CN105913415A - Image sub-pixel edge extraction method having extensive adaptability - Google Patents

Abstract

The present invention proposes an image sub-pixel edge extraction method with wide adaptability, adopts an adaptive high and low threshold value calculation method, and performs a local maximum central value selection operation on the gradient image in combination with the gradient direction information of the pixel point after obtaining the gradient image , take any pixel position as the origin, establish relative coordinates, take the eight neighborhood pixels around the point as the local maximum center value to select the data sample, obtain the comparison result of the neighborhood according to the gradient direction, and determine whether the current pixel position is a candidate position of the boundary point . Whether the extremum of the local gradient amplitude is an edge point needs to be judged in conjunction with a specific threshold. Marks greater than a given threshold are marked as edge points, and those smaller than a given threshold are judged as noise points or background points; using a Steger-based surface fitting method The Hessian matrix method to obtain the sub-pixel position of the edge points; finally, the edge points will be connected into a curve to form a set of directed continuous points. The method of the invention has excellent real-time performance.

Description

A Widely Adaptable Image Subpixel Edge Extraction Method

technical field

The invention relates to the technical field of image recognition, in particular to an image sub-pixel edge extraction method.

Background technique

In machine vision, in order to perform target positioning, measurement, detection or geometric feature extraction, etc., it is necessary to extract the edge of the target with sub-pixel precision. For example, the template matching method using geometric features in target positioning requires sub-pixel edge extraction for templates and targets; in measurement applications, it is necessary to accurately detect the edges of objects to perform accurate measurements; in detection applications, such as optical characters Verification of OCV, edge defect detection, etc. all require stable detection of sub-pixel edges of objects.

Commonly used edge extraction algorithms include Roberts operator, Sobel operator, Prewitt operator, Laplacian operator and Canny operator, etc. Edge extraction algorithms with sub-pixel accuracy include spatial moment method, gray moment method, Zernike moment method and digital correlation method. Other edge extraction algorithms with sub-pixel accuracy include polynomial fitting method, ellipse fitting method, Gaussian surface fitting method, Sigmoid curve fitting method, etc. Li Shuai et al. proposed a sub-pixel detection algorithm based on Gaussian surface fitting. Sun Chengqiu et al. In "A Method of Edge Detection with Sub-pixel Accuracy", it is proposed to use the Bessel edge model for sub-pixel edge extraction. Zhang Wujie et al. proposed a method of sub-pixel edge detection based on Sigmoid function fitting. Patent Document 1 (Chinese Patent Publication No. CN10465002A) discloses a sub-pixel edge location method for an ellipse object based on Sobel edge extraction, which calculates ellipse geometric parameters from pixel edges and calculates sub-pixel edges from pixel edges.

Patent Document 2 (Chinese Patent Publication No. CN102737377A) discloses an improved sub-pixel edge extraction algorithm, which first performs rough positioning of pixel accuracy, uses the edge image to crop the target image to narrow the search range, and then extracts sub-pixels within the reduced range edge. Patent Document 3 (Chinese Patent Publication No. CN103530878A) discloses an edge extraction method based on a fusion strategy. The results of three traditional edge extraction algorithms are used to obtain voting weights reflecting the possibility of belonging to an edge, and then the relationship between pixels and neighborhoods is analyzed. The difference between the maximum luminance difference and the minimum luminance difference is used to obtain the weight of the difference that describes the degree of sudden change in brightness; the variance distribution of the decentralized neighborhood is calculated to obtain the edge distribution weights of all pixels, and the edge decision is made to output the edge image. Patent Document 4 (Chinese Patent Publication No. CN103886589A) discloses a target-oriented automatic high-precision edge extraction method, including a model training stage and an edge extraction stage. Patent Document 5 (Chinese Patent Publication No. CN103955911A) discloses an edge detection method based on relative variation, including image preprocessing and edge detection based on a neural network method. Patent Document 6 (Chinese Patent Publication No. CN104268857A) discloses a fast sub-pixel edge detection and positioning method. The basic idea is to first obtain the pixel-level edge position, and then use the cosine look-up table method to calculate the sub-pixel edge point. Patent Document 7 (Chinese Patent Publication No. CN104268872A) discloses a consistency-based edge detection method. Patent Document 8 (Chinese Patent Publication No. CN104732536A) discloses a sub-pixel edge detection method based on improved morphology, which uses an improved morphological edge detection operator to smooth image edge information, and uses Canny operator to obtain pixels in object edge contours Level edges, and then fit the pixel-level edges to the sub-pixel edges of the product. Patent Document 9 (Chinese Patent Publication No. CN105005981A) discloses a method for extracting the center of the laser light stripe with sub-pixel precision, by locating the center of the initial light stripe in the smoothed image, and then using Gaussian function fitting to obtain the width of the light stripe , and then use the variance of the fitted Gaussian function and the parameters of the Gaussian convolution kernel to calculate the Hessian matrix, and calculate the sub-pixel center position of the laser light bar according to the Hessian matrix. The use of the Hessian matrix method is the same as that of the present invention, but there is an essential difference in pixel precision position calculation, which also leads to completely different applicability of the two methods.

