of the output result rectangular frame and the real target rectangular frame is the maximum, the average tracking failure frequency is relatively small, the average expected overlapping rate is the maximum, and the accuracy is high.
2. The existing target tracking method can not effectively and quickly combine the context information around the target with the scale prediction of the target, so that when the scale of the target changes, the existing tracking method can not accurately position the target boundary, and the weight parameters in the subsequent frames can not effectively learn the complete characteristics of the target, thereby causing tracking failure.
3. According to the method, the upper, left and right environmental information of the target vehicle is extracted and used as noise samples, and inhibition is carried out in the training process; taking the road texture information of the area below the target vehicle as a positive sample for auxiliary positioning, training by a ridge regression algorithm to obtain a first weight parameter matrix w, a second weight parameter matrix alpha and a scale estimation weight parameter matrix h, and using the first weight parameter matrix w and the second weight parameter matrix alpha to determine the central position of the target vehicle in a subsequent frame; the method adds a multi-scale tracking function and can accurately predict the size of the target vehicle.
4. Multiple experiments show that the specific gravity lambda of the contextual information of the texture of the road surface1When the average tracking failure frequency is 0.6, compared with the traditional tracking algorithm based on the target, the average overlapping rate of the output result rectangular frame of the algorithm and the real target rectangular frame is maximum, the average tracking failure frequency is relatively small, the average expected overlapping rate is maximum, and the performance of the method is better under the condition that the target is shielded; the contextual information of the pavement texture area is combined with a multi-scale method, and the tracking method can be more accurately adapted to the scale change of the target, so that the failure times of the tracking method are effectively reduced.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention.
Fig. 1 is a flow chart of a multi-scale vehicle tracking method based on contextual road texture information according to embodiment 1 of the present invention.
Fig. 2 is a schematic diagram illustrating a comparison of areas of target vehicles in a multi-scale vehicle tracking method based on contextual information of road surface texture according to embodiment 1 of the present invention.
Fig. 3 is a schematic structural diagram of a multi-scale vehicle tracking device based on contextual road texture information according to embodiment 2 of the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantageous effects to be solved by the present invention more clearly apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Example 1
A multi-scale vehicle tracking method based on contextual road texture information comprises the following steps: the method for tracking the spatial road texture in the context correlation filtering mode comprises the following specific steps:
s1, acquiring the central position of the target vehicle under the condition of linear space road texture;
processing a plurality of background areas of the target vehicle by using a least square method to obtain a ridge regression formula, wherein the least square method is a common algorithm in machine learning and is not described here; wherein, the plurality of background areas comprise road texture areas;
taking into account information of the road surface area under the target vehicle and other directions around the target vehicle, as shown in fig. 1, fig. 1 is a schematic diagram of a relative relationship between the target vehicle area and the surrounding area, where a0The corresponding zone represents the central zone of the target vehicle, A1The corresponding areas represent road surface texture areas, A2The corresponding region represents the noise region on the left side of the target vehicle, A3The corresponding region represents a noise region of the upper end of the target vehicle, A4The corresponding region represents a noise region on the right side of the target vehicle;
the ridge regression formula is shown in formula (1):
Figure GDA0003068994030000121
formula (1) is divided into four parts:
the first part is
Figure GDA0003068994030000122
Representing training the target area as a positive sample; the second part is
Figure GDA0003068994030000123
The road area under the target is used as a positive sample for training, and the parameter lambda is1Controlling the degree of contribution to the loss; the third part is
Figure GDA0003068994030000124
Representing the sum of the noise training with the left, upper and right regions of the target vehicle as the parameter lambda2Controlling the degree of contribution to the loss; the fourth part is
Figure GDA0003068994030000125
Represents the complexity of the control weight parameter through training by regularization, which is represented by a parameter lambda3Controlling the degree of contribution to the loss;
wherein the content of the first and second substances,
Figure GDA0003068994030000126
represents a two-norm, A0A feature matrix representing samples after cyclic shift of the target vehicle; a. the1A feature matrix representing samples after cyclic displacement of a road surface area under a target vehicle; a. theiA feature matrix representing samples after cyclic shifting of background areas on the left side, the upper end and the right side of the target vehicle; lambda [ alpha ]1Represents the proportion of the information of the texture area of the road surface in the training process, lambda2A representing the surroundings of the target vehicle during training2Proportion of corresponding noise area (A)3、A4The ratio of noise region to A2The proportion of the corresponding noise areas is the same); lambda [ alpha ]3Representing a regularization parameter and controlling the complexity of the first weight parameter matrix;
y0a two-dimensional Gaussian matrix label representing a target vehicle; w represents a first weight parameter matrix needing regression; k is a radical of1Indicates the number of background regions around the target vehicle, k in the present embodiment1The value is four; a. the0、A1、A2、A3、A4The corresponding five regions can be independently calculated, and the five region pairsThe corresponding parts are combined to obtain a simplified formula (2):
Figure GDA0003068994030000131
wherein B is a circulant matrix, in A0、A1、A2、A3、A4In the corresponding five regions, circularly moving a position in the horizontal direction and the longitudinal direction by unit pixels to obtain a training sample space, and then calculating HOG characteristics of the samples to form a sample matrix, namely a circular matrix B; the HOG (Histogram of Oriented gradients) feature is a feature description used for object detection in computer vision and image processing, and is formed by calculating and counting the Histogram of Gradient orientation of local areas of an image;
Figure GDA0003068994030000132
a label matrix, which represents label values corresponding to samples in the sample space of each part; b and
Figure GDA0003068994030000133
is represented by formula (3):
Figure GDA0003068994030000134
equation (2) is a convex function, where the optimal solution exists in the real number domain, by letting
Figure GDA0003068994030000135
Thereby obtaining a first weight parameter matrix w, as shown in equation (4):
Figure GDA0003068994030000141
BTwhich is the transpose of B, I denotes the identity matrix,
Figure GDA0003068994030000142
a function representing the composition of w and B differentiates w to be zero; at the same time, A0、A1、A2、A3、A4The corresponding five regions are mutually independent, and the feature matrix of each region can be calculated in parallel according to the property of the cyclic matrix, so that the real-time performance of the algorithm can be improved, and the calculation efficiency is accelerated;
after Fourier transformation is respectively carried out on two sides of the formula (4), the formula (5) is obtained:
Figure GDA0003068994030000143
wherein, aiA vector formed by a first row of a sample characteristic matrix in a sample space corresponding to the i-th area;
Figure GDA0003068994030000144
is a vector aiAfter fourier transform processing, in the frequency domain;
Figure GDA0003068994030000145
to represent
Figure GDA0003068994030000146
The conjugate transpose of (a) is performed,
Figure GDA0003068994030000147
is a representation of the tag matrix in the frequency domain.
