CN102156996B - Image edge detection method - Google Patents

Abstract

The invention discloses an image edge detection method in the field of image detection. The method comprises the following steps of: acquiring an image by using a camera and then calculating gradient amplitude and direction by using a method for calculating first-order partial derivative difference of x direction and y direction in 12 neighborhood pixels, thereby suppressing noise in the image and preventing edge blur of the image; then establishing a mapping relation between inverse difference moment characteristic values of a gray level co-occurrence matrix and Gaussian space factors as well as thresholds, adaptively varying the Gaussian space factors and high and low thresholds of edge detection to guarantee continuous extraction of image edge points; and finally detecting the image edge points according to a non-local maximum inhibition principle, thereby improving accuracy of image edge detection.

Description

A kind of method of Image Edge-Detection

Technical field:

The present invention relates to the detection to the image border in the automatic field, relate in particular to a kind of method of Image Edge-Detection, be applicable to that image texture characteristic analysis, image in the computer vision field cut apart and graphic feature extraction etc.

Background technology:

In order to improve the performance of Image Edge-Detection, Canny proposed in 1986 a good edge detection operator should satisfy following three criterions (John CANNY.A computational approach to edgedetection[J] .IEEE Trans Pattern Analysis and Machine Intelligence, 1986,8 (6): 679～698): (1) good signal-to-noise, it is low that to be non-marginal point be judged as by mistake marginal point or marginal point is judged as the probability of non-marginal point by mistake, makes the signal to noise ratio (S/N ratio) of output reach maximum; (2) good positioning performance, namely detected image border point will be as far as possible at the center at real image edge; (3) monolateral response criteria will guarantee that namely single edge has only a pixel response, and the response of false edge is inhibited to the full extent.

Based on above 3 judgment criterion, Canny has derived a kind of best edge detection algorithm, is called the Canny operator, and the step of its algorithm is as follows:

(1) comes image filtering with Gaussian filter, remove the very noisy in the image.

(2) the single order differential with Gauss operator carries out filtering to image, obtains the Grad of each pixel.

(3) gradient is carried out " non-very big inhibition ".

(4) the dual threshold method detects and the connection edge.

Compare with traditional differentiating operator, the Canny operator has fast operation and the high advantage of accuracy of detection when being applied to the detected image edge, thereby the Canny operator is widely used in practice.But there are following three major defects in this algorithm: (1) Canny operator just asks the method for finite difference average to come the compute gradient amplitude in 2 * 2 neighborhoods, though accurate edge positioning, noise resisting ability is poor; (2) in non-maximum value process of inhibition, the Canny algorithm adopts is that the Grad of eight neighborhood territory pixels judges whether current point has local maximum, and this can influence the degree of accuracy of rim detection; (3) the height threshold value of Canny algorithm is all fixed, and high low threshold relies on artificial setting fully, so its automaticity is lower.

Summary of the invention:

In order to address the above problem, the present invention proposes a kind of method for detecting image edge, is the improvement to the Canny edge detection method.At first utilize the gradient based on 12 neighborhood method computed image, introduce unfavourable balance moment characteristics value adaptive change Gauss space factor and threshold value then, make this method edge of detected image accurately.

Technical scheme of the present invention is: a kind of method for detecting image edge relates to following two steps:

(1) utilizes 12 neighborhoods to calculate x direction and y direction single order partial derivative, suppressed the noise in the image and avoided the edge of image fuzzy;

(2) utilize the unfavourable balance moment characteristics value of gray level co-occurrence matrixes and the mapping relations between Gauss's space factor and the threshold value, the height threshold value of adaptively modifying Gauss space factor and rim detection.

The described method of utilizing 12 neighborhoods to calculate x direction and y direction single order partial derivative, be to utilize this point (i, four consecutive point j) (i, j+1), (i, j-1), (i+1, j), (i-1, j) and all the other eight points adjacent with these four points (i-2, j), (i-1, j+1), (i-1, j-1), (i, j+2), (i, j-2), (i+1, j+1), (i+1, j-1), (i+2, j), the point of position about x direction and y direction symmetry subtracted each other respectively, and obtain mean value, can calculate this point (i, x direction j) and y direction single order partial derivative respectively.

