An adaptive image compression transmission method based on Beidou short message communication

Abstract

The application relates to the field of communication technology, and particularly discloses a self-adaptive image compression transmission method based on Beidou short message communication. The method first judges network conditions and image characteristics, and if the conditions are met, the original image is directly transmitted; otherwise, the compression process is entered. The compression process adaptively divides the image into different compression channels by analyzing the statistical distribution characteristics of the image color (calculating the color frequency variance), for the image with uneven color distribution, an adaptive weighted clustering algorithm based on color frequency ranking is used for color quantization and entropy coding; for the image with uniform color distribution and color gradient, an improved singular value decomposition (SVD) compression method optimized for extremely low bandwidth is used. The application solves the key technical problem of efficiently transmitting images through the Beidou short message channel with extremely limited bandwidth in emergency scenes such as power and disaster monitoring, and greatly improves the transmission efficiency under the premise of ensuring that the key information of the image can be identified.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of communication technology and image processing technology, and in particular relates to a method for transmitting image data in a bandwidth-limited satellite communication channel. Specifically, it is an adaptive image compression transmission method based on BeiDou short message communication, which is applicable to the short message communication service of the BeiDou satellite navigation system and can be widely used in fields such as power line inspection, fishing vessel location monitoring, civil defense emergency communication, road construction personnel and vehicle safety supervision, and natural disaster on-site monitoring. Background Technology

[0002] The short message communication function of the BeiDou Navigation Satellite System is an important communication method that my country can independently control. It plays an irreplaceable role in remote areas without terrestrial network coverage or in emergency scenarios where communication is interrupted after disasters. However, the single communication capacity of BeiDou short messages is limited (only 1835 bits, or about 229 bytes, for a secondary card), which severely restricts the real-time transmission of large amounts of information such as images and videos.

[0003] In existing technologies, there are standards such as JPEG and JPEG2000 for image compression. However, when these general standards reach extremely high compression ratios (e.g., >50:1), image quality deteriorates significantly, potentially resulting in noticeable blockiness or blurring, leading to the loss of critical information and making it difficult to meet the accuracy requirements of emergency monitoring. On the other hand, some compression algorithms designed for specific content (such as encoding based on key regions) lack universality.

[0004] Therefore, there is an urgent need in this field for a method that can intelligently perceive the features of image content and adaptively adopt the optimal compression strategy in order to maximize the preservation and transmission of useful information in images under the extremely stringent bandwidth constraints of BeiDou short messages. Summary of the Invention

[0005] To address the shortcomings of the existing technologies, this invention proposes an adaptive image compression and transmission method based on BeiDou short message communication. This method solves the problem of how to adaptively select a compression strategy under the limited bandwidth of BeiDou short message communication, so as to achieve an extremely high compression ratio while ensuring that the key visual information of the reconstructed image can be used for professional analysis such as power fault identification and disaster assessment.

[0006] The technical solution adopted in this invention is as follows: An adaptive image compression and transmission method based on BeiDou short message communication includes the following steps: S1. If the detected 4G / 5G signal strength is greater than the set threshold, or the image data volume is less than the set threshold, or the user specifies that lossless transmission is required, then the original image data is directly transmitted after adding the preamble "00"; otherwise, proceed to S2. S2. Perform color histogram statistics on the original image to be transmitted to obtain the RGB vector of each color and its frequency of occurrence, and sort them from high to low frequency. S3. Calculate the variance Var(F) of all color frequencies and compare it with the preset variance threshold Th_var; if Var(F) > Th_var, proceed to S4; if Var(F) ≤ Th_var, proceed to S5. S4. Starting with the color that appears most frequently in the image, dynamically calculate the clustering distance threshold based on its frequency value; perform iterative clustering on each color according to the clustering distance threshold until all colors are classified, and obtain the total number of categories K; if K is less than the preset threshold Th_k, generate an index image and perform entropy encoding, and output a data stream with a preamble "01"; if K is greater than or equal to Th_k, perform histogram equalization on the image and relax the distance threshold to re-cluster and encode, and finally output a data stream with a preamble "10". S5. Convert the original image to the YCbCr color space, perform singular value decomposition on the three components Y, Cb and Cr obtained after conversion, and select the number of singular values ​​k_y, k_cb and k_cr to retain for each component according to the set total data volume of the Beidou short message target; then quantize and entropy encode the matrix composed of the singular values ​​of each component, and add a preamble "11" before transmitting the encoded data stream.