Acquiring a first response matrix R, wherein an index corresponding to the maximum response value in the first response matrix R is the position of the center of the target vehicle of the current frame image; the position of the target vehicle in the previous frame is used as a center, and the target vehicle expands outwards along the periphery by N times of width and N times of height of the target vehicle respectively to be used as a search area;
in this embodiment, the value of N is 2.5 times, a position is cyclically moved in the horizontal and vertical directions in a search area by taking a pixel as a unit to obtain a sample space to be detected, and a sample feature matrix to be detected is represented by Z1To express, sample characteristicsSign matrix Z1Performing matrix operation with the first weight parameter matrix w to obtain a response matrix R;
R＝Z1w (6)
as shown in formula (6), the index corresponding to the maximum response value in the first response matrix R is the position of the center of the target vehicle in the current frame image, and the target vehicle can be tracked; fourier transform is carried out on the first response matrix R, and the formula (6) is equal to the formula (7) in horizontal direction; the Fourier transform converts the time domain signal (waveform) which is difficult to process originally into a frequency domain signal (frequency spectrum of the signal) which is easy to analyze, thereby facilitating analysis and calculation; the formula (7) is as follows:
Figure GDA0003068994030000151
Figure GDA0003068994030000152
representing a sample feature matrix Z1The form in the frequency domain after fourier transform;
Figure GDA0003068994030000153
representing the form of the first weight parameter matrix w in the frequency domain after fourier transformation,
Figure GDA0003068994030000154
representing the form of the first response matrix R in the frequency domain after Fourier transform processing;
Figure GDA0003068994030000155
indicating a dot product operation.
S2, for the condition of the nonlinear space road texture, acquiring the central position of the target vehicle in the dual space;
the classification regression problem is generally classified into a linear problem and a nonlinear problem, and for the linear problem, the solution is directly performed through a linear function, while for the nonlinear problem, the sample space needs to be converted into a new linear space, i.e., a dual space, so that the samples can be linearly divided in the dual space, and the problem can be converted into a linear divisible problem.
By kernel function
Figure GDA0003068994030000156
And mapping the samples in the nonlinear sample space to a linearly separable dual space, wherein the sample space corresponding to the five regions in the dual space is shown as the formula (8):
Figure GDA0003068994030000157
wherein i is 0, 1, 2, 3, 4, aimFeature vector, A, of the m-th sample representing the i-th regioniA feature matrix formed by samples representing the ith region,
Figure GDA0003068994030000158
is a feature matrix AiA representation mapped into a linearly separable dual space,
Figure GDA0003068994030000159
mapping the circulant matrix B to a representation in a linearly separable dual space;
Figure GDA00030689940300001510
mapping the feature vector of the mth sample of the ith area to a representation form in a linearly separable dual space;
in dual space, a dual space weight parameter matrix wDualMatrix w of dual spatial weight parametersDualIs represented by a linear combination of the feature vectors of all samples, as shown in equation (9):
Figure GDA0003068994030000161
wherein the content of the first and second substances,
Figure GDA0003068994030000162
to represent
Figure GDA0003068994030000163
A denotes a second weight parameter matrix, aiRepresenting the ith column vector in the second weight parameter matrix, biA feature vector representing the ith sample,
Figure GDA0003068994030000164
the feature vector representing the ith sample is mapped to a feature vector in a high-dimensional linear space,
Figure GDA0003068994030000165
representation matrix
Figure GDA0003068994030000166
A matrix form linearly combined with the second weight parameter matrix α; 5m denotes a dimension of the second weight parameter matrix;
in dual space, the second weight parameter matrix α is solved using a loss function J (α), which is shown as equation (10):
Figure GDA0003068994030000167
by making
Figure GDA0003068994030000168
That is, the derivative of the second weight parameter matrix α to the function composed of the second weight parameter matrix α and B is equal to zero, so as to solve the second weight parameter matrix α, as shown in formula (11)
Figure GDA0003068994030000169
Wherein, the matrix
Figure GDA00030689940300001610
K2Is a matrix;
by selecting appropriate kernel functions
Figure GDA00030689940300001611
So that the matrix K2The medium elements are changed in sequence, the calculation result of the kernel function is not influenced, and the matrix K is ensured2Still a circulant matrix, several classes of kernel functions satisfy this property:
polynomial kernel function: k (x, y) ═ f (x)Ty)；
RBF kernel function: k (x, y) ═ f (| | | x-y | | | non-luminous phosphor2)；
Will be provided with
Figure GDA0003068994030000171
Substituted type
Figure GDA0003068994030000172
And finally obtaining the frequency domain representation of the second weight parameter matrix alpha in the dual space according to the property of the block circulant matrix and the Fourier diagonalization property of the circulant matrix
Figure GDA0003068994030000173
The formula is shown in formula (12):
Figure GDA0003068994030000174
wherein, Deltaij＝diag(mij+λ3),{(i,j)∈{(0,0)}}
Δij＝λ1diag(mij+λ3),{(i,j)∈{(1,1)}}
Δij＝λ2diag(mij+λ3),{(i,j)∈{(2,2),(3,3),(4,4)}}
Figure GDA0003068994030000175
Figure GDA0003068994030000176
Figure GDA0003068994030000177
Figure GDA0003068994030000178
diag(mij) The diagonal matrix corresponding to the ith row and the jth column of the block diagonal matrix is shown as formula (13)
Figure GDA0003068994030000179
Wherein, ai0A 0 th sample feature vector representing an ith region; a isj0A 0 th sample feature vector representing a jth region; a isjmAn m-th sample feature vector representing a j-th region; kappa (a)i0,aj0) Representing a kernel function between the 0 th sample feature vector of the ith region and the 0 th sample feature vector of the jth region; k (a)im，ajm) Representing a kernel function between an m-th sample feature vector of the i-th region and an m-th sample feature vector of the j-th region;
using the second weight parameter matrix alpha and the frequency domain form
Figure GDA0003068994030000181
Solving for a second response matrix in the frequency domain
Figure GDA0003068994030000182
As shown in formula (14);
the target position of the frame is used as the center, the frame is respectively outwards expanded by N times of the width and the height of a target vehicle and is used as a search area, N in the embodiment is 2.5, in the search area, pixels are used as units, the frame is circularly moved by one position in the transverse direction and the longitudinal direction to obtain a sample space to be detected, and a sample characteristic matrix to be detected uses Z2Representing, by a sample feature matrix Z2And a second weight parameterThe matrix alpha is of the type (14) and a second response matrix in the frequency domain is solved in the frequency domain
Figure GDA0003068994030000183
Second matrix
Figure GDA0003068994030000184
The index corresponding to the medium and maximum response value is the position of the center of the target vehicle of the current frame image;
Figure GDA0003068994030000185
wherein Z is2A feature matrix of a sample space that is a search area;
Figure GDA0003068994030000187
is Z2Representation in the frequency domain after fourier transform;
Figure GDA0003068994030000188
representing the parameter weight vector corresponding to the ith area in a frequency domain after Fourier transform;
s3, introducing an adaptive scale model;
in the vehicle tracking process of the road environment, the scale of the front vehicle collected by the vehicle-mounted camera is easy to change due to the change of the relative speed of the front vehicle and the current vehicle, and the traditional nuclear correlation filter cannot adapt to the condition that the scale of the target vehicle is changed greatly. Therefore, an adaptive scale model is introduced on the basis of the traditional kernel correlation filtering.
