CN108960296B - Model fitting method based on continuous latent semantic analysis - Google Patents
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Abstract
A model fitting method based on continuous latent semantic analysis relates to a computer vision technology. A data set is prepared. And constructing a potential semantic space by fusing the preference analysis and the potential semantic analysis. The data distribution of the latent semantic space is analyzed. Outliers are adaptively removed in the underlying semantic space. And performing cluster analysis on the rest data points in the potential semantic space. And estimating model parameters according to the clustering result to complete model fitting. A potential semantic space is quickly and effectively constructed by fusing continuous preference analysis and potential semantic analysis, and input data are projected into the constructed potential semantic space, so that outliers are close to an origin point, and interior points from different model instances are distributed in different subspaces, and a complex model fitting problem is regarded as a subspace recovery problem in the potential semantic space. The method can quickly and effectively process the problem of model fitting.
Description
Technical Field
The invention relates to a computer vision technology, in particular to a model fitting method based on continuous latent semantic analysis.
Background
Geometric model fitting is one of the most challenging tasks in computer vision. Its main task is to efficiently estimate the appropriate model parameters from the observed data. Model fitting methods have been widely used in the field of computer vision, such as motion segmentation, image stitching, optical flow computation, homography estimation, basis matrix estimation, three-dimensional reconstruction, and so on.
Over the past few decades, a number of model fitting algorithms have been proposed. Among them, Random Sample Consensus (RANSAC) (M.A. Fischler and R.C. balls.random Sample Consensus: a parallel for model fitting with applications to image analysis and automated card mapping. Comm. ACM,24(6): 381- "395, 1981) is a more popular fitting algorithm. On the one hand, RANSAC is widely used in different computer vision tasks. On the other hand, researchers have proposed a number of variants of RANSAC to improve its performance. However, RANSAC has some significant limitations. For example, RANSAC employs a "fit-remove" framework. The computational effectiveness of this framework is not very high and requires a significant amount of computational time. In general, a model fitting method comprises two steps: 1) generating a plurality of model hypotheses by sampling; 2) parameters of the model instance are estimated from these model hypotheses. Many works propose effective improvements for two steps, such as development (y.kanazawa and h.kawakami, Detection of planar regions with underlying spatial utilization of features of.
Current model fitting methods can be divided into two categories, namely model fitting methods based on consistency analysis and model fitting methods based on preference analysis. Model fitting methods based on consistency analysis, such as GPbM (s.misttal, s.anand, and p.meer, Generalized project-based m-estimator, IEEE trans.pattern animal.mach.intell., vol.34, No.12, pp.2351-2364,2012), AKSWH (h.wang, t.j.chi, and d.suter, simultane output fixing and setting subset data threads, IEEE trans.pattern animal.mach.intell., vol.34, No.6, pp.1177-1192,2012) and MSH (h.wang, g.xiao, y.yan, and d.suter, model-setting for high order analysis), map, graph, and map, have good robustness distribution. However, their performance tends to depend on the quality of the model assumptions. Preference analysis-based model fitting methods such as HF (g.xiao, h.wang, t.lai, and d.suter, Hypergraph modeling for geometry model fitting, Pattern recogn, vol.60, No.1, pp.748-760,2016), RPA (l.major and da.fusello, Multiple structure recovery view robustprediction analysis, Image and Vision fitting, vol.67, pp.1-15,2017) and T-link (l.major and da.functional, T-link: actions relay j-link for multi-model fitting, ieee pro.conf.picture, Pattern, 3954), tend to achieve higher fitting accuracy. However, they are computationally inefficient.
Disclosure of Invention
The invention aims to provide a model fitting method based on continuous latent semantic analysis.
Firstly, generating a certain number of model hypotheses by a sampling method; then calculating a preference matrix based on the generated model hypothesis, then fusing preference analysis and potential semantic analysis to construct a potential semantic space, and projecting input data into the space; and finally, removing outliers and intra-cluster points by analyzing the constructed potential semantic space, and completing model fitting.
The invention comprises the following steps:
1) a data set is prepared.
2) And constructing a potential semantic space by fusing the preference analysis and the potential semantic analysis.
3) The data distribution of the latent semantic space is analyzed.
4) Outliers are adaptively removed in the underlying semantic space.
5) And performing cluster analysis on the rest data points in the potential semantic space.
6) And estimating model parameters according to the clustering result to complete model fitting.
In step 1), the specific steps of preparing the data set may be:
extracting the features of the image by adopting a feature extraction algorithm to obtain X ═ XiN, n is the total number of data, and n is a natural number.
