CN115861349A - Color image edge extraction method based on reduction concept structural elements and matrix sequence - Google Patents
Color image edge extraction method based on reduction concept structural elements and matrix sequence Download PDFInfo
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Abstract
The invention discloses a color image edge extraction method based on reduction concept structure elements and matrix sequences, which comprises the following implementation steps: constructing a pixel window of each pixel point in the color image of the edge to be 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 reduction concept structure element for each pixel; generating a matrix order for each element in each reduction concept structure element; determining a maximum pixel value in each reduction concept structure element; calculating difference value pixels; edges in the color image are extracted. The invention overcomes the defects of the prior art that the definition of the color image processing result is reduced and the edge is fuzzy, and improves the definition and the integrity of the edge of the color image after morphological processing.
Description
Technical Field
The invention belongs to the technical field of image processing, and further relates to a color image edge extraction method based on reduction concept structure elements and matrix sequences in the technical field of color image edge extraction. The invention uses the reduced object relation matrix to extract the structural elements of the reduced concept and uses the matrix sequence to perform morphological operation on the color image, thereby realizing the operation of extracting the edge of the color image.
Background
Color images are the main source of information acquired and exchanged by humans, and edges are one of the most basic features of color images. The edge of the color image is the place where the color of the object shape structure is changed violently under the change of external environment illumination, and directly reflects the outline and the topological structure of the object. In the digital color image processing technology, edges are important as an important approach for expressing information in color images, and are important research objects in the fields of graphic color image processing, computer vision, and the like. The edge extraction is used as a basis for researching the edge information of the color image, and the quality of the extraction result directly influences the next operation. The traditional edge extraction method needs to select a proper threshold, and meanwhile, a large amount of noise exists in an edge extraction result, so that the extracted boundary can be widened and even connected, and the requirement of the current digital color image processing technology on edge precision cannot be met.
A method of extracting an edge of a color image is disclosed in "a method of color image edge extraction" of patent document filed by zheng zhong university of light industry "(patent application No. 202110787844.5, application publication No. CN 113469916A). The method comprises the following implementation steps that 1, a noise reduction method based on a threshold value is adopted to reduce noise of a color image; 2. carrying out color analysis on the color image structure through an RGB model and an HSI model; 3. and comparing the threshold value by a design algorithm, determining color edge points, and forming a color edge by the edge points. The method has the disadvantages that when determining whether each pixel is a color image edge point, the method needs to compare the total gradient of the pixel with a set threshold, and the threshold is a fixed value for each pixel of the whole color image, so that the edge extracted by the color image in a low-contrast area is connected with the image, and the extracted image of the color image in the low-contrast area is not clear.
The title method is disclosed in "color image edge extraction method based on concept structure elements and matrix norm" (patent application No. 202210207060.5, application publication No. CN 114565656563A) of the university of sienna electronic technology. The method comprises the following steps of 1, selecting an unselected pixel from a color image, and taking the selected pixel as a center to extract a pixel window; 2. generating a background matrix of all pixels in the pixel window; 3. generating an object relationship matrix describing the relationship between any two pixels in the pixel window; 4. determining a conceptual structural element of the selected pixel; 5. determining a maximum pixel element in the concept structure element set by using the matrix norm of the pixel; 6. constructing a result graph with the length and the width equal to those of the color image, setting a difference pixel obtained by subtracting the selected pixel from the maximum pixel in the result graph, wherein the position of the difference pixel in the result graph corresponds to the position of the selected pixel in the color image; 7. and (5) performing edge extraction on each pixel point in the color image of the edge to be extracted successively by adopting the same method as the steps 1 to 6 to obtain the color image after edge extraction. The method has the defects that the definition of the color image processed by morphological dilation corrosion is low, and the edge of the color image extracted by morphological open-close operation is fuzzy.
Disclosure of Invention
The invention aims to provide a color image edge extraction method based on reduction concept structural elements and matrix sequences aiming at solving the problems of low definition after color image processing and edge blurring extracted by color image opening and closing operation when the color image edge is extracted.