The problem related to the scale is solved by adopting an image pyramid or filter pyramid model, and the scale estimation is carried out by sampling images with different scales at certain intervals, but the problem of sharply increased calculated amount is caused, and the real-time performance of a tracking algorithm is influenced. Therefore, according to the characteristics of target tracking in a road environment, a dimension processing scale problem is added, and the steps are as follows:
extracting a plurality of images with different scales as training samples; calculating a scale sequence of the training sample by a least square method;
the size of the target vehicle image in the current frame is W multiplied by H, and a plurality of samples of the sample space are extracted and recorded as S;
preferably, the number of samples in this embodiment is selected to be 33, that is, 33 images with different scales are extracted as training samples, and the scale sequence size of the training samples is as shown in equation (15):
Figure GDA0003068994030000191
wherein: b represents a scale factor, the empirical value in this embodiment is 1.05, W represents the width of the rectangular frame region of the target vehicle, H1Representing the height of the rectangular frame area of the target vehicle, S representing the number of samples of the sample space;
Figure GDA0003068994030000192
is a rounded-down symbol;
according to the formula (15), in the peripheral area of the center position of the target vehicle, the loss function of the scale training is obtained through the least square method calculation, and the formula (16) is shown as follows:
Figure GDA0003068994030000193
wherein: y' represents a label vector generated by a one-dimensional Gaussian function, h represents a scale estimation weight parameter matrix, and f is a sample set characteristic matrix extracted at different scales;
processing the formula (16) by using Fourier transform, and converting the processed formula (16) into a frequency domain for optimization, as shown in a formula (17);
Figure GDA0003068994030000194
wherein: y isiThe value of the i-th element of the corresponding vector in the frequency domain for the label vector y' after Fourier transformation；H*Performing Fourier transform on the scale estimation weight parameter matrix h to represent a conjugate transpose in a frequency domain; fiA representation form of Fourier transform of an ith sample feature vector in a sample feature matrix f in a frequency domain; Σ is the summation sign, and the value of N is the same as the value of S, where N is 33.
Order to
Figure GDA0003068994030000201
The derivation H of the formula (17)*Equal to zero, and then solved to obtain a third weight parameter matrix H in the frequency domain, as shown in equation (18):
Figure GDA0003068994030000202
the scale response matrix R is calculated using equation (19)sThe scale corresponding to the index corresponding to the medium maximum value is the optimal scale of the current frame, and equation (19) is as follows:
Rs＝F·H (19)
taking the central position of a target vehicle in a current frame image as a reference coordinate, taking a target scale in a previous frame image as an initial scale, sampling samples under different scales according to a formula (15), calculating a sample characteristic matrix, and expressing the sample characteristic matrix by using F, wherein F is a representation form of the sample characteristic matrix F in a frequency domain after Fourier transformation;
Figure GDA0003068994030000203
is composed of
Figure GDA0003068994030000204
The conjugate transpose of (1); rsA scale response matrix R representing a calculated target vehiclesThe scale response matrix RsThe scale corresponding to the index corresponding to the medium maximum value is the optimal scale of the current frame, and the obtained optimal scale is combined with the central position of the target vehicle, so that the boundary of the target vehicle is more accurately positioned, and the aim of tracking the vehicle is fulfilled.
The embodiment adopts the tracking algorithm based on the road texture information to locate the most probable central position of the target vehicle in the image; then, sampling a plurality of image areas with different scales, generating a label vector through a one-dimensional Gaussian function, still adopting a kernel correlation filtering algorithm to perform scale learning again to obtain a one-dimensional filtering vector h, sampling the positioned images with different scales in a tracking stage, and calculating the obtained characteristic vector with the h, wherein in the final response vector, the scale corresponding to the position with the maximum response value is the ideal target scale.
Multiple experiments show that the specific gravity lambda of the contextual information of the texture of the road surface1When the value is 0.6, compared with the traditional tracking algorithm based on the target, the average overlapping rate of the output result rectangular frame of the algorithm and the real target rectangular frame is the largest, the average tracking failure frequency is relatively smaller, and the average expected overlapping rate is the largest.