However, in industrial environment applications, images are disturbed by various factors, resulting in reduced image quality, including strong noise, edge blur, etc. How to stably detect sub-pixel-accurate edge features in low-quality images has not been well resolved. . Traditional pixel-accurate edge extraction algorithms cannot meet the accuracy requirements in industrial automation applications such as 3C automation equipment, electronic manufacturing, and industrial robot vision. Sub-pixel edge extraction algorithms such as spatial moment method, gray moment method, Zernike moment method and digital correlation method have their own shortcomings in detection accuracy, calculation speed and anti-noise ability, and it is difficult to adapt to the harsh detection work in industrial environments. condition.

Patent Document 1 can only extract the sub-pixel position of an elliptical object, which has insufficient versatility, and cannot deal with the edge extraction problem of blurry objects. In the method disclosed in Patent Document 3, Sobel, Canny and LoG operators are used for edge detection, and then the results of the three operators are used for weighted voting statistics, and the sub-pixel coordinates are obtained according to the voting weight matrix. The problems of this method It is slow, the accuracy depends on the weight matrix, and it cannot solve the edge extraction problems of images such as strong noise and blur. The methods disclosed in Patent Document 4 and Patent Document 5 use the results of Canny and relative variation, and use machine learning methods for edge extraction, which are slow and cannot perform stable edge extraction in low-quality images. The method disclosed in Patent Document 6 performs sub-pixel edge detection in 8 gradient directions on the basis of coarse positioning of pixel coordinates. This method has a good calculation speed, but does not consider the processing of strong noise and blurred images. Patent Document 7 and Patent Document 8 also have low computational efficiency and cannot handle edge extraction of strong noise and blurred images. The method disclosed in Patent Document 9 adopts multi-level Gaussian convolution operation, and the algorithm complexity is high. It cannot realize the robust extraction of the centerline of the light bar for the non-linear shadow changes in different areas caused by illumination changes and other reasons. This method is only applicable to laser light. The extraction of centerlines cannot achieve general image edge feature extraction.

Contents of the invention

The purpose of the present invention is to provide a high-speed, high-precision template matching and positioning method based on image edge information, which can simultaneously output the position, rotation angle and scaling factor of the template image in the target image with sub-pixel accuracy, and aim at the appearance of the target image. Displacement, rotation, scaling, partial occlusion, light and dark changes, uneven illumination, messy background, etc. can all achieve fast, stable, and high-precision positioning and recognition. The present invention can be applied to occasions requiring target positioning and identification through machine vision: such as robot guidance, semiconductor packaging, electronic manufacturing, automatic assembly, product visual inspection, visual measurement, video tracking and other fields.

The method disclosed in the invention can stably detect the edge characteristics of sub-pixel precision in low-quality images.

For reaching above-mentioned object, the present invention realizes by following technical scheme:

An image sub-pixel edge extraction method with wide adaptability, comprising the following steps: Step 1: Preprocessing the image using variable-scale image blur smoothing filter; Step 2: Computing the first-order derivative of the preprocessed image, first ensuring that The obtained gradient amplitude satisfies that the error rate of this point is less than the set value α _p , and the first derivative of the image is obtained by convolving the image space with the target kernel; the edge line of the image is at the ridge line of the first derivative of the image, where the ridge line is the gradient A collection of adjacent continuous local maxima in the image; Step 3: Apply the chain threshold edge extraction and selection principle in the edge candidate point selection process to realize pixel-level boundary position extraction. The high and low thresholds are obtained in two ways: External parameter input or adaptive threshold calculation; Step 4: After obtaining the gradient image, in order to find the single-pixel width position of the ridge conveniently and quickly, combine the gradient direction information of the pixel to perform a local maximum central value selection operation on the gradient image; Step 5: Whether the extremum of the local gradient amplitude is an edge point needs to be judged in conjunction with a specific threshold. Markings greater than a given threshold are edge points, and smaller than a given threshold are judged as noise points or background points; Step 6: Calculation Edge position with sub-pixel accuracy; Step 7: Connect the edge points into a curve to form a set of directed continuous points.

As a further improvement of the present invention in step 2, assume that the image I (x, y) is subjected to an edge extraction operation to obtain a boundary point error rate α _I , and the image size is n=w×h, then the single point detection error The probability is α _p =1-(1-α _I ) ^{1 /n} , where α _I ranges from 0 to 1.0, the image I(x, y) has only Gaussian noise and the noise signal variance is s _n ; The step characteristic has the following equation:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; \&prime;</span>}\end{array}\right.<span\; class="notranslate">\; ,</span>$

The gradient amplitude of each point is obtained as Make the error rate of the gradient amplitude of each point lower than the set value α _p , which satisfies the equation: M(x, y, σ)≥c(σ), where,

$\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\sqrt{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&rsqb;</span>}<span\; class="notranslate">\; ,</span>$

The variables in the above formula are scale variables σ, and other variables are global setting parameters.

As a further improvement of the present invention, the calculation of the high and low thresholds in the step 3 is specifically: first find the peak point (i, H _i ) of the histogram curve, and the non-zero cumulative value coordinate point in the last histogram is (j, H _j ), 0≤i<j≤255 and 0≤H _j <Hj<1.0, connect the above two points to get a straight line ax+by+c=0; find the histogram curve coordinate point from i to j to the straight line The maximum distance position d _max , which satisfies d _{max x} =arg max _k |ak+bH _k +c|, the abscissa of the point coordinate (k, H _k ) is the first threshold T _low =k; then from Starting from this point, connect to the end point (j, H _j ) of the straight line to form a straight line αx+βy+λ=0, and find the relationship between the curve and the straight line (α, β, λ) on the interval k to j of the histogram curve The maximum distance position D _max also satisfies D _max =arg max _t |α _t +βH _t +λ|, and the abscissa of the point coordinate (t, H _t ) is marked as the second threshold T _high =t.

As a further improvement of the present invention, the step 4 is specifically: the gradient direction of any pixel position is θ=tan ^-1 (f _y /f _x ), tangent to the trend direction of the ridge line; taking any pixel position as the origin, Establish a relative coordinate, take the eight neighboring pixels around the point as the local maximum center value to select data samples, and obtain the comparison result of the neighborhood according to the gradient direction to determine whether the current pixel position is a candidate position of the boundary point.

As a further improvement of the present invention, said step 5 adopts Canny's dual threshold setting (T _low , T _high ); when the local extremum G ₀ is higher than T _high , the point p ₀ is an edge point; G ₀ is lower than the threshold T _low indicates that the current point is a non-boundary point attribute; when G ₀ is between the high and low thresholds, the chain effect takes effect, that is, there are boundary points in the eight neighborhoods of point p ₀ , and the current position is confirmed as a boundary point.

As a further improvement of the present invention, said step 6 uses the Hessian matrix method based on the Steger surface fitting method to obtain the sub-pixel position of the edge point, and performs the interpolation algorithm f(r of the surface fitting in the small area of the pixel-level edge point , c)=k ₀ +k ₁ r+k ₂ c+k ₃ r ² +k ₄ rc+k ₅ c ² ; calculate the first and second derivatives of the unknowns of the surface equation and combine them into a Hessian matrix; solve The eigenvalues of the Hessian matrix and their respective eigenvectors, the eigenvector corresponding to the largest absolute eigenvalue is the normal direction (n _x , n _y ) of the edge point; using the normal direction and the Taylor expansion of the surface equation, the edge is calculated The subpixel location of the point.

As a further improvement of the present invention, one of the principles that need to be paid attention to in the edge connection process of step 7 is to select the nearest trend that forms a straight line or a smooth curve as much as possible, while also avoiding the formation of two interconnected lines. Curve, there is and can only be one and only one curve for the wave curve.