The idea for realizing the purpose of the invention is that the invention extracts a corresponding pixel window by taking each pixel point in the color image as the center, constructs a reduction relation matrix to describe the pixel window, obtains a reduction object relation matrix after carrying out a series of matrix operations on the reduction matrix, and extracts the reduction concept structure element of the selected pixel by using the generated reduction object relation matrix. When a reduction relation matrix is constructed to describe a pixel window, each pixel in the pixel window and a selected pixel are selected within a certain range in the aspects of red, green and blue channel pixel values and Euclidean color distance, so that the generated reduction object relation matrixes are different due to different pixel selection thresholds, and further the extracted reduction concept structural elements are different, so that singular points with overlarge pixel value difference can be eliminated in the process of adaptively processing each pixel point in a color image. The invention can then obtain the actual edge of the color image when the selected pixels have a relatively large number of surrounding singularities. The invention introduces FCA to generate a reduction background matrix, constructs a reduction concept structure element through the reduction background matrix, defines a matrix sequence to calculate the maximum pixel value of the reduction concept structure element, and obtains a difference value pixel by making a difference between the maximum pixel and the selected pixel. And assigning the difference pixel to the color image after the edge extraction, wherein if the difference pixel is a black pixel, the difference pixel represents that the selected pixel is not an edge point, and if the difference pixel is a color pixel, the difference pixel represents that the selected pixel is an edge point. Therefore, the color image after edge extraction composed of all the difference pixels is the result of edge extraction of the image.
The specific steps for realizing the purpose of the invention are as follows:
step 1, constructing a pixel window of each pixel point in a color image of an edge to be extracted:
step 2, generating a reduced background matrix of all pixels in each pixel window:
constructing a background matrix with N rows and 4 columns of each pixel window, wherein each row of the reduced background matrix represents a corresponding pixel in the pixel window, the 1 st column to the 4 th column of the background matrix respectively describe four relation quantities of the distance between the pixel represented by each row and the selected pixel in a red channel, a green channel, a blue channel and a Euclidean color, the pixel value of each point in the matrix is different from the pixel value corresponding to the selected pixel point, if the difference value is smaller than a threshold value C, the point is marked as 1, otherwise, the point is marked as 0, wherein N represents the total number of the pixels in the pixel window, and C is a value selected in [80,120 ];
step 3, generating a reduction object relation matrix of each pixel window;
and 4, generating a reduction concept structure element of each pixel:
selecting all elements with the element value of 1 in the reduction object relation matrix of each pixel window to form a reduction concept structural element of the pixel window;
and 5, generating a matrix sequence of each element in each reduction concept structure element according to the following formula:
where ρ is pq Representing the matrix order of the q pixel in the structural element of the p reduction concept, the value of p is equal to that of i, and U m Representing the pixel value of the mth element in the pixel window after the expansion of the qth pixel in the pth reduction concept structure element set, wherein sigma represents the summation operation;
and 6, determining the maximum pixel value in each reduction concept structure element:
taking the pixel value corresponding to the maximum matrix order in each reduction concept structure element as the maximum pixel value in the reduction concept structure element;
step 7, calculating difference value pixels:
subtracting the pixel value of a central pixel point in each reduction concept structure element from the maximum pixel value of each reduction concept structure element to obtain a difference pixel corresponding to the reduction concept structure element;
step 8, extracting edges in the color image:
step 8.1, constructing a result graph with the same length and width as those of the color image of the edge to be extracted;
and 8.2, assigning all the difference pixels to corresponding positions in the constructed result image and the edge color image to be extracted to obtain an edge image.
Compared with the prior art, the invention has the following advantages:
the invention has the advantages that 1, the local relevance is enhanced when the background matrix is selected by introducing FCA reduction concept structure elements, and then the reduction object relation matrix is generated after a series of matrix operations, so that the defect that the definition of a color image processing result is reduced under the condition of more singular points due to the fact that all pixel points are selected in a general mode in the prior art is overcome, the reduction concept structure elements of the selected pixels can be extracted in a self-adaptive mode by utilizing the generated reduction object relation matrix, and the definition of the color image after morphological processing is improved.