A multi-scale vehicle tracking device based on road texture context information comprises:
a first obtaining module 301, configured to obtain a center position of a target vehicle in a linear space road texture condition;
the first obtaining module 301 further comprises processing a plurality of background areas of the target vehicle by using a least square method to obtain a ridge regression formula, and performing cyclic shift merging simplification on ridge regression formula parts corresponding to the plurality of background areas; calculating the simplified ridge regression formula to obtain a first weight parameter matrix in the frequency domain
Figure GDA0003068994030000211
Using a first weight parameter matrix
Figure GDA0003068994030000212
Obtaining a first response matrix R, and carrying out Fourier transform on the first response matrix R to obtain the first response matrix in the frequency domain
Figure GDA0003068994030000213
Calculating to obtain a first response matrix in the frequency domain
Figure GDA0003068994030000214
The index corresponding to the maximum response value, namely the center position of the corresponding target vehicle;
the obtained ridge regression formula is shown as the formula (1):
Figure GDA0003068994030000215
wherein, it is called
Figure GDA0003068994030000216
Represents a two-norm, A0A feature matrix representing samples after cyclic shift of the target vehicle; a. the1A feature matrix representing samples after cyclic displacement of a road surface area under a target vehicle; a. theiA feature matrix representing samples after cyclic shift of a background area of a left area or an upper end area or a right area of the target vehicle;
λ1representing the proportion of the information of the texture area of the road surface in the training process; lambda [ alpha ]2Represents A in the training processiProportion of corresponding noise area, lambda3Representing a regularization parameter and controlling the complexity of the first weight parameter matrix; y is0A two-dimensional Gaussian matrix label representing a target vehicle; w represents a first weight parameter matrix needing regression; k is a radical of1Representing the number of background areas around the target vehicle;
the formula (1) is divided into the following parts: the first part is
Figure GDA0003068994030000221
Representing training the target area as a positive sample; the second part is
Figure GDA0003068994030000222
Indicating a road area under the objectThe field is trained as a positive sample, with a parameter λ1Controlling the degree of contribution to the loss; the third part is
Figure GDA0003068994030000223
Representing the sum of the noise training with the left, upper and right regions of the target vehicle as the parameter lambda2Controlling the degree of contribution to the loss; the fourth part is
Figure GDA0003068994030000224
Represents the complexity of the control weight parameter through training by regularization, which is represented by a parameter lambda3Controlling the degree of contribution to the loss;
then, combining the areas corresponding to the formula (1) to obtain a simplified formula (2):
Figure GDA0003068994030000225
wherein B and
Figure GDA0003068994030000226
is represented by formula (3):
Figure GDA0003068994030000227
b is a cyclic matrix, and B is a cyclic matrix,
Figure GDA0003068994030000228
a label matrix, which represents label values corresponding to samples in the sample space of each part;
by making
Figure GDA0003068994030000229
Obtaining a first weight parameter matrix w as formula (4):
Figure GDA00030689940300002210
wherein, BTWhich is the transpose of B, I denotes the identity matrix,
Figure GDA0003068994030000231
expressing that equation (2) derives w to be equal to zero;
fourier transformation is respectively carried out on two sides of the formula (4) to obtain a first weight parameter matrix in the frequency domain
Figure GDA0003068994030000232
The following were used:
Figure GDA0003068994030000233
wherein, aiA vector formed by a first row of a sample characteristic matrix in a sample space corresponding to the i-th area; an indication of a dot product operation;
Figure GDA0003068994030000234
is a vector aiAfter fourier transform processing, in the frequency domain;
Figure GDA0003068994030000235
to represent
Figure GDA0003068994030000236
The conjugate transpose of (a) is performed,
Figure GDA0003068994030000237
is a representation of the tag matrix in the frequency domain; a first response matrix in the frequency domain
Figure GDA0003068994030000238
The acquisition method comprises the following steps:
respectively expanding outwards by taking the position of the target vehicle in the previous frame as the center by taking the width N times and the height N times of the target vehicle, and taking the expanded region as a search region;
depending on the nature of the circulant matrix, in the search area,performing horizontal and vertical cyclic shift by taking pixels as units, obtaining a sample to be detected once per cyclic shift, forming a sample space to be detected by the sample to be detected, and using Z as a sample characteristic matrix formed by characteristic values of the sample space to be detected1Representing, sample feature matrix Z1Performing matrix operation with the first weight parameter matrix w to obtain a first response matrix R, as shown in formula (6)
R＝Z1w (6)
And performing fourier transform on the first response matrix R to obtain equation (7), where equation (7) is as follows:
Figure GDA0003068994030000239
wherein the content of the first and second substances,
Figure GDA00030689940300002310
representing a sample feature matrix Z1The form in the frequency domain after fourier transform;
Figure GDA00030689940300002311
representing the form of the first weight parameter matrix w in the frequency domain after fourier transformation,
Figure GDA00030689940300002312
representing the form of the response matrix R in the frequency domain after Fourier transform processing to obtain
Figure GDA0003068994030000241
Namely, a first response matrix R is obtained, and the center position of the target vehicle is determined.
