Color Image Edge Extraction Method Based on Reduced Concept Structure Elements and Matrix Order

Abstract

The present invention discloses a method for extracting edges of a color image based on reduced concept structure elements and matrix order. The implementation steps are as follows: constructing a pixel window for each pixel point in the color image to be edge-extracted; generating a reduced background matrix for all pixels in each pixel window; generating a reduced object relationship matrix for each pixel window; generating a reduced concept structure element for each pixel; generating a matrix order for each element in each reduced concept structure element; determining the maximum pixel value in each reduced concept structure element; calculating the difference pixels; and extracting the edges in the color image. The present invention overcomes the defects in the prior art of the decreased clarity of the color image processing result and the blurred edge extraction, and improves the clarity and the integrity of the edge after the morphological processing of the color image.

Description

Technical Field

[0001] The present invention belongs to the technical field of image processing, and further relates to a method for extracting edges of a color image based on a reduced concept structure element and matrix order in the technical field of color image edge extraction. The present invention extracts a reduced concept structure element by applying a reduced object relationship matrix and performs morphological operations on a color image by applying matrix order, so as to realize the operation of extracting the edges of the color image. Background Art

[0002] Color images are the main source for humans to obtain and exchange information, and edges are one of the most basic features of color images. The edges of a color image are the places where the color changes drastically under the illumination change of the external environment of the object shape structure, directly reflecting the contour and topological structure of the object. In digital color image processing technology, edges, as an important way to express information in color images, are important research objects in fields such as graphic color image processing and computer vision. Edge extraction, as the basis for studying edge information of color images, the quality of its extraction results will directly affect the next step of operation. Traditional edge extraction methods need to select appropriate thresholds, and there are also a large number of noises in the edge extraction results, resulting in the possibility that the extracted boundaries may become wider or even connected, unable to meet the requirements of current digital color image processing technology for edge accuracy.

[0003] Zhengzhou University of Light Industry disclosed a method for extracting edges of a color image in its patent document "A Method for Extracting Edges of a Color Image" (Patent Application No. 202110787844.5, Publication No. CN 113469916 A). The implementation steps of this method are as follows: 1. Adopt a noise reduction method based on a threshold to perform noise reduction on the color image; 2. Through the RGB model and HSI model, perform color analysis on the color image structure; 3. Design an algorithm to compare thresholds to determine color edge points, and form a color edge from the edge points. The disadvantages of this method are that when determining whether each pixel is an edge point of the color image, the total gradient of the pixel point needs to be compared with a set threshold, and this threshold is a fixed value for each pixel of the entire color image, resulting in the edges extracted in the low-contrast area of the color image being connected to each other in the figure, making the image extracted in the low-contrast area of the color image unclear.

[0004] Xidian University discloses a method for extracting the edges of a color image in its patent document "Color Image Edge Extraction Method Based on Concept Structure Elements and Matrix Norms" (Patent Application No. 202210207060.5, Publication No. CN 114565633 A). The implementation steps of this method are as follows: 1. Select an unselected pixel from the color image and extract a pixel window centered on the selected pixel; 2. Generate the background matrix of all pixels in the pixel window; 3. Generate an object relationship matrix describing the relationship between any two pixels in the pixel window; 4. Determine the concept structure element of the selected pixel; 5. Use the matrix norm of the pixel to determine the maximum pixel element in the set of concept structure elements; 6. Construct a result image with the same length and width as the color image. Set the difference pixel obtained by subtracting the maximum pixel from the selected pixel in the result image. The position of the difference pixel in the result image corresponds to the position of the selected pixel in the color image; 7. Use the same method as steps 1 to 6 to successively perform edge extraction on each pixel point of the color image to be edge-extracted, and obtain the color image after edge extraction. The deficiencies of this method are that the clarity of the color image processed by morphological dilation and erosion is low, and at the same time, the edges of the color image extracted by morphological opening and closing operations are blurred. Summary of the Invention

[0005] The object of the present invention is to propose a color image edge extraction method based on reduced concept structure elements and matrix order in view of the above-mentioned deficiencies of the prior art, aiming to solve the problems of low clarity after color image processing and blurred edges extracted by color image opening and closing operations when extracting the edges of a color image.

