The paper considers the operators for detecting characteristic features on complex color images. Such operators are used to highlight characteristic features in the image, from which a vector of quantitative values is formed for further recognition. The existing operators of Roberts, Sobel and Prewitt are considered, as well as on the basis of cellular automata using the averaging value in the neighborhood of cells. Edge selection operators based on cellular automata technologies are proposed. The color image is divided into binary layers, to each of which local transition functions are applied, allowing to select edge cells. Based on the results obtained, an updated image is formed, on which the main information elements are highlighted, which display the edges of the brightness and color differences. The application of edge selection operators based on the von Neumann and Moore neighborhoods was studied. Differences in the results of applying the operators used are presented. The results showed that the use of edge selection operators allows you to preserve color and highlight the most informative edges in the image. The use of thresholding allows you to select only information elements that form color and brightness differences between image elements. cell neighborhood Edge detection operator, cellular automata, local transition function, color image, binary layer,
Modern computer vision systems are characterized by the use of a wide range of image processing
and recognition methods. [
2022 Copyright for this paper by its authors.
In this paper, we solve the problem of using cellular technologies to detect edges in a color image, which reduces the time spent on the implementation of the operator, and also does not use complex mathematical calculations inherent in known edge detection operators. The problem is solved by splitting a raster image into binary slices, which form a set of binary images and to which the rules of two-dimensional cellular automata (CA) are applied to detect edge pixels.
Operators for detecting edges in an image are described in many literature sources [
Another approach to edge detection in an image is to use CA technologies, which give good results
for binary images. [
In practically almost all described operators, after their application, do not make it possible to determine the chromaticity of pixels inside the edges. In practically almost all of them use quantitative values obtained as a result of implementing a certain formula for each pixel, which requires many passes of all image pixels to implement the operator. The time it takes to implement the operators depends on the time it takes to analyze the states of the neighborhood cells and on the implementation of the computational algorithm for each pixel. The execution time of the computational algorithm also depends on the dimension of the mask, which is used to implement the corresponding edge detection operator. To solve this problem, this paper uses CA technologies that simplify calculations and implement the operation of detecting edges in one cycle of scanning the image field for computer systems. The most successful use of CA is provided by their hardware implementation. A single-bit memory element and a control combination circuit represent each cell. For hardware implementation, edge detection is carried out in one cycle, since each binary layer is implemented by hardware, and all cells perform calculations in parallel and transmit signals to the cells of each subsequent layer also in parallel. In such vision systems, scanning of the entire image field is not required, one binary layer performs operations in one cycle, which depends on the response time of the combinational circuit and the time it takes to switch one memory element (trigger).
To implement the edge detection operator based on CA technologies, the initial color image is represented in RGB coding, which is currently the most promising (among all existing ones) in their representation in computer vision systems. Each pixel is encoded with 24 bits, which are divided into three bytes. In this sequence, from left to right, bytes are arranged, which, respectively, encode blue, green and red colors. In this encoding, the properties of each pixel can be represented from zero (black) to 16777215 (white). Since each pixel in this encoding is represented by 24 bits, and all image pixels represent a matrix of binary codes of a certain size, the corresponding weight bits in the codes of each pixel can be separated into a separate bit weight matrix (binary layer). In this case, in RGB encoding, the image can be divided into 24 binary layers. Grayscale images are represented by 8 bit code for each pixel. Grayscale images can be split into 8 binary layers (8 binary images). In the early stages of development, images with a color encoding depth of 4 bits were used. Figure 1 shows an example of splitting a code fragment represented by four bits into four binary layers.
The image fragment by 3×3 pixel on Figure 1 is presented. Each pixel is encoded with a 4-bit code.