2, because the local correlation is enhanced by using the expansion operation, the local correlation is weakened by the corrosion operation, and the defect of fuzzy color image edge extracted by the morphological open-close operation is overcome
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a color image to be processed according to the present invention;
FIG. 3 is a diagram showing the result of the digital morphological open/close operation of the present invention, wherein FIG. 3 (a) is a diagram showing the result of the close operation and FIG. 3 (b) is a diagram showing the result of the open operation;
FIG. 4 is an edge extraction image corresponding to the three phases of the figure, wherein FIG. 4 (a) is an edge image extracted by a close operation, and FIG. 4 (b) is an edge image extracted by an open operation.
Detailed Description
The invention is further described below with reference to the figures and examples.
The steps of the present invention will be further described with reference to fig. 1.
An embodiment of the present invention selects a color image having a size of 5 x 5 as shown in fig. 2.
Step 1, an unselected pixel is selected from the color image, and the selected pixel is taken as the center.
The following describes in detail a complete processing procedure of a pixel point selected from the color image according to the embodiment of the present invention with reference to fig. 2.
In the embodiment of the present invention, the color pixels at the position of the color image (3, 3) are selected, and the pixel values of the three channels of the color pixels red, green and blue are 237,174 and 203 respectively.
Step 1, a pixel window with the size of n × n is selected from the color image with the selected pixel as the center.
The embodiment of the invention takes n =3, and takes the selected pixel {237,174,203} as the center, 8 pixels around the pixel are selected from the color image, the 8 pixels are (2,3), (4,3), (3,2), (3,4), (2,2), (4,2),
(2,4), (4,4), the pixel values of the pixels above the selected pixel in the three channels of red, green and blue are 242, 199, 227, respectively, the pixel values of the pixels below the selected pixel in the three channels of red, green and blue are 255, 169, 185, respectively, the pixel values of the pixels to the left of the selected pixel in the three channels of red, green and blue are 96, 218, 103, respectively, the pixel values of the pixels to the right of the selected pixel in the three channels of red, green and blue are 254, 188, 232, respectively, the pixel values of the pixels to the left of the selected pixel in the three channels of red, green and blue are 69, 229, 51, the pixel values of the pixels to the left of the selected pixel in the three channels of red, green and blue are 247, 201, 232, respectively, the pixel values of the pixels to the right of the pixels to the upper of the selected pixel in the three channels of red, green and blue are 241, 39, 211, respectively, and the pixel values of the pixels to the right of the selected pixel in the three channels of red, green and blue are 231, 54, respectively. These 8 pixels together with the selected pixel constitute a pixel window of size 3 x 3.
And step 2, numbering the pixels in the pixel window: the pixel at the upper left corner of the pixel window is numbered 1, and the numbers of other pixels are gradually increased towards the right and downwards in sequence, so thatThe number of the selected pixel in the pixel window is
The pixel at the bottom right corner of the window is numbered n 2 。
In the embodiment of the present invention, the number of the selected pixel is 5, and the numbers of the upper left, upper right, upper left, right, lower left, lower right, and lower right around the selected pixel are 1, 2,3, 4, 6, 7, 8, and 9, respectively.
And 2, generating a reduced background matrix of all pixels in the pixel window.
Step 1, calculating the Euclidean color distance of each pixel in the pixel window.
When calculating the Euclidean color distance of the pixel, the pixel values of the red, green and blue channels can be taken as r 0 ,g 0 ,b 0 As a reference.
In the embodiment of the invention, a black pixel with pixel values of 0 in red, green and blue channels is taken as a reference, and r is made 0 ＝0,g 0 ＝0,b 0 And =0. Calculating the Euclidean color distance of each pixel in the pixel window of the selected pixels by using the following Euclidean color distance formula:
wherein d is j Representing the Euclidean color distance, r, of the jth pixel in the pixel window j ,g j ,b j Respectively representing the pixel values of the red, green and blue channels of the jth pixel,
indicating a rounding down operation.