The present invention adopts above technical scheme, can be than the accurate in locating edge of image, having avoided edge of image to blur again can be too responsive to noise, improved the ability that suppresses false edge, can adaptively modifying Gauss space factor and the high low valve valve of rim detection, guarantee the continuous extraction of image border point, improved automaticity.

Embodiment:

The object of the invention is at the deficiencies in the prior art, analyzing and concluding on Canny algorithm and forefathers' the improvement algorithm basis, proposes a kind of method for detecting image edge, is the improvement to the Canny edge detection method.At first utilize the gradient based on 12 neighborhood method computed image, introduce unfavourable balance moment characteristics value adaptive change Gauss space factor and threshold value then, make this method edge of detected image accurately.The solution of the present invention is:

1, improves the computing method of gradient magnitude

Traditional C anny operator is to come the compute gradient amplitude by the method for asking for difference in 2 * 2 neighborhoods, and this method is responsive for noise ratio, and this paper proposes a kind of method of calculating x direction and y direction single order partial derivative difference in 12 neighborhood territory pixels at this defective.Point (i, j) position view such as table 1:

Table 1 (i, j) position view

		(i，j+2)
						(i-1，j+1)	(i，j+1)	(i+1，j+1)
(i-2，j)	(i-1，j)	(i，j)	(i+1，j)	(i+2，j)
						(i-1，j-1)	(i，j-1)	(i+1，j-1)
		(i，j-2)

The partial derivative of x direction, y direction is:

$\frac{\∂f}{\∂x}=[I(i,j+1)-I(i,j-1)+I(i-1,j+1)-I(i-1,j-1)+I(i+1,j+1)-I(i+1,j-1)+I(i,j+2)-I(i,j-2)]/4---\left(1\right)$

$\frac{\∂f}{\∂y}=[I(i+1,j)-I(i-1,j)+I(i+1,j-1)-I(i-1,j-1)+I(i+1,j+1)-I(i-1,j+1)+I(i+2,j)-I(i-2,j)]/4---\left(2\right)$

The size of gradient magnitude | M (i, j) | and direction angle alpha is:

$\left|M(x,y)\right|={[{\left(\frac{\∂f}{\∂x}\right)}^2+{\left(\frac{\∂f}{\∂y}\right)}^2]}^{\frac{1}{2}}---\left(3\right)$

$\mathrm{\α}={\tan }^{-1}\frac{\∂f}{\∂x}\·\frac{\∂y}{\∂f}---\left(4\right)$

Can obtain gradient magnitude to value substitution formula (3) and (4) that try to achieve formula (1) and (2) | M (i, j) | and direction angle alpha.In gradient magnitude computation process, this method can be than the accurate in locating edge of image, and having avoided edge of image to blur again can be too responsive to noise, has improved the ability that suppresses false edge.

2, the self-adaptation of Gauss's space factor and threshold value is determined

Canny operator algorithm is to utilize Gaussian filter to come image filtering is removed very noisy in the image, establishes the two-dimensional Gaussian function expression formula and is:

$G(x,y)=\frac{1}{2\mathrm{\π}{\mathrm{\σ}}^2}\exp (-\frac{x^2+y^2}{2{\mathrm{\σ}}^2})---\left(5\right)$

Wherein, σ is the width of gaussian filtering convolution kernel, is controlling the level and smooth degree of image.This shows that the quality of the performance of Canny operator mainly is by the width cs of gaussian filtering convolution kernel in the smoothing process and the high threshold T2 in the tracing process and low threshold value T1 decision.The width cs of increase gaussian filtering convolution kernel can reduce the susceptibility to noise, but but can make object edge fuzzy.In experimentation, can find that the effect of rim detection is subjected to the influence of threshold value T2, T1 bigger.If the value of T2 obtains too big, only keep the bigger edge of gray-value variation, just lose the less edge of some gray-value variation; If it is too little that the value of T2 obtains, then when detecting all edges, increased false edge.Low threshold value T1 is controlling the terminating point character that detects, and plays a part to connect discontinuous profile, here we to get low threshold value T1 be 0.4 times of high threshold T2.

For different images, the best value of Gauss's space factor σ and threshold value T1, T2 is inequality.In actual applications, the σ in the Canny operator algorithm and the best value of T1, T2 not only depend on the gray difference between pixel, also are subjected to the influence of gray difference space distribution.Because the eigenwert of gray level co-occurrence matrixes can reflect the integrated information of direction, distribution and the amplitude of variation of gradation of image, therefore, we introduce the Image Edge-Detection field with gray level co-occurrence matrixes.