[0006] The idea to achieve the object of the present invention is that the present invention extracts corresponding pixel windows centered on each pixel point in a color image, constructs a reduction relation matrix to describe the pixel windows, obtains a reduction object relation matrix after a series of matrix operations on the reduction matrix, and extracts the reduction concept structure elements of the selected pixels by using the generated reduction object relation matrix. When constructing the reduction relation matrix to describe the pixel windows, each pixel in the pixel window is selected within a certain range in terms of the pixel values of the red, green, and blue channels of the selected pixel and the Euclidean color distance. Therefore, different pixel selection thresholds result in different generated reduction object relation matrices, and thus different extracted reduction concept structure elements, which can exclude singular points with too large pixel value differences in the process of adaptively processing each pixel point in the color image. When there are many surrounding singular points for the selected pixel, the present invention can still obtain the actual edge of the color image. The present invention introduces FCA, generates a reduction background matrix, constructs reduction concept structure elements through the reduction background matrix, and at the same time defines a matrix order to calculate the maximum pixel value of the reduction concept structure elements. The difference pixel is obtained by subtracting the maximum pixel from the selected pixel. The difference pixel is assigned to the color image after edge extraction. If the difference pixel is a black pixel, it means that the selected pixel is not an edge point. If the difference pixel is a color pixel, it means that the selected pixel is an edge point. Therefore, the color image after edge extraction composed of all difference pixels is the edge extraction result of the image.

[0007] The specific steps to achieve the object of the present invention are as follows:

[0008] Step 1, construct a pixel window for each pixel point in the color image to be extracted with edges:

[0009] Step 2, generate a reduction background matrix for all pixels in each pixel window:

[0010] Construct a background matrix with N rows and 4 columns for each pixel window. Each row of this reduction background matrix represents the corresponding pixel in the pixel window. The first to fourth columns of this background matrix respectively describe the four relationship quantities of the pixel represented by each row with the selected pixel in the red channel, green channel, blue channel, and Euclidean color distance. Subtract the pixel value of each point in the matrix from the corresponding pixel value of the selected pixel point. If the difference is less than the threshold C, mark this point as 1; otherwise, mark it as 0, where N represents the total number of pixels in the pixel window, and C is a value selected from [80, 120];

[0011] Step 3, generate a reduction object relation matrix for each pixel window;

[0012] Step 4, generate a reduction concept structure element for each pixel:

[0013] Select all elements with element values of 1 in the reduction object relationship matrix of each pixel window to form the reduction concept structure elements of the pixel window;

[0014] Step 5, generate the matrix order of each element in each reduction concept structure element according to the following formula:

[0015]

[0016] where ρ pq represents the matrix order of the q-th pixel in the p-th reduction concept structure element, and the value of p corresponds to i. U m represents the pixel value of the m-th element in the pixel window after expansion of the q-th pixel in the p-th reduction concept structure element set. Σ represents the summation operation;

[0017] Step 6, determine the maximum pixel value in each reduction concept structure element:

[0018] Take the pixel value corresponding to the largest matrix order in each reduction concept structure element as the maximum pixel value in the reduction concept structure element;

[0019] Step 7, calculate the difference pixel:

[0020] Subtract the pixel value of the central pixel point in each reduction concept structure element from the maximum pixel value of the reduction concept structure element to obtain the difference pixel corresponding to the reduction concept structure element;

[0021] Step 8, extract the edges in the color image:

[0022] Step 8.1, construct a result image with the same length and width as the color image from which the edges are to be extracted;

[0023] Step 8.2, assign all the difference pixels to the corresponding positions in the constructed result image and the color image from which the edges are to be extracted to obtain the edge image.

[0024] The present invention has the following advantages compared with the existing technologies:

[0025] First, since the present invention enhances the local relevance when selecting the background matrix by introducing the FCA reduction concept structure elements, and then generates the reduction object relationship matrix after a series of matrix operations, it overcomes the defect of the existing technology that all pixel points are generally selected, resulting in a decrease in the clarity of the color image processing result in the case of many singular points. The present invention can adaptively extract the reduction concept structure elements of the selected pixels by using the generated reduction object relationship matrix, improving the clarity of the color image after morphological processing.