In an embodiment of the present invention, the euclidean color distances of pixels No. 1-9 in the pixel window of the selected pixels are respectively: 244. 386, 322, 259, 357, 392, 393, 357, 253.
And 2, constructing a background matrix for describing the relation between each pixel in the pixel window and the selected pixel.
Constructing a background matrix K with N rows and 4 columns, wherein the ith row of the background matrix represents the jth pixel in a pixel window, i = j, and the 1 st column to the 4 th column of the background matrix respectively describe four relation quantities of the pixel represented by the ith row and the distance of the selected pixel in a red channel, a green channel, a blue channel and a Euclidean color, wherein i is more than or equal to 1 and less than or equal to N, N represents the total number of the pixels in the pixel window, and N = N 2 。
Since the selected pixel is located in the center of the pixel window, the number of the row of the selected pixel in the pixel matrix corresponds to the same number as the selected pixel in the pixel window,
if the absolute value of the interpolation between the 1 st column of the representative pixel and the 1 st column of the selected pixel in the ith row of the reduced background matrix is less than the set threshold value 100, the element value with (i, 1) in the background matrix is set to 1, K i1 =1, otherwise, set to 0,k i1 ＝0。
If the 2 nd column of the representative pixel of the ith row of the reduced form background matrix is greater than or equal to the absolute value of the interpolation of the 2 nd column of the selected pixel, which is less than the set threshold value 100, the matrix element value with (i, 2) in the background matrix is set to 1, K i2 =1, otherwise set to 0,k i2 ＝0。
If the 3 rd column of the representative pixel of the ith row of the reduced form background matrix is larger than or equal to the 3 rd column of the selected pixel, the absolute value of the interpolation is less than the set threshold value 100, the matrix element value with (i, 3) in the background matrix is set to 1,K i3 =1, otherwise set to 0,k i3 ＝0。
If the 4 th column of the representative pixel of the ith row of the background matrix is larger than or equal to the 4 th column of the selected pixel, the absolute value of the interpolation is smaller than the set threshold value 100, the matrix element value with (i, 4) in the background matrix is set to be 1,K i4 =1, otherwise set to 0,k i4 ＝0。
In an embodiment of the invention, the background matrix of each pixel and the selected pixel in the pixel window is:
and 3, generating a reduction object relation matrix for describing the relation between any two pixels in the pixel window.
Step 1: transposing the reduced background matrix of the selected pixels to obtain a temporary matrix M 1 。
In an embodiment of the invention, the temporary matrix M 1 Comprises the following steps:
step 2: the temporary matrix M obtained in the step 1 in the step 1 Performing matrix complement operation to obtain a temporary matrix M 2 。
The complement operation of the matrix means that an all-1 matrix with the same size as the operated matrix is obtained first, and then the obtained all-1 matrix and the operated matrix are subjected to subtraction operation.
In an embodiment of the invention, the temporary matrix M 2 Is obtained by the following formula:
and 3, step 3: the reduced background matrix describing all the pixels in the pixel window and the temporary matrix M obtained in the step 2 2 Performing matrix multiplication operation to obtain a temporary matrix M 3 。
In an embodiment of the invention, the temporary matrix M 3 Is obtained by the following formula:
and 4, step 4: the temporary matrix M obtained in the step 3 in the step 3 Operation matrix supplementary operationThen, an object relation matrix W of the background matrix is obtained.
In an embodiment of the present invention, the object relationship matrix W of the background matrix is obtained by:
and 4, determining the reduction concept structural element of the selected pixel.
And judging pixels corresponding to all columns of which the element values of the rows corresponding to the selected pixels are 1 in the reduction object relation matrix as one element in a concept structure element set.