3, gray level co-occurrence matrixes principle

Gray level co-occurrence matrixes is a kind of important method of analysis image textural characteristics, the complexity of the reflection image texture that it can be strong, it according to certain spatial relationship describe pixel to the gray scale correlativity.The description of gray level co-occurrence matrixes from image (x, y) gray scale is that the pixel of i is set out, statistics is δ with distance, gray scale be probability that the pixel (x+ Δ x, y+ Δ y) of j occurs simultaneously be P (i, j, δ, α), then its mathematic(al) representation is:

P(i，j，δ，α)＝{[(x，y)，(x+Δx，y+Δy)]

f(x，y)＝i；

f(x+Δx，y+Δy)＝j；

x＝0，1，…，Nx-1；

y＝0，1，…，Ny-1}

In the following formula: i, j=0,1 ..., L-1; X, y are the pixel coordinates of image; L is the gray scale value of image; Nx and Ny are respectively line number and the columns of image.Relation between them is as follows:

Gray level co-occurrence matrixes

When α and δ are selected, P (i, j, δ, α) also can note by abridging into P (i, j), obviously gray level co-occurrence matrixes is a symmetric matrix, its exponent number determines that by the number of greyscale levels of image even number of greyscale levels is N, then gray level co-occurrence matrixes is the square formation of N * N.Generally choosing α is 0o, 45o, and 90o, the 135o four direction calculates gray level co-occurrence matrixes, and δ chooses with image-related, determines according to experiment.Assigned direction and apart from the time, generally by the pixel logarithm that calculates gray scale i and j represent P (i, j, δ, α).

4, gray level co-occurrence matrixes characteristic parameter

Features such as the inertial matrix of gray level co-occurrence matrixes, angle second moment, unfavourable balance matrix and difference entropy matrix are the space distribution complexity of energy resolution image gray scale all.We obtain the tolerance best results of unfavourable balance moment characteristics through experiment, and it is with the maximum that the difference of the space distribution complexity of gradation of image is drawn back, and expression formula is:

$W(\mathrm{\δ},\mathrm{\α})=\underset{i=0}{\overset{n-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{n-1}{\mathrm{\Σ}}}\frac{p(i,j,\mathrm{\δ},\mathrm{\α})}{1+{(i-j)}^2}---\left(6\right)$

In the mild image of grey scale change, and P (i, j, δ, numeric ratio α) concentrates on the near zone of matrix principal diagonal, and the difference of (i-j) is less at this moment, so corresponding unfavourable balance moment characteristics value is also less; In like manner, the unfavourable balance moment characteristics value of complicated image is bigger.Therefore, according to actual conditions, from the eigenwert of unfavourable balance matrix and Gauss's space factor σ and threshold value T1, T2 funtcional relationship obtain best value.

Owing to depositing in certain functional relation between Gauss's space factor σ and threshold value T1, the T2, to realize that therefore it is the comparison difficulty that the unfavourable balance square shines upon time the two.In order to deal with problems, we taked fixing T obtain the corresponding relation of W and σ and fixedly σ obtain the method for the corresponding relation of W and T1, T2.We find just can set up certain linear relationship between W, σ, T1, T2 after unfavourable balance moment characteristics value W is taken the logarithm.Set up the approximate formula of mapping relations between unfavourable balance moment characteristics value and Gauss's space factor σ and threshold value T1, the T2 according to above reasoning:

σ＝0.12log ₃(W+0.96)+1 (7)

$T1=\frac{\mathrm{\π}}{2}{\log }_3(W+0.96)+\frac{e}{2}---\left(8\right)$

T2＝2.5*T1 (9)

According to above description, specific implementation step of the present invention is as follows:

1) image pre-service utilizes Gaussian filter that original image is carried out smoothing processing, removes the very noisy that may contain in the image.

2) by improved gradient calculation formula (1) and (2) calculate point (substitution formula (3) and (4) calculate the size of gradient for i, partial derivative j) | M (i, j) | and the direction α of gradient.

3) obtained the unfavourable balance moment characteristics value W of image by formula (6).