[0026] Second, since the present invention enhances local correlation by dilation operation and weakens local correlation by erosion operation, it overcomes the defect of blurred edges in the extraction of color images by morphological opening and closing operations. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is a flowchart of the present invention;

[0028] Figure 2 is the color image to be processed by the present invention;

[0029] Figure 3 is the result diagram after digital morphological opening and closing operations of the present invention, where Figure 3 (a) is the result diagram after closing operation, Figure 3 (b) is the result diagram after opening operation;

[0030] Figure 4 is the present invention and Figure 3 the corresponding edge extraction image, where Figure 4 (a) is the edge image extracted by closing operation, Figure 4 (b) is the edge image extracted by opening operation. DETAILED DESCRIPTION OF THE INVENTION

[0031] The present invention will be further described below with reference to the drawings and embodiments.

[0032] Refer to Figure 1 for a further description of the specific implementation steps of the present invention.

[0033] In the embodiment of the present invention, a color image with a size of 5×5 is selected, as Figure 2 shown.

[0034] Step 1: Select an unselected pixel from the color image and use the selected pixel as the center.

[0035] The following combines Figure 2 for a further detailed description of the complete processing process of a pixel point selected from the color image in the embodiment of the present invention.

[0036] In the embodiment of the present invention, the color pixel at the position (3,3) of the color image is selected, and the pixel values of the red, green, and blue channels of this color pixel are 237, 174, and 203 respectively.

[0037] Step 1: Use the selected pixel as the center and select a pixel window with a size of n×n from the color image.

[0038] In an embodiment of the present invention, n = 3 is taken. With the selected pixel {237, 174, 203} as the center, 8 pixels around this pixel are selected from the color image, namely the pixels above, below, left, right, upper left, lower left, upper right, and lower right of this pixel. The coordinates of these 8 pixels in the color image are respectively (2, 3), (4, 3), (3, 2), (3, 4), (2, 2), (4, 2),

[0039] (2, 4), (4, 4). The pixel values of the pixel located above the selected pixel in the red, green, and blue channels are 242, 199, and 227 respectively. The pixel values of the pixel located below the selected pixel in the red, green, and blue channels are 255, 169, and 185 respectively. The pixel values of the pixel located to the left of the selected pixel in the red, green, and blue channels are 96, 218, and 103 respectively. The pixel values of the pixel located to the right of the selected pixel in the red, green, and blue channels are 254, 188, and 232 respectively. The pixel values of the pixel located in the upper left of the selected pixel in the red, green, and blue channels are 69, 229, and 51 respectively. The pixel values of the pixel located in the lower left of the selected pixel in the red, green, and blue channels are 247, 201, and 232 respectively. The pixel values of the pixel located in the upper right of the selected pixel in the red, green, and blue channels are 241, 39, and 211 respectively. The pixel values of the pixel located in the lower right of the selected pixel in the red, green, and blue channels are 54, 90, and 231 respectively. These 8 pixels together with the selected pixel jointly form a pixel window with a size of 3×3.

[0040] Step 2, number the pixels in the pixel window: The number of the pixel in the upper left corner of the pixel window is 1, and the numbers of other pixels increase gradually to the right and downwards in sequence. Then the number of the selected pixel in the pixel window is The number of the pixel in the lower right corner of the window is n 2 .

[0041] In the embodiment of the present invention, the number of the selected pixel is 5, and the numbers of the upper left, upper, upper right, left, right, lower left, lower, and lower right around the selected pixel are 1, 2, 3, 4, 6, 7, 8, and 9 respectively.

[0042] Step 2, generate the reduced background matrix of all pixels in the pixel window.

[0043] Step 1, calculate the Euclidean color distance of each pixel in the pixel window.

[0044] When calculating the Euclidean color distance of a pixel, any color pixel with pixel values of r0, g0, b0 in the red, green, and blue channels can be used as a reference.

[0045] Embodiments of the present invention use a black pixel with pixel values of 0 in all three red, green, and blue channels as a reference, and let r0 = 0, g0 = 0, b0 = 0. Using the following Euclidean color distance formula, calculate the Euclidean color distance of each pixel in the pixel window of the selected pixel:

[0046]

[0047] where d j represents the Euclidean color distance of the j-th pixel in the pixel window, and r j , g j , b j represent the pixel values of the red, green, and blue channels of the j-th pixel respectively, represents the floor operation.