A second obtaining module 302, configured to obtain a dual-space module of a center position of the target vehicle in a dual space in a case of a road texture in a nonlinear space;
the second obtaining module 302 further includes: by kernel function
Figure GDA0003068994030000242
Sampling in a nonlinear sample spaceMapping to a linearly separable dual space, and combining the eigenvectors of all samples in the dual space to obtain a dual space weight parameter matrix wDualTraining a dual spatial weight parameter matrix wDualObtaining a second weight parameter matrix in the frequency domain
Figure GDA0003068994030000243
Solving a second response matrix in the frequency domain
Figure GDA0003068994030000244
The index corresponding to the maximum response value is the central position of the target vehicle;
several regions of the target vehicle pass through the kernel function in dual space
Figure GDA0003068994030000245
After mapping, the corresponding sample space is as shown in equation (8):
Figure GDA0003068994030000246
wherein i represents an integer of zero or more and less than the number of target vehicle regions, aimFeature vector, A, of the m-th sample representing the i-th regioniRepresenting a feature matrix formed by samples of the ith area;
Figure GDA0003068994030000247
is a feature matrix AiA representation mapped into a linearly separable dual space,
Figure GDA0003068994030000248
mapping the circulant matrix B to a representation in a linearly separable dual space;
Figure GDA0003068994030000249
mapping the feature vector of the mth sample of the ith area to a representation form in a linearly separable dual space;
calculating a dual spatial weight parameter matrix w using equation (9)DualThe formula (9) is as follows:
Figure GDA00030689940300002410
wherein the content of the first and second substances,
Figure GDA0003068994030000251
to represent
Figure GDA0003068994030000252
A denotes a second weight parameter matrix, aiRepresenting the ith column vector in the second weight parameter matrix, biA feature vector representing the ith sample,
Figure GDA0003068994030000253
the eigenvector representing the ith sample is mapped to the eigenvector in the high-dimensional linear space, and 5m represents the dimension of the second weight parameter matrix;
obtaining a second weight parameter matrix in the frequency domain
Figure GDA0003068994030000254
The method comprises the following steps:
solving the second weight parameter matrix α loss function J (α) in conjunction with the loss function J (α) is shown in equation (10):
Figure GDA0003068994030000255
order to
Figure GDA0003068994030000256
Solving to obtain a second weight parameter matrix alpha, as shown in formula (11)
Figure GDA0003068994030000257
Wherein the content of the first and second substances,
Figure GDA0003068994030000258
K2is a matrix; by selecting kernel functions
Figure GDA0003068994030000259
So that the matrix K2The medium elements are changed in sequence, and the guarantee matrix K2Still a circulant matrix;
then will be
Figure GDA00030689940300002510
Substituted type
Figure GDA00030689940300002511
Obtaining a frequency domain representation of a second weight parameter matrix alpha in dual space
Figure GDA00030689940300002512
The formula is shown in formula (12):
Figure GDA00030689940300002513
wherein, Deltaij＝diag(mij+λ3),{(i,j)∈{(0,0)}}
Δij＝λ1diag(mij+λ3),{(i,j)∈{(1,1)}}
Δij＝λ2diag(mij+λ3),{(i,j)∈{(2,2),(3,3),(4,4)}}
Figure GDA0003068994030000261
Figure GDA0003068994030000262
Figure GDA0003068994030000263
Figure GDA0003068994030000264
diag(mij) The diagonal matrix corresponding to the ith row and the jth column of the block diagonal matrix is shown as formula (13)
Figure GDA0003068994030000265
Wherein, ai0A 0 th sample feature vector representing an ith region; a isj0A 0 th sample feature vector representing a jth region; a isjmAn m-th sample feature vector representing a j-th region; kappa (a)i0,aj0) Representing a kernel function between the 0 th sample feature vector of the ith region and the 0 th sample feature vector of the jth region;
Figure GDA0003068994030000266
representing a kernel function between the m-th sample feature vector of the i-th region and the m-th sample feature vector of the j-th region,
solving a second response matrix in the frequency domain
Figure GDA0003068994030000267
The calculation formula is as (14):
Figure GDA0003068994030000268
Z2represents: taking the position of the target vehicle in the previous frame as a center, respectively expanding outwards by N times of the width and the height of the target vehicle, taking the area after the outward expansion as a search area, in the search area, taking pixels as units, and circularly shifting transversely and longitudinally to obtain a sample space to be detected, wherein a sample characteristic matrix of the sample space uses Z2Represents;
Figure GDA0003068994030000271
is Z2Representation in the frequency domain after fourier transform;
Figure GDA0003068994030000272
obtaining a second response matrix in the frequency domain for the representation form of the parameter weight vector corresponding to the ith region in the frequency domain after Fourier transform
Figure GDA0003068994030000273
The maximum response value is the central position of the target vehicle;
the scale module 303 is configured to obtain a central position of the target vehicle, and combine the central position with the optimal scale of the image of the current frame to obtain a more accurate position of the target vehicle;
the scale module further comprises 303: extracting different scale images of a plurality of target vehicles as training samples, training the scale sequence of the training samples by a least square method to obtain loss functions J (H), and processing the loss functions J (H) by Fourier transform to obtain J (H)*) To J (H)*) Calculating to obtain a third weight parameter matrix H in the frequency domain; then obtaining a scale response matrix RsCalculating a scale response matrix RsThe scale corresponding to the index corresponding to the medium maximum value is the optimal image scale of the current frame, and a more accurate target vehicle position is obtained;
let the size of the image of the target vehicle in the current frame be W × H1Extracting a plurality of images with different scales as training samples and recording the training samples as S, wherein the scale sequence of the training samples is shown as the formula (15):
Figure GDA0003068994030000274
wherein b represents a scale factor; w represents the width of the rectangular frame area of the target vehicle; h1Representing the height of the target vehicle rectangular frame area; s represents the number of samples in the sample space;
Figure GDA0003068994030000275
is a rounded-down symbol;
the loss function obtained by calculating equation (15) by the least square method is shown in equation (16):
Figure GDA0003068994030000276
wherein y' represents a label vector generated by a one-dimensional Gaussian function, h represents a scale estimation weight parameter matrix, and f represents a sample set characteristic matrix extracted at different scales;
fourier transform is carried out on J (H) to obtain J (H)*) As shown in equation (17):
Figure GDA0003068994030000281
wherein, YiThe value of the ith element of the vector corresponding to the label vector y' in the frequency domain through Fourier transform; h*Performing Fourier transform on the scale estimation weight parameter matrix h to represent a conjugate transpose in a frequency domain; fiA representation form of Fourier transform of an ith sample feature vector in a sample feature matrix f in a frequency domain; sigma is a summation symbol, and the value of N is the same as that of S;
order to
Figure GDA0003068994030000282
And solving to obtain a third weight parameter matrix H in the frequency domain, as shown in formula (18):
Figure GDA0003068994030000283
the scale response matrix R is calculated using equation (19)sThe scale corresponding to the index corresponding to the medium maximum value is the optimal scale of the current frame, and equation (19) is as follows:
Rs＝F·H (19)
wherein F is the representation in the frequency domain after Fourier transform of the sample feature matrix FForms thereof;
Figure GDA0003068994030000284
is composed of
Figure GDA0003068994030000285
The conjugate transpose of (1); rsA scale response matrix R representing a calculated target vehiclesThe scale response matrix RsAnd the scale corresponding to the index corresponding to the medium maximum value is the optimal scale of the current frame, so that the more accurate position of the target vehicle is obtained.