Description of drawings

Fig. 1 is method flowchart of the present invention;

Fig. 2 is a schematic diagram of one-dimensional image data and corresponding derivative results;

Figure 3 is a schematic diagram of the edge extraction results of the fixed-scale Gaussian filter combined with the Canny algorithm;

Fig. 4 is an image area fitting and ridge trend chart;

Fig. 5 is a schematic diagram of threshold segmentation;

Figure 6(a) is a schematic representation of the center point pixel and eight neighborhoods;

Figure 6(b) is a schematic representation of the eight-neighborhood coordinates;

Fig. 7 is a schematic diagram of the search direction and order of the subsequent points of the current point;

Fig. 8 is a schematic diagram of an example of image sub-pixel edge extraction with strong noise;

Fig. 9 is a schematic diagram of the detection result of the image variable-scale blurred image;

Fig. 10 is a schematic diagram of comparison of detection results obtained by the method of the present invention and commercial software.

specific implementation plan

The present invention will be further described in detail below through specific embodiments in conjunction with the accompanying drawings.

Edge detection is a widely used algorithm in image processing. Many operators in machine vision technology need to be based on good edge extraction results, such as geometric template matching, line detection, circle detection, character recognition, defect detection, size measurement, etc. The invention provides a method capable of stably detecting edges of strong noise images or images with strong fuzzy scale changes, and the method can provide subpixel-accurate edge positions, connection relations of edge points, and length information of edge points. The edge detection efficiency is extremely efficient, which is very suitable for application in machine vision real-time systems. The invention can provide an important basis for the positioning and measurement technology in machine vision.

The flow chart of the method of the present invention is shown in Figure 1, including the following steps: Step 1: Image preprocessing, smoothing and filtering the image; Step 2: Scale state first-order discrete kernel convolution image; Step 3: Adaptive high and low threshold calculation ; Step 4: Calculation of approximate gradient direction and selection of local maximum center value; Step 5: Judgment and selection of pixel boundary points; Step 6: Calculation of edge positions with sub-pixel accuracy; Step 7: Sequential connection of boundary points with the same attribute.

Each step is described in detail below.

1. Image preprocessing

Before finding edge points, it is necessary to establish an edge model that satisfies certain conditions. Most edge detection algorithms, such as Marr, Hildreth, Poggio, Canny, etc., define the edge position at the position where the gray level of the image changes suddenly, that is, the position where the first-order derivative amplitude data is higher than a certain threshold or the second-order derivative is equal to zero and not A flat inflection point satisfies the condition g′(x,y)g ^m (x,y)<0. In accompanying drawing 2, g(s) is a one-dimensional grayscale distribution, in the figure g′(s) is the first-order derivative curve of one-dimensional grayscale distribution, and g″(s) is the second-order derivative curve of one-dimensional grayscale distribution Both the first-order and second-order derivatives can represent image edge features, but the first-order derivative has the advantages of fast calculation speed and strong anti-noise ability, and the first-order derivative is used as the basis for judging the edge in the present invention.

The curve g(s) shown in Figure 2 represents the original data. From this figure, it can be assumed that the step edge model is ku(x)+h, where k is the unknown gradient magnitude, h represents the gray value of the background image, and u (x) is the gray distribution curve equation. The purpose of using preprocessing in edge extraction is to process all possible edge positions close to the edge model g(s) in Fig. 2, which is also the processing requirement of step ① in the method flow. Image preprocessing is completed through Gaussian filtering, and the processed objects include: uncertain types of noise interference images, blurred images of different reasons and degrees, and non-step edge models. The Gaussian blur kernel for a 2D image is defined as follows:

$\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&pi;\&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

The unknown variable scale information is the curve variance σ parameter. In order to adapt to different types of images and ensure that the problems encountered in Fig. 3 can be solved, the variable-scale image blur smoothing filter is used as an image preprocessing means. What needs to be solved is that when the performance of edge points in some areas is satisfied, other edge points are detected as non-single-pixel wide boundary points.