[0048] In the embodiments of the present invention, the Euclidean color distances of pixels 1-9 in the pixel window of the selected pixel are: 244, 386, 322, 259, 357, 392, 393, 357, 253 respectively.

[0049] Step 2: Construct a background matrix for describing the relationship between each pixel in the pixel window and the selected pixel.

[0050] Construct a background matrix K with N rows and 4 columns. The i-th row of this background matrix represents the j-th pixel in the pixel window, where i = j. The first to fourth columns of this background matrix respectively describe the four relationship quantities of the pixel represented by the i-th row with the selected pixel in the red channel, green channel, blue channel, and Euclidean color distance. Among them, 1 ≤ i ≤ N, and N represents the total number of pixels in the pixel window, N = n 2 .

[0051] Since the selected pixel is located at the center position of the pixel window, the row number of the selected pixel in the pixel matrix is equal to its number in the pixel window.

[0052] If the absolute value of the interpolation of the first column of the pixel represented by the i-th row of the reduced background matrix and the first column of the selected pixel is less than the set threshold of 100, then set the element value at position (i, 1) in the background matrix to 1, K i1 = 1, otherwise, set it to 0, K i1 = 0.

[0053] If the absolute value of the interpolation of the second column of the pixel represented by the i-th row of the reduced background matrix is greater than or equal to the second column of the selected pixel and less than the set threshold of 100, then set the matrix element value at position (i, 2) in the background matrix to 1, K i2 = 1, otherwise set it to 0, K i2 = 0.

[0054] If the absolute value of the interpolation of the third column of the pixel represented by the i-th row of the reduced-form background matrix is greater than or equal to the absolute value of the interpolation of the third column of the selected pixel and less than the set threshold of 100, then set the value of the matrix element at position (i, 3) in the background matrix to 1, K i3 = 1, otherwise set it to 0, K i3 = 0.

[0055] If the absolute value of the interpolation of the fourth column of the pixel represented by the i-th row of the background matrix is greater than or equal to the absolute value of the interpolation of the fourth column of the selected pixel and less than the set threshold of 100, then set the value of the matrix element at position (i, 4) in the background matrix to 1, K i4 = 1, otherwise set it to 0, K i4 = 0.

[0056] In an embodiment of the present invention, the background matrix of each pixel in the pixel window and the selected pixel is:

[0057]

[0058] Step 3, generate a reduced object relationship matrix describing the relationship between any two pixels in the pixel window.

[0059] Step 1: Transpose the reduced background matrix of the selected pixel to obtain a temporary matrix M1.

[0060] In an embodiment of the present invention, the temporary matrix M1 is:

[0061]

[0062] Step 2: Perform a matrix complement operation on the temporary matrix M1 obtained in Step 1 of this step to obtain a temporary matrix M2.

[0063] The matrix complement operation refers to first obtaining a matrix of all 1s with the same size as the matrix to be operated on, and then subtracting the obtained matrix of all 1s from the matrix to be operated on.

[0064] In an embodiment of the present invention, the temporary matrix M2 is obtained by the following formula:

[0065]

[0066] Step 3: Perform a matrix multiplication operation on the reduced background matrix describing all pixels in the pixel window and the temporary matrix M2 obtained in Step 2 of this step to obtain a temporary matrix M3.

[0067] In an embodiment of the present invention, the temporary matrix M3 is obtained by the following formula:

[0068]

[0069] Step 4: Perform matrix completion operation on the temporary matrix M3 obtained in Step 3 of this step to obtain the object relationship matrix W of the background matrix.

[0070] In the embodiment of the present invention, the object relationship matrix W of the background matrix is obtained by the following formula:

[0071]

[0072] Step 4, determine the reduced concept structure elements of the selected pixels.

[0073] In the reduced object relationship matrix, all the pixels corresponding to the columns with the element value of 1 in the row corresponding to the selected pixel are determined as an element in a set of concept structure elements.