In the embodiment of the present invention, according to the description of step 2 in step 2, the 5 th row in the background matrix represents the selected pixel, so in the object relationship matrix, the 5 th row of the object relationship matrix is taken as follows:
[0 1 1 0 1 1 0 0 0]
in row 5, the columns with element value 1 are 2,3, 5, 6, respectively, and the set of pixels corresponding to columns 2,3, 5, 6 is a reduced concept structure element.
The reduced concept structural element has 4 pixels, the pixel value of the corresponding pixel in the 2 nd column is 242, 199 and 227 of the red channel, the green channel and the blue channel, and the coordinate in the color image is (2, 3); the pixel values of the three channels of red, green and blue of the pixel corresponding to the 3 rd column are 241, 39 and 211 respectively, and the coordinate in the color image is (2, 4); the pixel values of the corresponding pixels of the 5 th column of the three channels of red, green and blue are 237,174 and 203 respectively, and the coordinates in the color image are (3, 3); the pixel values of the red, green and blue channels of the pixel corresponding to column 6 are 254, 188 and 232, respectively, and the coordinates in the color image are (3, 4).
And 5, generating a matrix order of each element in each reduction concept structure element according to the following formula.
Where ρ is pq Representing the matrix sequence of the q pixel in the structure element of the p-th reduction concept, the value of p is equal to that of i, and U m Representing the pixel value of the mth element in the expanded pixel window of the qth pixel in the set of pth reduced concept structure elements, Σ representing the summation operation.
In the embodiment of the present invention, the reduction concept structural element has 4 pixels, and the positions of the 4 pixels in the color image are: (2, 3), (3, 4), (4, 2), the matrix order of the 4 pixels is: 924, 1003, 959, 815.
And 6, determining the maximum pixel value in each reduction concept structural element.
And determining the pixel corresponding to the maximum value in the matrix order as the maximum pixel in the reduction concept structural element.
In an embodiment of the invention, the maximum value of the matrix order is ρ 33 =1003, and thus, a pixel positioned at (3,3) in a color image is a maximum pixel in the reduction concept structural element, and pixel values of three channels of the maximum pixel red, green, and blue are 237,174, and 203, respectively.
And 7, calculating the difference value pixel.
And subtracting the pixel value of the central pixel point in each reduction concept structure element from the maximum pixel value of each reduction concept structure element to obtain a difference pixel corresponding to the reduction concept structure element.
And 8, extracting edges in the color image.
Step 8.1, constructing 2 result graphs with the same length and width as those of the color image of the edge to be extracted by utilizing digital morphology open operation and closed operation, as shown in fig. 3, wherein fig. 3 (a) is a closed operation processing result graph, and fig. 3 (b) is an open operation processing result graph.
And 8.2, respectively assigning all the difference pixels to positions corresponding to the color image to be processed in the result graph constructed by the closing operation and the opening operation to obtain edge extraction images of the opening operation and the closing operation, as shown in fig. 4, wherein fig. 4 (a) is the edge extraction image of the closing operation, and fig. 4 (b) is the edge extraction image of the opening operation.
The effect of the present invention is further explained by combining the simulation experiment as follows:
simulation experiment conditions are as follows:
the hardware platform of the simulation experiment of the invention is as follows: the processor is an Intel Core i5-8300H CPU, the main frequency is 2.3GHz, and the memory is 8GB.
The software platform of the simulation experiment of the invention is as follows: windows 10 operating system and Mtalab R2018b.
Simulation parameters of the invention: take a window of 3 x 3 pixels.
Simulation content and result analysis thereof:
the simulation experiment of the present invention is to perform an edge extraction operation on the input color image shown in fig. 2 by using the method of the present invention, and obtain a result graph after the digital morphology opening and closing operation processing shown in fig. 3 and an edge extraction image shown in fig. 4.
The simulation experiment of the present invention uses the input color image shown in fig. 2 as a color image of size 666 × 479 in the color image format jpg.
After the digital morphological open operation and close operation are performed on the input color image by using the method of the present invention, a corresponding result graph is obtained, as shown in fig. 3, fig. 3 (a) is a result graph after the close operation processing of the present invention, and fig. 3 (b) is a result graph after the open operation processing of the present invention.
