CN102521802A - Mathematical morphology and LoG operator combined edge detection algorithm - Google Patents

Abstract

The invention discloses a mathematical morphology and LoG operator combined edge detection algorithm. The method comprises the following steps of: smoothing an image through a mathematical morphology method; and using the LoG operator to perform edge detection on the image treated by the mathematical morphology method. Since the mathematical morphology has the advantages of simplifying image data, keeping basic shape characteristics of the image, removing unrelated structures, being easy for realizing hardware and the like, when executing edge detection on the image with noise, by combining the mathematical morphology method with the LoG operator, the noise is removed better without influence on the detection efficiency of the LoG operator. The mathematical morphology and LoG operator combined edge detection algorithm is suitable for the edge detection field.

Description

The edge detection algorithm that a kind of mathematical morphology and LoG operator combine

Technical field

The invention belongs to the rim detection field, relate in particular to the edge detection algorithm that a kind of mathematical morphology and LoG operator combine.

Background technology

The edge is the reflection of gradation of image uncontinuity, and it has comprised the bulk information of image, has reflected the essential characteristic of object.Rim detection plays an important role in application such as computer vision, image segmentation, feature extraction and images match, is the important step of graphical analysis and identification.

The method of rim detection has a lot, can be divided into two types substantially: the spatial domain is detected and transform domain detects.Classical edge detection algorithm is based on the spatial domain mostly and detects, like Laplace operator, Sobel operator, Canny operator and LoG operator etc.Various operators are each targeted and characteristic all, and wherein, LoG operator (Gauss-Laplace operator) method that is proposed by Marr and Hildreth has the high characteristics of rim detection efficient.Its basic thought is: carry out smoothing processing with the Gauss function earlier and suppress noise, detect the edge with the image after the processing smoothly of Laplace operator then.Because the threshold value of LoG operator can be calculated by computing machine fully, calculated amount is also few relatively, thereby makes that the detection speed of LoG operator is faster.But because these operators mainly act on is high-pass filtering, all relates to directivity, generally responsive to noise ratio, therefore is difficult to detect complex edge.And can suppress noise effectively based on the edge detection method of transform domain, but this type algorithm computation amount is bigger, is difficult to requirement of real time in a lot of occasions.

In recent years, in order to improve the real-time of rim detection, improve the performance of rim detection, the application of mathematical morphology is more and more paid attention to.Mathematical morphology is to be based upon on random collection opinion and the integral geometry basis, and basic thought is to survey and extract image as basic tool with a structural element.It comprises that mainly expansion, burn into are opened, closed these four kinds of computings, and makes up and derive other algorithm by these four kinds of computings, thereby realizes the rim detection to detected image, accomplishes the pictures different analysis.

Summary of the invention

The purpose of this invention is to provide to having noise image, not only processing speed is fast, and the good again a kind of mathematical morphology of effect and the edge detection algorithm of LoG operator combination.

The edge detection algorithm that a kind of mathematical morphology of the present invention and LoG operator combine may further comprise the steps:

Adopt Mathematical Morphology Method that image is carried out smoothing processing;

Use the LoG operator, carry out rim detection adopting the image after Mathematical Morphology Method is handled.

Further, said employing Mathematical Morphology Method is carried out smoothing processing to image and is specially image is carried out closure operation.

The invention has the beneficial effects as follows: since mathematical morphology have the simplified image data, keep image the grown form characteristic, remove irrelevant structure, be easy to advantage such as hardware realization; When the image that contains noise is carried out rim detection; Through combining Mathematical Morphology Method with the LoG operator; In the detection efficiency that does not influence the LoG operator, can well remove noise again.

Description of drawings

Be described further below in conjunction with the accompanying drawing specific embodiments of the invention:

Fig. 1 is the inventive method flow chart of steps;

Fig. 2 is the glass fragmentation image that contains salt-pepper noise;

Fig. 3 uses the LoG operator image shown in Figure 1 is carried out the image after the rim detection;

To be the edge detection algorithm that adopts mathematical morphology of the present invention and the combination of LoG operator carry out the image after the rim detection to image shown in Figure 1 to Fig. 4.