[0074] In the embodiment of the present invention, according to the description of Step 2 in Step 2, the 5th row in the background matrix represents the selected pixel. Therefore, in the object relationship matrix, take the 5th row of the object relationship matrix as follows: [0 1 1 0 1 1 0 0 0]

[0076] In the 5th row, the columns with the element value of 1 are the 2nd, 3rd, 5th, and 6th columns respectively. Then the set of pixels corresponding to the 2nd, 3rd, 5th, and 6th columns is a reduced concept structure element.

[0077] There are 4 pixels in the reduced concept structure element. For the pixel corresponding to the 2nd column, the pixel values of its red, green, and blue channels are 242, 199, and 227 respectively, and its coordinates in the color image are (2, 3); for the pixel corresponding to the 3rd column, the pixel values of its red, green, and blue channels are 241, 39, and 211 respectively, and its coordinates in the color image are (2, 4); for the pixel corresponding to the 5th column, the pixel values of its red, green, and blue channels are 237, 174, and 203 respectively, and its coordinates in the color image are (3, 3); for the pixel corresponding to the 6th column, the pixel values of its red, green, and blue channels are 254, 188, and 232 respectively, and its coordinates in the color image are (3, 4).

[0078] Step 5, generate the matrix order of each element in each reduced concept structure element according to the following formula.

[0079]

[0080] Among them, ρ pq represents the matrix order of the qth pixel in the pth reduced concept structure element, and the value of p corresponds to i. U m represents the pixel value of the mth element in the pixel window after expansion of the qth pixel in the set of the pth reduced concept structure element, and Σ represents the summation operation.

[0081] In an embodiment of the present invention, there are 4 pixels in the reduced concept structure element, and the positions of these 4 pixels in the color image are respectively: (2, 3), (3, 3), (3, 4), (4, 2), and the matrix orders of these 4 pixels are respectively: 924, 1003, 959, 815.

[0082] Step 6, determine the maximum pixel value in each reduced concept structure element.

[0083] Determine the pixel corresponding to the maximum value in the matrix order as the maximum pixel in the reduced concept structure element.

[0084] In an embodiment of the present invention, the maximum value of the matrix order is ρ 33 = 1003. Therefore, the pixel at the position (3, 3) in the color image is the maximum pixel in the reduced concept structure element, and the pixel values of the maximum pixel in the red, green, and blue channels are 237, 174, and 203 respectively.

[0085] Step 7, calculate the difference pixels.

[0086] Subtract the pixel value of the central pixel point in each reduced concept structure element from the maximum pixel value of the reduced concept structure element to obtain the difference pixel corresponding to the reduced concept structure element.

[0087] Step 8, extract the edges in the color image.

[0088] Step 8.1, use digital morphological opening operation and closing operation to construct 2 result images with the same length and width as the length and width of the color image of the edge to be extracted, as Figure 3 shown, where Figure 3 (a) is the result image processed by the closing operation, Figure 3 (b) is the result image processed by the opening operation.

[0089] Step 8.2, assign all the difference pixels to the corresponding positions in the result images constructed by the closing operation and the opening operation that are corresponding to the color image to be processed, to obtain the edge extraction images of the opening operation and the closing operation, as Figure 4 shown, where Figure 4 (a) is the edge extraction image of the closing operation, Figure 4 (b) is the edge extraction image of the opening operation.

[0090] The effects of the present invention will be further described below in combination with simulation experiments:

[0091] Simulation experiment conditions:

[0092] The hardware platform for the simulation experiment of the present invention is: the processor is an Intel Core i5-8300H CPU with a main frequency of 2.3 GHz and 8 GB of memory.

[0093] The software platform for the simulation experiment of the present invention is: Windows 10 operating system and Matlab R2018b.

[0094] The simulation parameters of the present invention: A 3*3 pixel window is taken.

[0095] Simulation content and its result analysis:

[0096] The simulation experiment of the present invention uses the method of the present invention to Figure 2 perform edge extraction operation on the input color image shown, and obtain as Figure 3 the result image after digital morphological opening and closing operations shown and as Figure 4 the edge extraction image shown.

[0097] The simulation experiment of the present invention uses the input color image shown as Figure 2 a color image with a size of 666×479, and the color image format is jpg.