In the description of the present invention, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (8)

1. A multi-scale vehicle tracking method based on contextual road texture information is characterized by comprising the following steps:
s1, acquiring the central position of the target vehicle under the condition of linear space road texture;
the step S1 includes: processing a plurality of background areas of the target vehicle by using a least square method to obtain a ridge regression formula, and performing cyclic shift merging simplification on ridge regression formula parts corresponding to the plurality of background areas; calculating the simplified ridge regression formula to obtain a first weight parameter matrix in the frequency domain
Figure FDA0003068994020000015
Using a first weight parameter matrix
Figure FDA0003068994020000016
Obtaining a first response matrix R, and carrying out Fourier transform on the first response matrix R to obtain the first response matrix in the frequency domain
Figure FDA0003068994020000017
Calculating to obtain a first response matrix in the frequency domain
Figure FDA0003068994020000014
The index corresponding to the maximum response value, namely the center position of the corresponding target vehicle;
wherein, the plurality of background areas comprise road texture areas;
the step S1 further includes:
the obtained ridge regression formula is shown as the formula (1):
Figure FDA0003068994020000011
wherein, it is called
Figure FDA0003068994020000012
Represents a two-norm, A0A feature matrix representing samples after cyclic shift of the target vehicle; a. the1A feature matrix representing samples after cyclic displacement of a road surface area under a target vehicle; a. theiA feature matrix representing samples after cyclic shift of a background area of a left area or an upper end area or a right area of the target vehicle;
λ1representing the proportion of the information of the texture area of the road surface in the training process; lambda [ alpha ]2Represents A in the training processiProportion of corresponding noise area, lambda3Representing a regularization parameter and controlling the complexity of the first weight parameter matrix; y is0A two-dimensional Gaussian matrix label representing a target vehicle; w represents a first weight parameter matrix requiring regression；k1Representing the number of background areas around the target vehicle;
the formula (1) is divided into the following parts: the first part is
Figure FDA0003068994020000013
Representing training the target area as a positive sample; the second part is
Figure FDA0003068994020000021
The road area under the target is used as a positive sample for training, and the parameter lambda is1Controlling the degree of contribution to the loss; the third part is
Figure FDA0003068994020000022
Representing the sum of the noise training with the left, upper and right regions of the target vehicle as the parameter lambda2Controlling the degree of contribution to the loss; the fourth part is
Figure FDA0003068994020000023
Represents the complexity of the control weight parameter through training by regularization, which is represented by a parameter lambda3Controlling the degree of contribution to the loss;
then, combining the areas corresponding to the formula (1) to obtain a simplified formula (2):
Figure FDA0003068994020000024
wherein B and
Figure FDA0003068994020000025
is represented by formula (3):
Figure FDA0003068994020000026
b is a cyclic matrix, and B is a cyclic matrix,
Figure FDA0003068994020000027
a label matrix, which represents label values corresponding to samples in the sample space of each part;
by making
Figure FDA0003068994020000028
Obtaining a first weight parameter matrix w as formula (4):
Figure FDA0003068994020000029
wherein, BTWhich is the transpose of B, I denotes the identity matrix,
Figure FDA00030689940200000210
expressing that equation (2) derives w to be equal to zero;
fourier transformation is respectively carried out on two sides of the formula (4) to obtain a first weight parameter matrix in the frequency domain
Figure FDA00030689940200000211
The following were used:
Figure FDA00030689940200000212
wherein, aiA vector formed by a first row of a sample characteristic matrix in a sample space corresponding to the i-th area; an indication of a dot product operation;
Figure FDA0003068994020000031
is a vector aiAfter fourier transform processing, in the frequency domain;
Figure FDA0003068994020000032
to represent
Figure FDA0003068994020000033
The conjugate transpose of (a) is performed,
Figure FDA0003068994020000034
is a representation of the tag matrix in the frequency domain; a first response matrix in the frequency domain
Figure FDA0003068994020000035
The acquisition method comprises the following steps:
respectively expanding outwards by taking the position of the target vehicle in the previous frame as the center by taking the width N times and the height N times of the target vehicle, and taking the expanded region as a search region;
according to the property of the cyclic matrix, in the search area, cyclic shift is carried out in the horizontal direction and the vertical direction by taking pixels as units, a sample to be detected is obtained by each cyclic shift, the sample to be detected forms a sample space to be detected, and a sample characteristic matrix formed by characteristic values of the sample space to be detected uses Z1Representing, sample feature matrix Z1Performing matrix operation with the first weight parameter matrix w to obtain a first response matrix R, as shown in formula (6)
R＝Z1w (6)
And performing fourier transform on the first response matrix R to obtain equation (7), where equation (7) is as follows:
Figure FDA0003068994020000036
wherein the content of the first and second substances,
Figure FDA0003068994020000037
representing a sample feature matrix Z1The form in the frequency domain after fourier transform;
Figure FDA0003068994020000038
representing the form of the first weight parameter matrix w in the frequency domain after fourier transformation,
Figure FDA0003068994020000039
representing the form of the response matrix R in the frequency domain after Fourier transform processing to obtain
Figure FDA00030689940200000310
Obtaining a first response matrix R, and determining the central position of the target vehicle;
s2, for the condition of the nonlinear space road texture, acquiring the central position of the target vehicle in the dual space;
and S3, obtaining the central position of the target vehicle, and combining the central position with the optimal scale of the image of the current frame to obtain a more accurate position of the target vehicle.
2. The method for multi-scale vehicle tracking based on contextual road texture information according to claim 1, wherein said step S2 comprises: by kernel function
Figure FDA00030689940200000411
Mapping the samples in the nonlinear sample space to a linearly separable dual space, and combining the eigenvectors of all the samples in the dual space to obtain a dual space weight parameter matrix wDualTraining a dual spatial weight parameter matrix wDualObtaining a second weight parameter matrix in the frequency domain
Figure FDA0003068994020000041
Solving a second response matrix in the frequency domain
Figure FDA0003068994020000042
And the index corresponding to the maximum response value is the center position of the target vehicle.