Embodiment

LoG operator, just Gauss-Laplace operator.Laplace operator is a kind of second derivative operator, and its expression formula is:

${\▿}^{2}f(x,y)=\frac{{\∂}^{2}f(x,y)}{{\∂x}^2}+\frac{{\∂}^{2}f(x,y)}{{\∂y}^2}$

When being applied to digital picture, then can with difference approximation be expressed as:

${\▿}^{2}f(x,y)=f(x+1,y)+f(x-1,y)+f(x,y+1)+f(x,y-1)-4f(x,y)$

Because Laplace operator is a scalar, so it only needs a template just passable when calculating.Because Laplace operator is a second derivative operator, thereby it is very sensitive to noise, so when carrying out Flame Image Process, generally will carry out smothing filtering earlier and carry out second-order differential again.The most frequently used smooth function is exactly a Gaussian function, because Gauss's smoothing filter to the noise effects of removing Normal Distribution clearly.Two-dimensional Gaussian function and it one, second-order partial differential coefficient is as follows:

$h(x,y)=\frac{1}{{2\mathrm{\π\σ}}^2}{e}^{-\frac{x^2+y^2}{{2\mathrm{\σ}}^2}}$

$\frac{\∂h(x,y)}{\∂x}=\frac{-x}{{2\mathrm{\π\σ}}^4}{e}^{-\frac{x^2+y^2}{{2\mathrm{\σ}}^2}},$ $\frac{\∂h(x,y)}{\∂y}=\frac{-y}{{2\mathrm{\π\σ}}^4}{e}^{-\frac{x^2+y^2}{{2\mathrm{\σ}}^2}}$

$\frac{{\∂}^{2}h(x,y)}{{\∂x}^2}=\frac{1}{{2\mathrm{\π\σ}}^4}[\frac{x^2}{{\mathrm{\σ}}^2}-1]e^{-\frac{x^2+y^2}{{2\mathrm{\σ}}^2}},$ $\frac{{\∂}^{2}h(x,y)}{{\∂y}^2}=\frac{1}{{2\mathrm{\π\σ}}^4}[\frac{y^2}{{\mathrm{\σ}}^2}-1]e^{-\frac{x^2+y^2}{{2\mathrm{\σ}}^2}}$

Wherein σ is the standard variance of Gaussian distribution, and it has determined the width of Gaussian filter, uses this function to the result that image carries out behind the smothing filtering to be:

$g(x,y)=h(x,y)\⊗f(x,y)$

Wherein

is the convolution symbol; Image is used Laplace operator again after level and smooth, the result is:

${\▿}^{2}g(x,y)={\▿}^2(h(x,y)\⊗f(x,y))$

In linear system, the order of differential and convolution can exchange, so have:

${\▿}^2(h(x,y)\⊗f(x,y))={\▿}^{2}h(x,y)\⊗f(x,y)=\frac{1}{{\mathrm{\π\σ}}^4}[\frac{x^2+y^2}{{2\mathrm{\σ}}^2}-1]e^{-\frac{x^2+y^2}{{2\mathrm{\σ}}^2}}\⊗f(x,y)$

Operator after wherein level and smooth and differential merges

${\▿}^{2}h(x,y)=\frac{1}{{\mathrm{\π\σ}}^4}[\frac{x^2+y^2}{{2\mathrm{\σ}}^2}-1]e^{-\frac{x^2+y^2}{{2\mathrm{\σ}}^2}}$

Be exactly Gauss-Laplace operator (Laplacian of Gaussian, LoG).

LoG can remove the noise in the certain size effectively, just more can suppress interference of noise.Because LoG is isotropic, so can save many calculated amount.And its bearing accuracy is high, and detected edge continuity is better.But LoG has some very important shortcomings, because it is to utilize the zero cross point of the second derivative of image to obtain the edge, so very sensitive to noise.

Mathematical morphology is recent emerging a kind of image processing method, and it is based upon on random collection opinion and the integral geometry basis, and basic thought is to survey and extract image as basic tool with a structural element.It comprises that mainly expansion, burn into are opened, closed these four kinds of computings, and makes up and derive other algorithm by these four kinds of computings, thereby realizes the rim detection to detected image, accomplishes the pictures different analysis.