[0098] After performing digital morphological opening and closing operations on the input color image using the method of the present invention, the corresponding result images are obtained, as Figure 3 shown, Figure 3 (a) is the result image after the closing operation of the present invention, Figure 3 (b) is the result image after the opening operation of the present invention.

[0099] The edge-extracted color image obtained by performing edge extraction on the input color image using the method of the present invention is a color image with a size of 666×479 and a color image format of jpg, as Figure 4 shown. Figure 4 (a) is the edge extraction image of the closing operation, Figure 4 (b) is the edge extraction image of the opening operation.

[0100] The simulation results of the present invention show that: As can be seen from Figure 3 and Figure 4 the result images of the present invention for processing color images are clear, and the edges extracted by the opening and closing operations are complete.

Claims

1. A color image edge extraction method based on reducing concept structure elements and matrix order, characterized in that Generate the reduced background matrix for each pixel window and generate the matrix order of each element in each reduced concept structure element; the steps of the method are as follows: Step 1, construct a pixel window for each pixel point in the color image from which edges are to be extracted: Step 2, generate the reduced background matrix for each pixel window: Construct a background matrix with N rows and 4 columns for each pixel window. Each row of this reduced background matrix represents the corresponding pixel in the pixel window. The first to fourth columns of this background matrix respectively describe the four relational quantities of the pixel represented by each row with the selected pixel in the red channel, green channel, blue channel, and Euclidean color distance. Subtract the pixel value of each point in the matrix from the pixel value corresponding to the selected pixel point. If the difference is less than the threshold C, mark this point as 1, otherwise, mark it as 0, where N represents the total number of pixels in the pixel window, and C is a value selected from [80, 120]; Step 3, generate the reduced object relationship matrix for each pixel window; Step 4, select all elements with an element value of 1 in the reduced object relationship matrix of each pixel window to form the reduced concept structure element of this pixel window; Step 5, calculate the matrix order of each element in each reduced concept structure element according to the following formula: Among them, ρ pq represents the matrix order of the q-th pixel in the p-th reduced concept structure element, and U m represents the pixel value of the m-th element in the pixel window after expansion of the q-th pixel in the set of the p-th reduced concept structure elements. Σ represents the summation operation, and k represents the total number of pixels in the expanded pixel window; Step 6, determine the maximum pixel value in each reduced concept structure element: Take the pixel value corresponding to the largest matrix order in each reduced concept structure element as the maximum pixel value in this reduced concept structure element; Step 7, calculate the difference pixel: Subtract the pixel value of the central pixel point in each reduced concept structure element from the maximum pixel value of this reduced concept structure element to obtain the difference pixel corresponding to this reduced concept structure element; Step 8, extract the edges in the color image: Step 8.1, use digital morphological opening and closing operations to construct two result images with the same length and width as the length and width of the color image from which edges are to be extracted; Step 8.2, assign all the difference pixels to the corresponding positions in the result images constructed by the closing operation and the opening operation that are corresponding to the color image to be processed to obtain the edge extraction images after the opening operation and the closing operation.

2. The color image edge extraction method based on the reduced concept structure elements and matrix order according to claim 1, characterized in that The steps of constructing a pixel window for each pixel point in the color image from which edges are to be extracted described in Step 1 are as follows: The first step, select an unselected pixel point from the color image from which edges are to be extracted; The second step, expand n pixels along eight directions: up, down, left, right, upper left, lower left, upper right, and lower right with the selected pixel as the center to obtain a pixel window with the selected pixel as the center, where n is an odd number greater than or equal to 3; The third step, determine whether all pixel points in the color image have been selected. If so, obtain the pixel windows for each pixel point in the color image. Otherwise, execute the first step.

3. The color image edge extraction method based on the reduction of conceptual structure elements and matrix order according to claim 1, characterized in that The generation of the reduced object relationship matrix for each pixel window described in Step 3 is obtained by the following formula: W i = ~(K i *(~(K i Τ ))) Among them, W i represents the reduction object relationship matrix corresponding to the i-th pixel window, K i represents the background matrix corresponding to the i-th pixel window, Τ represents the transpose operation, ~ represents the complement operation on the matrix, and * represents the matrix multiplication operation.

Images