2. First-order scale Gaussian kernel derivation image edge gradient

After the image preprocessing operation, according to the definition that the edge point exists at the sudden change of the gray value of the image, the edge line is also at the ridge line (ridge) of the first derivative of the image, as shown in Figure 4. The ridge is a collection of adjacent continuous local maxima in the gradient image, and it is also the location of the edge curve.

When the image is generated, the boundary may be blurred due to various reasons (such as different refraction of light by the lens lens, shadows formed by non-parallel rays at the boundary, blurring of the edge itself, etc.) or the introduction of noise signals (such as Gaussian noise). The invention can overcome the above-mentioned problems and obtain single-pixel wide edge points. Assuming that the image I(x, y) is subjected to the edge extraction operation, the boundary point error rate is α _I , and the image size is n=w×h, then the single point detection error probability is α _p =1-(1-α _I ) ^{1/ n} ; where α _I ranges from 0 to 1.0. When calculating the first derivative of the image, firstly ensure that the obtained gradient amplitude satisfies that the error rate at this point is less than the set value α _p . The first derivative of the image is obtained by convolving the image space with the target kernel, and using the step-by-step nature of convolution, the following equation is obtained:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; \&prime;</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

The magnitude of the gradient at each point is

Assuming that the image I(x, y) has only Gaussian noise and the variance of the noise signal is s _n , the function U represents the positive interval semifunction of the Gaussian function, and its partial derivative expression is:

${\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\frac{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

The relationship between image signal variance and filter signal variance is s=||G′(x,y,σ)|| ₂ s _n , function f is diffeomorphism, and V=f(U), Then the partial derivative of the function V is:

${\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; V</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; v</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

The constructor f(u)=u ² , combined with formula (2) and formula (3), obtains the following formula:

${\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; V</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\sqrt{\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; v</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Combining the gradient of each axis in formula (1) and substituting it into function (4), the following expression is obtained:

${\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; v</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; V</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; V</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; dv</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Solving formula (5), we get v ∈ [0, ∞). To ensure that the error probability of the edge position of each point does not exceed α _p , the probability value is obtained by integrating the probability density function (5). Set the key parameter variable as c, which has the following expression:

${<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

_The L2 distance of the first derivative of the Gaussian function is: Combining the above related expressions, the expression of the parameter c is:

$\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\sqrt{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&rsqb;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

The variable in formula (7) is σ, which is a scale variable, and other variables are global setting parameters. From (5) (6), it can be obtained that the key of the variable scaling algorithm is to make the error rate of the gradient amplitude of each point lower than the set value α _p , that is, to satisfy the equation: M(x,y,σ)≥c( σ).

3. Adaptive high and low threshold calculation

The present invention applies the chain threshold edge extraction and selection principle in the edge candidate point selection process to realize pixel-level boundary position extraction, that is, step ③ in the process. The present invention adopts two ways to set high and low thresholds: external parameter input and adaptive threshold calculation. There is an obvious peak point in the histogram curve of image gradient information synthesis, and after the peak point, the value of the histogram decreases sharply until it drops to zero.

The invention discloses a simple and fast method for finding high and low thresholds. First find the peak point (i, H _i ) of the histogram curve, and the coordinate point of the non-zero cumulative value in the last histogram is (j, H _j ) (0≤i<j≤255) and 0≤H _j < H _i <1.0), connect the above two points to get a straight line ax+by+c=0. Find the maximum distance between the histogram curve coordinate point and the straight line between i and j, that is, satisfy d _max =arg max _k |ak+bH _k +c|. The abscissa of the point coordinates (k, H _k ) is the first threshold T _low =k. Then start from this point to the end point of the straight line (j, H _j ) and then connect to a straight line αx+βy+λ=0, on the interval k to j of the histogram curve, find the curve to the straight line (α, β, λ ), also satisfy D _max =arg max _t |αt+βH _t +λ|. The abscissa of the point coordinate (t, H _t ) is marked as the second threshold T _high =t. A simple representation of the calculation method is shown in Figure 5.

4. Calculation of approximate gradient direction and selection of local maximum central value

After obtaining the gradient image, in order to conveniently and quickly find the single-pixel width position of the ridge line, the local maximum center value selection operation is performed on the gradient image in combination with the gradient direction information of the pixel point, which is step ④ of the flowchart. The gradient direction of any pixel position is θ=tan ^-1 (f _y /f _x ), tangent to the trend direction of the ridge. Take any pixel position as the origin, establish a relative coordinate, take the eight neighboring pixels around the point as the local maximum center value to select the data sample, obtain the comparison result of the neighborhood according to the gradient direction, and determine whether the current pixel position is a candidate position of the boundary point .