The color image after edge extraction obtained by edge extraction of the input color image by the method of the present invention is a color image having a size of 666 × 479 and a color image format of jpg, as shown in fig. 4. Fig. 4 (a) shows an edge extraction image in the closed operation, and fig. 4 (b) shows an edge extraction image in the open operation.
The simulation result of the invention shows that: as can be seen from fig. 3 and 4, the result of processing the color image in the invention is clear, and the edge extracted by the opening and closing operation is complete.
Claims (3)
1. A color image edge extraction method based on reduction concept structure elements and matrix sequences is characterized in that a reduction background matrix of each pixel window is generated, and the matrix sequence of each element in each reduction concept structure element is generated; the method comprises the following steps:
step 1, constructing a pixel window of each pixel point in a color image of an edge to be extracted:
step 2, generating a reduced background matrix of each pixel window:
constructing a background matrix with N rows and 4 columns of each pixel window, wherein each row of the reduced background matrix represents a corresponding pixel in the pixel window, the 1 st column to the 4 th column of the background matrix respectively describe four relation quantities of the distance between the pixel represented by each row and the selected pixel in a red channel, a green channel, a blue channel and a Euclidean color, the pixel value of each point in the matrix is different from the pixel value corresponding to the selected pixel point, if the difference value is smaller than a threshold value C, the point is marked as 1, otherwise, the point is marked as 0, wherein N represents the total number of the pixels in the pixel window, and C is a value selected in [80,120 ];
step 3, generating a reduction object relation matrix of each pixel window;
step 4, selecting all elements with element values of 1 in the reduction object relation matrix of each pixel window to form a reduction concept structure element of the pixel window;
step 5, calculating the matrix order of each element in each reduction concept structure element according to the following formula:
where ρ is pq Representing the matrix order of the q pixel in the structural element of the p reduction concept, the value of p is equal to that of i, and U m Representing the pixel value of the mth element in the pixel window after the expansion of the qth pixel in the pth reduction concept structure element set, wherein sigma represents the summation operation;
step 6, determining the maximum pixel value in each reduction concept structure element:
taking the pixel value corresponding to the maximum matrix order in each reduction concept structure element as the maximum pixel value in the reduction concept structure element;
step 7, calculating difference value pixels:
subtracting the pixel value of a central pixel point in each reduction concept structure element from the maximum pixel value of each reduction concept structure element to obtain a difference pixel corresponding to the reduction concept structure element;
step 8, extracting edges in the color image:
step 8.1, constructing two result graphs with the same length and width as those of the edge color image to be extracted by utilizing digital morphology open operation and closed operation;
and 8.2, respectively assigning all the difference pixels to positions corresponding to the color image to be processed in a result graph constructed by the closing operation and the opening operation to obtain an edge extraction image after the opening operation and the closing operation.
2. The method for extracting an edge of a color image based on reduction concept structural elements and matrix sequences according to claim 1, wherein the step of constructing the pixel window of each pixel point in the color image of the edge to be extracted in step 1 is as follows:
firstly, selecting an unselected pixel point from a color image of an edge to be extracted;
secondly, expanding n pixels along eight directions of upper, lower, left, right, upper left, lower left, upper right and lower right by taking the selected pixel as a center to obtain a pixel window taking the selected pixel as the center, wherein n is an odd number which is more than or equal to 3;
and thirdly, judging whether all pixel points in the color image are selected, if so, obtaining a pixel window of each pixel point in the color image, and otherwise, executing the first step.
3. The method for color image edge extraction based on reduction concept structure elements and matrix order according to claim 1, wherein the generation of the reduction object relation matrix for each pixel window in step 3 is obtained by the following formula:
wherein, W i A reduced object relation matrix, K, representing the ith pixel window i Representing the background matrix corresponding to the ith pixel window, T representing the transpose operation,
denotes the complement operation on the matrix, and denotes the matrix multiplication operation. />
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