4) obtained Gauss's space factor σ, Grads threshold T1, the T2 of image respectively by formula (7), (8), (9).

5) gradient of image is carried out " non-maximum value inhibition ", if Grad | M (i, j) | 〉=T1, then (x y) is labeled as marginal point, carries out the edge search from this point, connects complete image border at last with point.

More than show and described ultimate principle of the present invention, principal character and advantage of the present invention.The technician of the industry should understand; the present invention is not restricted to the described embodiments; that describes in above-described embodiment and the instructions just illustrates principle of the present invention; without departing from the spirit and scope of the present invention; the present invention also has various changes and modifications, and these changes and improvements all fall in the claimed scope of the invention.The claimed scope of the present invention is defined by appending claims and equivalent thereof.

Claims (2)

1. method for detecting image edge, its feature relates to following two steps:

(1) utilizes 12 neighborhoods to calculate x direction and y direction single order partial derivative, suppressed the noise in the image and avoided the edge of image fuzzy;

(2) utilize the unfavourable balance moment characteristics value of gray level co-occurrence matrixes and the mapping relations between Gauss's space factor and the threshold value, the height threshold value of adaptively modifying Gauss space factor and rim detection;

The specific implementation step is as follows:

1) image pre-service utilizes Gaussian filter that original image is carried out smoothing processing, removes the very noisy that may contain in the image;

2) by improved gradient calculation formula (1) and (2) calculate point (substitution formula (3) and (4) calculate the size of gradient for i, partial derivative j) | M(i, j) | and the direction α of gradient;

3) obtained the unfavourable balance moment characteristics value W of image by formula (6);

4) obtained Gauss's space factor σ, Grads threshold T1, the T2 of image respectively by formula (7), (8), (9);

5) gradient of image is carried out " non-maximum value inhibition ", if Grad | M(i, j) | 〉=T1, then (i j) is labeled as marginal point, carries out the edge search from this point, connects complete image border at last with point;

Wherein formula (1) is:

$\frac{\∂f}{\∂x}=[I(i,j+1)-I(i,j-1)+I(i-1,j+1)-I(i-1,j-1)+I(i+1,j+1)-I(i+1,j-1)+I(i,j+2)-I(i,j-2)]/4$

Wherein

Partial derivative for the x direction;

Wherein formula (2) is:

$\frac{\∂f}{\∂y}=[I(i+1,j)-I(i-1,j)+I(i+1,j-1)-I(i-1,j-1)+I(i+1,j+1)-I(i-1,j+1)+I(i+2,j)-I(i-2,j)]/4$

Wherein

Partial derivative for the y direction;

Wherein formula (3) is:

$\left|M(i,j)\right|={[{\left(\frac{\∂f}{\∂x}\right)}^2+{\left(\frac{\∂f}{\∂y}\right)}^2]}^{1/2};$

Wherein formula (4) is:

$\mathrm{\α}={\tan }^{-1}\frac{\∂f}{\∂x}\·\frac{\∂y}{\∂f}$

Wherein formula (6) is:

Gray level co-occurrence matrixes describe from image (x, y) gray scale is that the pixel of k is set out, statistics is δ with distance, gray scale is the pixel (x+ of l _ΔX), (y+ _ΔY) probability that occurs simultaneously be P (k, l, δ, α), choosing α is 0 °, 45 °, 90 °, 135 ° of four directions calculate gray level co-occurrence matrixes, δ chooses with image-related;

Wherein formula (7) is:

σ＝0.12log ₃(W+0.96)+1

Wherein formula (8) is:

$T1=\frac{\mathrm{\π}}{2}{\log }_3(Q+0.96)+\frac{e}{2}$

Wherein formula (9) is:

T2＝2.5*T1。

2. method for detecting image edge according to claim 1, it is characterized in that: the described method of utilizing 12 neighborhoods to calculate x direction and y direction single order partial derivative is to utilize this point (i, four consecutive point (i j), j+1), (i, j-1), (i+1, j), (i-1, j) and all the other eight point (i-2s adjacent with these four points, j), (i-1, j+1), (i-1, j-1), (i, j+2), (i, j-2), (i+1, j+1), (i+1, j-1), (i+2, j), the point of position about x direction and y direction symmetry subtracted each other respectively, and obtain mean value, can calculate this point (i, x direction j) and y direction single order partial derivative respectively.