With 4-bit encoding, 24 colors of an image can be represented. The least significant bits of the code of
each pixel form the first layer (in Figure 1 this layer is represented by a matrix of 3 × 3 pixels on the
left in the bottom row), each pixel of which displays the value of the least significant bit from the pixel
codes of the original image. Similarly, from left to right, the remaining layers and the corresponding bit
values are represented for each pixel. Figure 1 shows four binary layers, which can be considered as
cellular automata with different neighborhood shapes. Each such binary layer and each cell (pixel) in it
can perform a local transition function, according to the given rules. For two-dimensional CA, a
different set of rules can be applied, the maximum number of which depends on the shape of the
neighborhood. For example, if the von Neumann neighborhood is used (the neighborhood is four cells),
then 65536 rules can be applied, and if we also take into account our own control cell (a total of five
cells), then 4294967296 rules can be applied. This is a large number, which shows the impossibility of
investigating all local transition functions at the present time. However, you can use some rules that
give the desired result for solving a particular problem. Thus, in [
However, these rules were considered as the evolution of two-dimensional CA, and the results of evolution were considered as a color image. Practically no studies were considered that were based on the application of such rules to the transformation of already formed color images. The transformation of each binary layer based on CA technologies gives different results, which allow for better image preprocessing compared to other methods.
To avoid various calculations to determine the quantitative value of each pixel, logical
transformations are used in the work, which are implemented using local transition functions in
twodimensional CA. Such local transition functions are used for binary images for different types of
neighborhoods [
With this encoding of the nearest cells, for the von Neumann neighborhood, the rule 715827882 is used, which is described by the following table 1. This rule allows you to select cells that form the contours of a binary image. If all cells (X2, X4, X6, X8) that form the von Neumann neighborhood of the analyzed cell (X0) have the state of logical "1", then the state of the analyzed cell (X0) goes into the state of logical "0". If at least one of the cells in the neighborhood has a state of logical "0", then the analyzed cell remains in the same state. Thus, in each binary layer (CA), single cells are selected that form the edges of the binary image.
To select a rule, it is important to place the value of the control cell in the code that is used. This
local transition function must use an additional control bit, since its value at the next time step may
depend on the state of the control cell (X0) at the previous time. A similar situation arises when using
the Moore neighborhood where the rules are represented by a large number of numbers (up to 15). It is
better to describe such rules by a system of logical functions, as presented in [
( ), 2( )⋀ 4( )⋀ 6( )⋀ 8( ) = 0 ( + 1) = { 0, 2( )⋀ 4( )⋀ 6( )⋀ 8( ) = 1 ( ), 1( )⋀ 2( ) ∧ … ⋀ 8( ) = 0 ( + 1) = { 0, 1( )⋀ 2( ) ∧ … ⋀ 8( ) = 1 (1) (2) where 1( ), 2( ), 3( ), …., 8( ) - signals at the outputs of neighboring cells in accordance with Figure 2 at time t; ( ) - state of the cell at time t.
Both rules change the state of the cell only in one case, when all the cells of its neighborhood and the control cell itself belong to the image (corresponding to the logical "1"), and not to the background. An example of the application of such rules in Fig. 3 is shown.
Figure 3 shows the differences in the results of applying different neighborhoods, which generally affects the further analysis of images. Applying the Moore neighborhood allows you to select more cells than after applying the von Neumann neighborhood. Highlighted edges in these cases may describe shapes that may differ in certain areas. The detected edges are thicker after applying the Moore neighborhood, and additional contours appear as not all neighboring (diagonal) cells have a logical "1" state. The more cells form the neighborhood, the more edge cells stand out in the binary image.
In this work, such rules are applied to all binary layers of a color image. In each binary layer, there are cells that already belong to the binary image (cell have the value of logical "1") and which change their state at the next time step of evolution (transition to the state of logical "1"). The cells that form the edges of the binary image in each binary layer remain in the logical "1" state. The binary image in each layer is not a binary version of the original image. The resulting binary layers at the next step of evolution form bits of codes for each pixel of a color image. In this case, the results of applying local transition functions are stored in the same layer and do not affect the next binary layer. In this case, the layer that performs the local transition function is transformed. Each binary layer is transformed according to its initial states. An example of applying the described rules for a color image in fig. 4 is shown. In this example (Fig. 4), the edge pixels are represented by a different color that distinguishes them from all other pixels in the image. If the edges in the original image are blurred, then the number of edge pixels stands out more. Moreover, the selected edges are thicker and can be represented by pixels of different colors. In fact, pixels of one color describe the edges of the image of a figure of one color that border the background pixels, and pixels of another color belong to the background pixels. In this case, you can reduce the thickness of the detected edges by selecting pixels of the same color from all selected pixels, and reset the rest to zero. On Figure 4 also a fragment of the matrix that encodes the properties of the pixels is shows. On this matrix, pixel codes are presented in decimal notation. Binary encoding allows you to split the image into binary layers.