In the process of edge extraction, non-maximum suppression is an effective means to quickly select local maxima. First, the gradient direction (0°-180°) is divided into several regions with a step size of 22.5°, as shown in Figure 6(a). Among them, A and A' are regarded as the same group when the two angles are complementary. The invention provides a fast gradient direction estimation algorithm, which can simply and conveniently determine the orientation of the gradient direction of the current point in the eight neighborhood directions. If the gradient direction θ of the current point p ₀ is The variables are the respective gradient derivative values, and the angle range is set between 0° and 90°, that is, only the states where the parameters are positive values are considered. When θ is less than 22.5°, n _y <n _x tan(22.5°), the gradient direction is located in the A range of Figure 6(a), then the eight-neighborhood direction of p ₀ is G _R in Figure 6(b); When θ is greater than 67.5°, n _y >n _x tan(67.5°), and the gradient direction is located in the C range of Figure 6(a), then the eight-neighborhood direction of p ₀ is _GT in Figure 6(b); When the range of θ is between 22.5° and 67.5°, n _y ≥n _x tan(22.5°) and n _y ≤n _x tan(67.5°), the gradient direction is located in the D range of Figure 6(a), then p ₀ The eight-neighborhood direction of is G _TR in Fig. 6(b). If the gradient direction G ₀ of point p ₀ falls within the range of A in Figure 6(a), then the two complementary directions of G _R and _GL in the eight neighborhood directions are marked as G ₊ and G _- respectively. The criteria for judging the local maximum value are: G ₀ >G ₊ and G ₀ ≥G _- or G ₀ ≥G ₊ and G ₀ >G _- , that is, the current point p ₀ is a maximum value of the local gradient amplitude. In the comparison judgment, if the two comparison symbols are both ">", then there will be no extreme value at the equal gradient amplitude; if both are "≥", then all positions with equal amplitude will be recognized as an extreme value.

5. Pixel boundary point judgment selection

Whether the extremum of the local gradient amplitude is an edge point needs to be judged in conjunction with a specific threshold. Marks greater than a given threshold are marked as edge points, and those smaller than a given threshold are judged as noise points or background points, that is, step ⑤ of the flowchart. Canny's dual threshold setting (T _low , T _high ) is adopted in the present invention. When the local extremum G ₀ is higher than T _high , the point p ₀ is an edge point; G ₀ is lower than the threshold T _low , indicating that the current point is a non-boundary point attribute; when G ₀ is between the high and low thresholds, a chain effect occurs Function, that is, there are boundary points in the eight neighborhoods of point p ₀ , then the current position is confirmed as the boundary point.

6. Calculate the edge position with sub-pixel accuracy

In general applications, the pixel-level boundary point position accuracy can meet the requirements, but in some applications, higher edge precision positions are required, that is, sub-pixel edge positions, step ⑥ of the flowchart. Use the Hessian matrix method based on the Steger surface fitting method to obtain the sub-pixel position of the edge point, and perform the surface fitting interpolation algorithm f(r, c)=k ₀ +k ₁ r+ in the small area of the pixel-level edge point k ₂ c+k ₃ r ² +k ₄ rc+k ₅ c ² ; Calculate the first-order and second-order derivatives of the unknowns of the surface equation, and combine them into a Hessian matrix; solve the eigenvalues and their respective eigenvectors of the Hessian matrix, The eigenvector corresponding to the largest absolute eigenvalue is the normal direction (n _x , _ny ) of the edge point; the sub-pixel position of the edge point is calculated by using the normal direction and the Taylor expansion of the surface equation. The matrix expression of the surface equation coefficients is as follows.

$\begin{array}{ccc}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}\left\{\begin{array}{ccc}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right\}& {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}\left\{\begin{array}{ccc}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right\}& {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}\left\{\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right\}\end{array}$

$\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}\left\{\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right\}& {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}\left\{\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right\}\end{array}$

7. Sequential connection of boundary points with the same attribute

So far, the detected edge information is discrete, disordered, and isolated points, but many later applications need a continuous set of boundary points (curves), flowchart step ⑦. Connect the edge points into a curve to form a set of directed continuous points. What needs to be noted in the process of edge connection is that one of the principles to be maintained in boundary connection is to choose the closest trend that forms a straight line or a smooth curve as much as possible. At the same time, it is also necessary to avoid forming two interconnected curves. There is only one and only one curve for the wavy curve.