In step 2), the fusion preference analysis and latent semantic analysis to construct a latent semantic space may include the following sub-steps:
(1) randomly sampling m minimum subsets from the data set, wherein a minimum subset refers to the minimum data set required for estimating a model, for example, 4 points are required for estimating a plane, 7 or 8 points are required for estimating a basic matrix, and the like;
(2) evaluating the model hypothesis parameters of each minimum subset;
(3) calculating the preference value of each data point and each model hypothesis, wherein the calculation formula of the preference value is as follows:
in the formula (I), the compound is shown in the specification,
data point xiTo the assumption of thetajIs (c) (which can be measured in sampson distance), ψ is a real number greater than zero;
(4) constructing a preference matrix F through the preference values, and decomposing the preference matrix, wherein the matrix decomposition formula is as follows:
F＝U∑VT
∑＝diag(σ1,...,σd)
in the formula, U and V respectively represent a left singular vector matrix and a right singular vector matrix, sigma is a diagonal matrix and is a singular value on the diagonal, and a non-emission reduction sequence, namely sigma is used1≥σ2≥…≥σd> 0, where d ═ rank (F), denotes the rank of matrix F;
(5) and further reducing the dimension of the preference matrix F, wherein the dimension reduction formula is as follows:
Fn×mVm×k≈Un×k∑k×k
in the formula, n and m respectively represent the number of data points and model hypotheses, and k represents the number of model instances contained in the input data;
(6) and constructing a potential semantic space based on the reduced-dimension preference matrix, and projecting the input data into the constructed space.
In step 4), the adaptively removing outliers in the potential semantic space may comprise the sub-steps of:
(1) calculating the Euclidean distance from the data points to the origin in the potential semantic space;
(2) in the potential semantic space, according to the Euclidean distance between the data points and the origin, the threshold value is set adaptively to remove the data points close to the origin.
In step 5), the clustering analysis of the remaining data points in the potential semantic space may include the following sub-steps:
(1) sampling the rest data points in the semantic space and fitting a straight line (the straight line is a straight line passing through the origin);
(2) and carrying out cluster analysis on the data points through the straight line obtained by fitting.
The method quickly and effectively constructs the potential semantic space by fusing continuous preference analysis and potential semantic analysis, and projects input data into the constructed potential semantic space, so that outliers are close to an origin point and interior points from different model instances are distributed in different subspaces, and the complex model fitting problem is regarded as the problem of recovering the subspaces in the potential semantic space. The method can quickly and effectively process the problem of model fitting.
Drawings
FIG. 1 is a schematic flow chart of an embodiment of the present invention.
FIG. 2 is a partial result of homography estimation performed on AdelaideRMF data set (H.S.Wong, T. -J.Chin, J.Yu, and D.Suter. dynamic and hierarchical multi-structure geometric model fixing. in ICCV, pages 1044-1051,2011) provided by H.S.Wong according to the present invention (wherein D1-D5 respectively represent Bonython, Elderhala, Library, Sene and Hartley). The first row is the real structure segmentation result, and the second row is the segmentation result of the invention.
Fig. 3 is a partial result of the basis matrix estimation performed on adelaidermmf dataset (h.s.wong, t. -j.chi, j.yu, and d.subject. dynamic and hierarchical multi-structure geographic model fixing. in ICCV, pages 1044-1051,2011) provided by h.s.wong according to the present invention (wherein D6-D10 represent biswatch, Breadcube, cleardie, gamebiwatch and cleardie, respectively). The first row is the real structure segmentation result, and the second row is the segmentation result of the invention.
Detailed Description
The method of the present invention is described in detail below with reference to the accompanying drawings and examples.
Referring to fig. 1, an implementation of an embodiment of the invention includes the steps of:
s1, preparing a data set.
The method specifically comprises the following steps: extracting the features of the image by adopting a feature extraction algorithm to obtain X ═ XiN, n is the total number of data, and n is a natural number.
And S2, integrating preference analysis and latent semantic analysis to construct a latent semantic space.
The method specifically comprises the following steps: m minimum subsets are randomly sampled from the data set, where a minimum subset refers to the minimum data set required to estimate a model, e.g., four points are required to estimate a plane, seven or eight points are required to estimate a basis matrix, etc.
The model hypothesis parameters for each minimum subset are evaluated.
The preference value for each data point and each model hypothesis is calculated. The calculation formula of the preference value is as follows:
in the formula (I), the compound is shown in the specification,
data point xiTo the assumption of thetajDistance (measurable in sampson distance). ψ is a real number greater than zero.
A preference matrix F is constructed from the preference values and decomposed. The matrix decomposition formula is as follows:
F＝U∑VT
∑＝diag(σ1,...,σd)
in the formula, U and V represent a left singular vector matrix and a right singular vector matrix, respectively. Σ is a diagonal matrix. Singular values on diagonal and using a non-reducing sequence, i.e. sigma1≥σ2≥…≥σd> 0, where d ═ rank (F), denotes the rank of the matrix F.
And further reducing the dimension of the preference matrix F, wherein the dimension reduction formula is as follows:
Fn×mVm×k≈Un×k∑k×k
in the formula, n and m represent the number of data points and model hypotheses, respectively. k represents the number of model instances contained in the input data.