Figure 5 shows the binary layers (5, 12, 21 and 24) after applying the local transition function. The fifth layer refers to the first byte, which encodes the red color and its shades, the twelfth layer refers to the second byte, which encodes the green color and its shades, and the 21st and 24th binary layers refer to the third byte, which encodes the blue color and its shades. Dark pixels encode the state of the logical "1". Different colors of selected pixels indicate the depth of color and brightness properties, as well as the predominance of bits and color bytes in the image. Binary slices (Figure 5) indicate the color byte that is involved in the formation of the local object. On Figure 4 the red rectangle is determined by the binary layers that form the byte of the red code of the pixel, since it is responsible for the formation of the red color. However, the first byte of the rectangle's pixels is merged with the bytes of the edge pixels, and so they go into a logical "0" state. The bits of the second byte of the boundary pixels remain in the single state, which form the green color. As a result, selected pixels display green color.
Layers also work on their own for images of objects of a different color and background color. All binary layers are arranged in parallel in a given order, and cells located at the same depth line form a binary code for each pixel. Accordingly, 24 binary layers are used, which form N×M 24 bit binary codes (where the dimensions of N×M correspond to the dimension of the image).
The priorities of using the edge detection method on the image depend on the task in the processing
of color images. If one of the tasks is to reduce the time spent on the implementation of the method, as
well as to simplify it, then the proposed operator is the most acceptable. At the same time, the
information content of the method is not inferior to already existing methods. On Figure 6 shows the
results of the selection of edge pixels for the proposed method, as well as for the Roberts, Sobel and
Prewitt operators.On Figure 6 are shows the results of applying the edge detection operator based on
CA technologies using the von Neumann and Moore neighborhoods. The visual difference of such
application of different neighborhoods is obvious. The difference with other operators is also obvious.
Different colors obtained from the application of the Roberts, Sobel and Prewitt operators are due to
different coefficient matrices that implement the corresponding operators. At the same time, threshold
processing was not applied after their application. Thresholding for the Roberts, Sobel, and Prewitt
operators in detail in [
On Figure 7 presents the results of thresholding for the edge detection operator based on the CA with the Moore neighborhood. Figure 7 shows the thresholding results for the example edge detection operator shown in Figure 5 using the Moore neighborhood. Cells were detected, the numerical values of the codes of which were greater than the threshold value. Such cells took the value 16777215 (white). Analysis of the results of thresholding allows you to determine the required threshold value, which gives the optimal number of selected pixels and does not reduce information content. Visual analysis showed that the most acceptable threshold value is 500000. In the resulting image, the smallest number of white pixels belonging to the edges are detected. For this option, the edge pixels clearly define the original image. For different edge selection operators, different quantitative threshold values are used. Such threshold values are determined by the formulas used and the matrices of the coefficients used. In this case, the most acceptable threshold values are determined experimentally.
In hardware implementation, the execution time of the edge selection operation depends on the trigger switching time in one cell. Since the cell is implemented on a simple combinational circuit that implements formulas (1) and (2), all cells of binary layers perform such an operation in parallel.
The paper considers and investigates edge detection operators in an image based on cellular automata technologies. A method for implementing such operators that do not require complex calculations and do not use the implementation of mathematical models using masks of coefficients of various dimensions is described. This approach greatly simplifies the implementation of the edge selection operator and reduces the time to one time cycle. It is shown that for different shapes of neighborhoods, the results have differences in the thickness of the selected edge pixels. Using twodimensional cellular automata technology preserves color. Although the colors are slightly changed in the converted image, the result allows you to determine the colors of the pixels in the original image. Studies have shown the possibility of applying thresholding, which allows you to save infor mation while maintaining a smaller number of selected pixels compared to the initial application of the operator. In further research, the author plans to use various forms of neighborhoods, as well as other rules for two-dimensional cellular automata. 7. References