The available conditions of edge connection are the edge point position in the image space and the presence or absence of the eight-neighborhood boundary point of the point. The starting point of the curve is searched from the upper left corner, and the first detected edge point is defined as the starting position. The order of the search direction of this point is to first search whether there is a boundary point satisfying the condition on the positive direction (ie, G _R , G _B , _GL , G _T as shown in the accompanying drawing 7), otherwise look for the bias direction (the other in the accompanying drawing 7) direction). In the same direction (forward direction, partial direction), the candidate points are selected in counterclockwise order. Let P ₀ be the current point, {P _i } _{i=R, B, T, BR, RT} are candidate points, and the sub-pixel coordinates of each point and gradient direction is a known condition. Given an evaluation function Select the neighbor point with the smallest score as the next neighbor point. Change and replace the current point cyclically until it encounters a non-edge point or an edge point on another edge curve before ending the search of the current curve. After the search in the current direction is completed, search in the reverse direction from the starting point of the curve until the end point.

In order to verify the effectiveness of the disclosed method of the present invention, the distribution adopts strong noise (see the left part of accompanying drawing 8) and fuzzy image (seeing the left part of accompanying drawing 9) to carry out the edge extraction test, the middle part of accompanying drawing 8 and accompanying drawing 9 It is the result of traditional edge detection, and the right part is the detection result of the present invention. It can be seen that the method disclosed in the present invention can stably detect edge features in strong noise and blurred images. Accompanying drawing 10 is the contrast effect that the edge detection result that method of the present invention obtains and the edge detection result that German commercialization machine vision software obtains, among the figure "+" is the edge result that the present invention detects, and "o" is foreign commercial software detection As a result, it can be seen from the figure that the method of the present invention can detect more edge information of the image.

The present invention proposes a method for stably extracting image sub-pixel edge features in a harsh environment, using an adaptive high and low threshold calculation method, after obtaining the gradient image, in order to find the single-pixel wide position of the ridge conveniently and quickly, combined with the pixel The gradient direction information of the point performs the selection operation of the local maximum central value on the gradient image, takes any pixel position as the origin, establishes the relative coordinates, takes the eight neighboring pixels around the point as the local maximum central value to select the data sample, and obtains according to the gradient direction The comparison result of the neighborhood determines whether the current pixel position is a candidate position of the boundary point. Whether the extremum of the local gradient amplitude is an edge point needs to be judged in conjunction with a specific threshold. Marks greater than a given threshold are edge points, and smaller than a given threshold are judged as noise points or background points. Using the Hessian matrix method based on the Steger surface fitting method to obtain the sub-pixel position of the edge point. Finally, the edge points will be connected into a curve to form a set of directed continuous points. It realizes the extraction of ordered edge feature information with sub-pixel accuracy in strong noise and blurred images. The method of the invention has excellent real-time performance and can be applied to the real-time application of machine vision systems.

The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be assumed that the specific implementation of the present invention is limited to these descriptions. For those of ordinary skill in the technical field of the present invention, without departing from the concept of the present invention, some simple deduction or replacement can be made, which should be regarded as belonging to the protection scope of the present invention.

Claims (7)