And constructing a potential semantic space based on the reduced-dimension preference matrix, and projecting the input data into the constructed space.
And S3, analyzing the data distribution of the potential semantic space.
And S4, adaptively removing outliers in the potential semantic space.
The method specifically comprises the following steps: calculating the Euclidean distance from the data points to the origin in the potential semantic space;
in the potential semantic space, according to the Euclidean distance between the data points and the origin, the threshold value is set adaptively to remove the data points close to the origin.
And S5, carrying out cluster analysis on the remaining data points in the potential semantic space.
The method specifically comprises the following steps: the remaining data points are sampled in semantic space and a line fit is made (the line is the line passing through the origin). And carrying out cluster analysis on the data points through the straight line obtained by fitting.
And S6, estimating model parameters according to the clustering result to complete model fitting.
Partial results of homography estimation of the AdelaideRMF dataset (H.S.Wong, T. -J.Chin, J.Yu, and D.Suter. dynamic and collaborative geological model in ICCV, pages 1044. 1051,2011) provided by H.S.Wong (wherein D1-D5 represent Bonyton, Elderhalal, Library, Sene and Hartley, respectively) are shown in FIG. 2.
Partial results of the estimation of the basis matrix (where D6-D10 respectively represent Biscuit, Breadcube, Breadtoy, Gamebiscure and Breaoacylar) were performed on the AdelaideRMF dataset (H.S.Wong, T.T. -J.Chin, J.Yu, and D.Suter. dynamic and scientific geological model in ICCV, pages1044 and 1051,2011) provided by H.S.Wong, see FIG. 3.
The error rate and time efficiency analysis of vanishing point detection by the CLSA of the present invention and other model fitting methods are compared and shown in Table 1.
TABLE 1
In Table 1, five methods of M1, M2, M3, M4 and M5 correspond to the methods proposed by H.Wang et al (H.Wang, G.Xiao, Y.Yan, and D.Suter, model-searching on Hypergraphics for robust geographic model fixing, in Proc.IEEE int.Conf.Compst.Vis., 2015, pp.2902-2910), the methods proposed by L.Magri et al (L.Magri and A.Fusiello, Multiple model fixing a. convergepromoter, in Proc.IEEE Conf.Vis.Vis.Regen, 2016, Im.8-3326), (L.Maysi A.K. Fulvox, T-linking A.82. Fulvin, Vis.82. filtration, Vis.1, Vis.82. Purch.1, and IEEE-1. discovery.
Claims (1)
1. A model fitting method based on continuous latent semantic analysis is characterized by comprising the following steps:
1) preparing a data set: extracting the features of the image by adopting a feature extraction algorithm to obtain X ═ XiN, n is the total number of data, and n is a natural number;
2) the method for constructing the latent semantic space by integrating the preference analysis and the latent semantic analysis comprises the following specific steps:
(1) randomly sampling m minimum subsets from a data set, wherein a minimum subset refers to a minimum data set required for estimating a model, and specifically comprises the following steps: four points are needed for estimating the plane, and 7 or 8 points are needed for estimating the basic matrix;
(2) evaluating the model hypothesis parameters of each minimum subset;
(3) calculating the preference value of each data point and each model hypothesis, wherein the calculation formula of the preference value is as follows:
in the formula, rxi(θj) Is a data point xiTo the assumption of thetajSampson distance of ψ is a real number greater than zero;
(4) constructing a preference matrix F through the preference values, and decomposing the preference matrix, wherein the matrix decomposition formula is as follows:
F＝U∑VT
∑＝diag(σ1,…,σd)
in the formula, U and V respectively represent a left singular vector matrix and a right singular vector matrix, sigma is a diagonal matrix and is a singular value on the diagonal, and a non-emission reduction sequence, namely sigma is used1≥σ2≥…≥σd> 0, where d ═ rank (F), denotes the rank of matrix F;
(5) and further reducing the dimension of the preference matrix F, wherein the dimension reduction formula is as follows:
Fn×mVm×k≈Un×k∑k×k
in the formula, n and m respectively represent the number of data points and model hypotheses, and k represents the number of model instances contained in the input data;
(6) constructing a potential semantic space based on the reduced preference matrix, and projecting input data into the constructed space;
3) analyzing data distribution of the potential semantic space;
4) self-adaptively removing outliers in a potential semantic space, and the specific method is as follows:
(1) calculating the Euclidean distance from the data points to the origin in the potential semantic space;
(2) in the potential semantic space, according to the Euclidean distance from the data point to the origin, a threshold is set in a self-adaptive mode to remove the data point close to the origin;
5) and performing cluster analysis on the remaining data points in the potential semantic space, wherein the specific method comprises the following steps:
(1) sampling the rest data points in the semantic space and performing straight line fitting;
(2) performing cluster analysis on the data points through the straight line obtained by fitting;
6) and estimating model parameters according to the clustering result to complete model fitting.
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