Expanding and corroding is operation the most basic in the mathematical morphology.If A and B are the set among the Z, wherein A is an original image, and B is a structural element, and Z is an integer space.Then have B to the dilation operation note work

of A:

Wherein

representes empty set;

is the reflection collection of set B:

can find out according to following formula; B is exactly in fact a set of being made up of all translational movement z to the expansion of A; These translational movements z satisfies: when the reflection collection translation of B after the z, with the common factor of set A be sky.The image pixel more shared than original image is many after overexpansion.

Equally, note A Θ B is the erosion operation of B to A, then:

$\mathrm{A\ΘB}=\left\{z\right|\left(B\right)z\⊆A\}$

B is the set of translational movement z to the corrosion of A, and these translational movements still belong to set A after satisfying set B translation z.Result images after the corrosion shrinks with respect to original image to some extent, and the image after the corrosion is a sub-set of original image.

Be expansion and corrode the compound operation that combines and open with closure.Open operation can play the effect of smoothed image, removes burr outstanding on the profile, blocks narrow mountain valley.Closed procedure also has smoothing effect to image outline, but the result is opposite, and it can remove the aperture in the zone, fills and leads up the profile breach.

The unlatching note of A is done A ο B to B, then has:

Just with structural element B image A is corroded earlier, with B Corrosion results is done expansive working then.

Similarly, the closed procedure note of A is done AB to B, then:

Opposite with open operation, it is earlier original image to be done dilation operation, again expansion results is corroded operation.

With reference to Fig. 1, the edge detection algorithm that a kind of mathematical morphology of the present invention and LoG operator combine may further comprise the steps:

Adopt Mathematical Morphology Method that image is carried out smoothing processing;

Use the LoG operator, carry out rim detection adopting the image after Mathematical Morphology Method is handled.

As the step of further optimization, when adopting Mathematical Morphology Method to handle, specifically adopt closure operation that image is carried out smoothing processing.

In order to prove the superiority that adopts the more simple LoG operator of edge detection algorithm provided by the present invention to handle, on the Matlab7.0 platform same image that has noise carried out handling relatively now.In the test, the threshold value of the LoG operator that both adopt is the same.

In test, be object with the glass fragmentation image, and former figure has been added certain salt-pepper noise, as shown in Figure 2, to have the image of noise in the simulation actual production processing procedure.

After with the LoG operator image shown in Figure 2 being carried out rim detection, result is as shown in Figure 3.

Adopt technical scheme provided by the present invention, earlier image is carried out closure operation, and then carry out edge extracting with the LoG operator, it is as shown in Figure 4 to handle the back result.

Through relatively finding out, for the image that contains noise, when independent use LoG operator carries out edge extracting, noise and graph outline have been hard to tell, and effect is unsatisfactory.And adopt technical scheme of the present invention, after image was carried out closure operation earlier, the LoG operator then can clearly detect the profile of figure.

Therefore, for noisy image, through adopting mathematical morphology earlier it is handled, in smooth noise, kept the elementary contour characteristic of image effectively, thereby helped the rim detection of LoG operator, it is also better to detect effect.

More than be that preferable enforcement of the present invention is specified; But the invention is not limited to said embodiment; Those of ordinary skill in the art make all equivalent variations or replacement under the prerequisite of spirit of the present invention, also can doing, and distortion that these are equal to or replacement all are included in the application's claim institute restricted portion.

Claims (2)

1. the edge detection algorithm that combines of mathematical morphology and LoG operator is characterized in that: may further comprise the steps:

Adopt Mathematical Morphology Method that image is carried out smoothing processing;

Use the LoG operator, carry out rim detection adopting the image after Mathematical Morphology Method is handled.

2. the edge detection algorithm that a kind of mathematical morphology according to claim 1 and LoG operator combine is characterized in that: said employing Mathematical Morphology Method is carried out smoothing processing to image and is specially image is carried out closure operation.

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