1. a kind of image sub-pixel edge extraction method with extensive adaptability, is characterized in that: described method comprises the following steps: Step 1: Preprocessing the image by using variable-scale image blur smoothing filter; Step 2: Calculate the first-order derivative of the preprocessed image. First, ensure that the obtained gradient magnitude satisfies that the error rate at this point is less than the set value α _p . The first-order derivative of the image is obtained by convolving the image space with the target kernel; the edge line of the image At the ridge line of the first derivative of the image, where the ridge line is a collection of adjacent continuous local maxima in the gradient image; Step 3: Apply the chain threshold edge extraction and selection principle in the edge candidate selection process to realize pixel-level boundary position extraction. The high and low thresholds are obtained in two ways: external parameter input or adaptive threshold calculation; Step 4: After obtaining the gradient image, in order to find the single-pixel width position of the ridge conveniently and quickly, combine the gradient direction information of the pixel to perform a local maximum central value selection operation on the gradient image; Step 5: Whether the extremum of the local gradient amplitude is an edge point needs to be judged in combination with a specific threshold, and the mark greater than a given threshold is an edge point, and less than a given threshold is judged as a noise point or a background point; Step 6: Calculate the edge position with sub-pixel accuracy; Step 7: Connect the edge points into a curve to form a set of directed continuous points. 2. method according to claim 1, it is characterized in that: in described step 2, suppose image I (x, y) obtains boundary point error rate α _I after performing edge extraction operation, image size is n=w ×h, then the probability of a single point detection error is α _p =1-(1-α _I ) ^1/n , where the range of α _I is between 0 and 1.0, the image I(x, y) has only Gaussian noise and the noise signal variance is s _n ; using the step-by-step feature of convolution, there are the following equations: $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; G</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; \&prime;</span>}\end{array}\right.<span\; class="notranslate">\; ,</span>$ The gradient amplitude of each point is obtained as Make the error rate of the gradient amplitude of each point lower than the set value α _p , which satisfies the equation: M(x, y, σ)≥c(σ), where, $\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\sqrt{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&rsqb;</span>}<span\; class="notranslate">\; ,</span>$ The variable in the above formula is the scale variable σ, and the other variables are global setting parameters. 3. The method according to claim 1, characterized in that: calculating the high and low thresholds in the step 3 is specifically: at first find the peak point (i, H _i ) of the histogram curve, the non-zero cumulative value in the last histogram The coordinate point is (j, H _j ), 0≤i<j≤255 and 0≤H _j <Hj<1.0, connect the above two points to get a straight line ax+by+c=0; between i and j Find the maximum distance position d _max from the coordinate point of the histogram curve to the straight line, which satisfies d _max =argmax _k |ak+bH _k +c|, and the abscissa of the point coordinate (k, H _k ) is the first threshold T _low = k; then starting from this point, to the end point of the straight line (j, H _j ) and then connected to a straight line αx+βy+λ=0, on the interval k to j of the histogram curve, find the curve to the straight line (α , β, λ), the maximum distance position D _max also satisfies D _max =argmax _t |αt+βH _t +λ|, and the abscissa of the point coordinate (t, H _t ) is marked as the second threshold T _high =t . 4. The method according to claim 1, characterized in that: said step 4 is specifically: the gradient direction of any pixel position is θ=tan ^-1 (f _y /f _x ), the trend direction of tangency and ridge line ; Take any pixel position as the origin, establish a relative coordinate, take the eight neighboring pixels around the point as the local maximum center value to select data samples, obtain the comparison result of the neighborhood according to the gradient direction, and determine whether the current pixel position is a candidate for a boundary point Location. 5. The method according to claim 4, characterized in that: said step 5 adopts Canny's dual threshold setting (T _low , T _high ); when local extremum G ₀ is higher than T _high , point p ₀ is Edge point; G ₀ lower than the threshold T _low indicates that the current point is a non-boundary point attribute; when G ₀ is between the high and low thresholds, the chain effect takes effect, that is, there are boundary points in the eight neighbors of point p ₀ , then The current position is confirmed as a boundary point. 6. The method according to claim 1, characterized in that: said step 6 adopts the Hessian matrix method based on the Steger surface fitting method to obtain the sub-pixel position of the edge point, and performs surface fitting in the small area of the pixel-level edge point. A combined interpolation algorithm f(r, c)=k ₀ +k ₁ r+k ₂ c+k ₃ r ² +k ₄ rc+k ₅ c ² ; the first-order and second-order The derivatives are combined into a Hessian matrix; the eigenvalues and their respective eigenvectors of the Hessian matrix are solved, and the eigenvector corresponding to the largest absolute eigenvalue is the normal direction (n _x , n _y ) of the edge point; using the normal direction and Taylor expansion of surface equations to compute sub-pixel locations of edge points. 7. The method according to claim 1, characterized in that: in the edge connection process of step 7, a principle to be kept in the boundary connection that needs attention is to select the trend that is closest and forms a straight line or a smooth curve as much as possible, and at the same time To avoid forming two interconnected curves, there can only be one and only one curve for a wave curve.