3. The method for multi-scale vehicle tracking based on contextual road texture information according to claim 2, wherein said step S2 further comprises:
several zones of the target vehicle in the dual spaceDomain passing kernel function
Figure FDA0003068994020000043
After mapping, the corresponding sample space is as shown in equation (8):
Figure FDA0003068994020000044
wherein i represents an integer of zero or more and less than the number of target vehicle regions, aimFeature vector, A, of the m-th sample representing the i-th regioniRepresenting a feature matrix formed by samples of the ith area;
Figure FDA0003068994020000045
is a feature matrix AiA representation mapped into a linearly separable dual space,
Figure FDA0003068994020000046
mapping the circulant matrix B to a representation in a linearly separable dual space;
Figure FDA0003068994020000047
mapping the feature vector of the mth sample of the ith area to a representation form in a linearly separable dual space;
calculating a dual spatial weight parameter matrix w using equation (9)DualThe formula (9) is as follows:
Figure FDA0003068994020000048
wherein the content of the first and second substances,
Figure FDA0003068994020000049
to represent
Figure FDA00030689940200000410
Transposed, alpha table ofShowing a second weight parameter matrix, alphaiRepresenting the ith column vector in the second weight parameter matrix, biA feature vector representing the ith sample,
Figure FDA0003068994020000051
the eigenvector representing the ith sample is mapped to the eigenvector in the high-dimensional linear space, and 5m represents the dimension of the second weight parameter matrix;
obtaining a second weight parameter matrix in the frequency domain
Figure FDA0003068994020000052
The method comprises the following steps:
solving the second weight parameter matrix α loss function J (α) in conjunction with the loss function J (α) is shown in equation (10):
Figure FDA0003068994020000053
order to
Figure FDA0003068994020000054
Solving to obtain a second weight parameter matrix alpha, as shown in formula (11)
Figure FDA0003068994020000055
Wherein the content of the first and second substances,
Figure FDA0003068994020000056
K2is a matrix; by selecting kernel functions
Figure FDA0003068994020000057
So that the matrix K2The medium elements are changed in sequence, and the guarantee matrix K2Still a circulant matrix;
then will be
Figure FDA0003068994020000058
Substituted type
Figure FDA0003068994020000059
Obtaining a frequency domain representation of a second weight parameter matrix alpha in dual space
Figure FDA00030689940200000510
The formula is shown in formula (12):
Figure FDA00030689940200000511
wherein, Deltaij＝diag(mij+λ3),{(i,j)∈{(0,0)}}
Δij＝λ1diag(mij+λ3),{(i,j)∈{(1,1)}}
Δij＝λ2diag(mij+λ3),{(i,j)∈{(2,2),(3,3),(4,4)}}
Figure FDA00030689940200000512
Figure FDA0003068994020000061
Figure FDA0003068994020000062
Figure FDA0003068994020000063
diag(mij) The diagonal matrix corresponding to the ith row and the jth column of the block diagonal matrix is shown as formula (13)
Figure FDA0003068994020000064
Wherein, ai0A 0 th sample feature vector representing an ith region; a isj0A 0 th sample feature vector representing a jth region; a isjmAn m-th sample feature vector representing a j-th region; k (a)i0,aj0) Representing a kernel function between the 0 th sample feature vector of the ith region and the 0 th sample feature vector of the jth region; k (a)im，ajm) Representing a kernel function between the m-th sample feature vector of the i-th region and the m-th sample feature vector of the j-th region,
finally solving a second response matrix in the frequency domain
Figure FDA0003068994020000065
Obtaining a second response matrix in the frequency domain
Figure FDA0003068994020000066
The maximum response value is the center position of the target vehicle.
4. The method of claim 3, wherein the solving of the second response matrix in the frequency domain is performed by using a multi-scale vehicle tracking method based on contextual information of road texture
Figure FDA0003068994020000067
The calculation formula is as (14):
Figure FDA0003068994020000068
Z2represents: the position of the target vehicle in the previous frame is taken as the center, the target vehicle is respectively expanded outwards by N times of the width and the height of the target vehicle, the expanded outwards area is taken as a search area, in the search area, pixels are taken as units, the horizontal and vertical cyclic shift is carried out, a sample space to be detected is obtained, and the sample spaceZ for sample feature matrix2Represents;
Figure FDA0003068994020000071
is Z2Representation in the frequency domain after fourier transform;
Figure FDA0003068994020000072
and representing the parameter weight vector corresponding to the ith area in a frequency domain after Fourier transform.
5. The method for multi-scale vehicle tracking based on contextual road texture information according to claim 1, wherein said step S3 comprises: extracting different scale images of a plurality of target vehicles as training samples, training the scale sequence of the training samples by a least square method to obtain loss functions J (H), and processing the loss functions J (H) by Fourier transform to obtain J (H)*) To J (H)*) Calculating to obtain a third weight parameter matrix H in the frequency domain; then obtaining a scale response matrix RsCalculating a scale response matrix RsAnd the scale corresponding to the index corresponding to the medium maximum value is the optimal image scale of the current frame, so that the more accurate target vehicle position is obtained.
6. The method for multi-scale vehicle tracking based on contextual road texture information according to claim 5, wherein said step S3 further comprises:
let the size of the image of the target vehicle in the current frame be W × H1Extracting a plurality of images with different scales as training samples and recording the training samples as S, wherein the scale sequence of the training samples is shown as the formula (15):
Figure FDA0003068994020000073
wherein b represents a scale factor; w represents the width of the rectangular frame area of the target vehicle; h1Rectangular frame for representing target vehicleThe height of the region; s represents the number of samples in the sample space;
Figure FDA0003068994020000074
is a rounded-down symbol;
the loss function obtained by calculating equation (15) by the least square method is shown in equation (16):
Figure FDA0003068994020000075
wherein y' represents a label vector generated by a one-dimensional Gaussian function, h represents a scale estimation weight parameter matrix, and f represents a sample set characteristic matrix extracted at different scales;
fourier transform is carried out on J (H) to obtain J (H)*) As shown in equation (17):
Figure FDA0003068994020000081
wherein, YiThe value of the ith element of the vector corresponding to the label vector y' in the frequency domain through Fourier transform; h*Performing Fourier transform on the scale estimation weight parameter matrix h to represent a conjugate transpose in a frequency domain; fiA representation form of Fourier transform of an ith sample feature vector in a sample feature matrix f in a frequency domain; sigma is a summation symbol, and the value of N is the same as that of S;
solving for J (H)*) The function obtains a third weight parameter matrix H, and a scale response matrix R is calculated by using a formula (19)sThe scale corresponding to the index corresponding to the medium maximum value is the optimal scale of the current frame, and equation (19) is as follows:
Rs＝F·H (19)
f is a representation form of a sample characteristic matrix F in a frequency domain after Fourier transformation;
Figure FDA0003068994020000082
is composed of
Figure FDA0003068994020000083
The conjugate transpose of (1); rsA scale response matrix R representing a calculated target vehiclesThe scale response matrix RsAnd the scale corresponding to the index corresponding to the medium maximum value is the optimal scale of the current frame, so that the more accurate position of the target vehicle can be obtained.
7. The method of claim 6, wherein the solution J (H) is obtained by solving for contextual information of road texture*) The method of the function is as follows:
order to
Figure FDA0003068994020000084
And solving to obtain a third weight parameter matrix H in the frequency domain, as shown in formula (18):
Figure FDA0003068994020000085
8. a multi-scale vehicle tracking device based on contextual road texture information, comprising:
a first acquisition module (301) for acquiring a center position of a target vehicle in the case of a linear space road texture;
the first acquisition module (301) comprises: processing a plurality of background areas of the target vehicle by using a least square method to obtain a ridge regression formula, and performing cyclic shift merging simplification on ridge regression formula parts corresponding to the plurality of background areas; calculating the simplified ridge regression formula to obtain a first weight parameter matrix in the frequency domain
Figure FDA0003068994020000091
Using a first weight parameter matrix
Figure FDA0003068994020000092
Obtaining a first response matrix R, and carrying out Fourier transform on the first response matrix R to obtain the first response matrix in the frequency domain
Figure FDA0003068994020000093
Calculating to obtain a first response matrix in the frequency domain
Figure FDA0003068994020000094
The index corresponding to the maximum response value, namely the center position of the corresponding target vehicle;
wherein, the plurality of background areas comprise road texture areas;
the first acquisition module (301) further comprises:
the obtained ridge regression formula is shown as the formula (1):
Figure FDA0003068994020000095
wherein, it is called
Figure FDA0003068994020000096
Represents a two-norm, A0A feature matrix representing samples after cyclic shift of the target vehicle; a. the1A feature matrix representing samples after cyclic displacement of a road surface area under a target vehicle; a. theiA feature matrix representing samples after cyclic shift of a background area of a left area or an upper end area or a right area of the target vehicle;
λ1representing the proportion of the information of the texture area of the road surface in the training process; lambda [ alpha ]2Represents A in the training processiProportion of corresponding noise area, lambda3Representing a regularization parameter and controlling the complexity of the first weight parameter matrix; y is0A two-dimensional Gaussian matrix label representing a target vehicle; w represents a first weight parameter matrix needing regression; k is a radical of1Representing the number of background areas around the target vehicle;
the formula (1) is divided into the following parts: the first part is
Figure FDA0003068994020000101
Representing training the target area as a positive sample; the second part is
Figure FDA0003068994020000102
The road area under the target is used as a positive sample for training, and the parameter lambda is1Controlling the degree of contribution to the loss; the third part is
Figure FDA0003068994020000103
Representing the sum of the noise training with the left, upper and right regions of the target vehicle as the parameter lambda2Controlling the degree of contribution to the loss; the fourth part is
Figure FDA0003068994020000104
Represents the complexity of the control weight parameter through training by regularization, which is represented by a parameter lambda3Controlling the degree of contribution to the loss;
then, combining the areas corresponding to the formula (1) to obtain a simplified formula (2):
Figure FDA0003068994020000105
wherein B and
Figure FDA0003068994020000106
is represented by formula (3):
Figure FDA0003068994020000107
b is a cyclic matrix, and B is a cyclic matrix,
Figure FDA0003068994020000108
for a label matrix, samples representing respective partsLabel values corresponding to samples in the space;
by making
Figure FDA0003068994020000109
Obtaining a first weight parameter matrix w as formula (4):
Figure FDA00030689940200001010
wherein, BTWhich is the transpose of B, I denotes the identity matrix,
Figure FDA00030689940200001011
expressing that equation (2) derives w to be equal to zero;
fourier transformation is respectively carried out on two sides of the formula (4) to obtain a first weight parameter matrix in the frequency domain
Figure FDA00030689940200001012
The following were used:
Figure FDA0003068994020000111
wherein, aiA vector formed by a first row of a sample characteristic matrix in a sample space corresponding to the i-th area; an indication of a dot product operation;
Figure FDA0003068994020000112
is a vector aiAfter fourier transform processing, in the frequency domain;
Figure FDA0003068994020000113
to represent
Figure FDA0003068994020000114
The conjugate transpose of (a) is performed,
Figure FDA0003068994020000115
is a representation of the tag matrix in the frequency domain; a first response matrix in the frequency domain
Figure FDA0003068994020000116
The acquisition method comprises the following steps:
respectively expanding outwards by taking the position of the target vehicle in the previous frame as the center by taking the width N times and the height N times of the target vehicle, and taking the expanded region as a search region;
according to the property of the cyclic matrix, in the search area, cyclic shift is carried out in the horizontal direction and the vertical direction by taking pixels as units, a sample to be detected is obtained by each cyclic shift, the sample to be detected forms a sample space to be detected, and a sample characteristic matrix formed by characteristic values of the sample space to be detected uses Z1Representing, sample feature matrix Z1Performing matrix operation with the first weight parameter matrix w to obtain a first response matrix R, as shown in formula (6)
R＝Z1w (6)
And performing fourier transform on the first response matrix R to obtain equation (7), where equation (7) is as follows:
Figure FDA0003068994020000117
wherein the content of the first and second substances,
Figure FDA0003068994020000118
representing a sample feature matrix Z1The form in the frequency domain after fourier transform;
Figure FDA0003068994020000119
representing the form of the first weight parameter matrix w in the frequency domain after fourier transformation,
Figure FDA00030689940200001110
representing the form of the response matrix R in the frequency domain after Fourier transform processing to obtain
Figure FDA00030689940200001111
Obtaining a first response matrix R, and determining the central position of the target vehicle;
a second obtaining module (302) for obtaining a center position dual space module of the target vehicle in the dual space in case of the road texture in the nonlinear space;
and the scale module (303) is used for obtaining the central position of the target vehicle and combining the central position with the optimal scale of the image of the current frame to obtain a more accurate position of the target vehicle.
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