[0007] Furthermore, the S4 process specifically includes: S41. Select the most frequent color from the unclassified colors. Dynamically calculate the clustering distance threshold T_i of the currently selected color based on its frequency value and the maximum and minimum distance thresholds. Calculate the distance D between other unclassified colors and the currently selected color in the RGB space. Group unclassified colors with a distance less than or equal to T_i into the same class. Where D = max(∣ΔR∣,∣ΔG∣,∣ΔB∣), ΔR, ΔG, and ΔB are the differences between the R, G, and B components of two vectors, respectively. S42. Return to S41 until all colors have been classified, obtain the total number of categories K, and assign an index number to each category; S43. If K < the preset threshold number of categories Th_k, then each pixel of the original image is replaced with the index number of its category to obtain an index image and entropy encoding is performed. Finally, a preamble "01" is added before the encoded data stream and then transmitted. If K ≥ the preset threshold number of categories Th_k, then histogram equalization is performed on the current image, and the distance threshold parameter in the adaptive weighted clustering algorithm is increased. Then, color histogram statistics are performed on the current image to obtain the RGB vectors of each color and their frequency of occurrence. The colors are sorted from high to low frequency, and the process returns to S41. After repeating the process a set number of times, each pixel of the original image is replaced with the index number of its category to obtain an index image and entropy encoding is performed. Finally, a preamble "10" is added before the encoded data stream and then transmitted.

[0008] Furthermore, the clustering distance threshold T_i in S41 is calculated as follows: T_i = T_max - [(f_i - f_min) / (f_max - f_min)] * (T_max - T_min) Where f_i is the frequency of the currently selected color, f_max and f_min are the maximum and minimum frequencies of all colors, respectively, and T_max and T_min are the preset maximum and minimum distance thresholds.

[0009] Furthermore, the number of singular values ​​k_y, k_cb, and k_cr retained for each component in S5 are calculated as follows: For the Y channel: k_y = floor( (TargetSize * W_y) / ((1 + m + n) * b) ) For channel Cb: k_cb = floor( (TargetSize * W_cb) / ((1 + m + n) * b) ) For the Cr channel: k_cr = floor( (TargetSize * W_cr) / ((1 + m + n) * b) ) Where m and n are the dimensions of the original image, b is the number of bytes occupied by each value in the final matrix, TargetSize is the target data volume, W_y, W_cb and W_cr are the data volume weights assigned to the corresponding components, W_y + W_cb + W_cr = 1 and Wy>Wcb= Wcr.

[0010] Compared with the prior art, the technical solution provided by the present invention has the following significant advantages: 1. High adaptability and scene versatility: By analyzing the image's own features for intelligent sorting, it can efficiently process both simple color chart images and rich color natural images, overcoming the limitations of single compression algorithms.

[0011] 2. Optimal compression efficiency: The most suitable compression tool is used for images with different characteristics, so that under the same bandwidth constraints, images with higher visual quality and more complete key information can be transmitted than those of general standard compression algorithms.

[0012] 3. Clear technical implementation and easy integration: The entire algorithm process is clear, highly modular, and easy to integrate into embedded devices or mobile terminals. It can be seamlessly connected with Beidou communication modules and has high practical value and industrialization prospects. Attached Figure Description

[0013] To more clearly describe this patent, one or more drawings are provided below, which are intended to assist in illustrating the background technology, technical principles and / or certain specific embodiments of this patent.

[0014] Figure 1 The overall flowchart of the adaptive image compression and transmission method provided in the embodiments of the present invention is shown.

[0015] Figure 2 A detailed flowchart of the adaptive weighted color clustering algorithm (S4).

[0016] Figure 3 A detailed flowchart of the improved SVD compression algorithm (S5). Detailed Implementation

[0017] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention, and should not be used to limit the scope of protection of the present invention.

[0018] This invention provides an adaptive image compression and transmission method based on BeiDou short message communication, the core of which lies in a multimodal decision-making and execution framework. The method first performs a preconditional judgment on the input image to determine whether compression is necessary. If compression is required, it then deeply analyzes the image's color statistical characteristics and, based on the uniformity of color distribution (measured by variance), splits the image into two distinct technical paths for processing: like Figure 1 As shown, the specific steps include: S1, Mode Decision Step: If the detected 4G / 5G signal strength is greater than the set threshold, or the image data volume is less than the set threshold, or the user specifies that lossless transmission is required, then the original image data is directly transmitted after adding the preamble "00"; otherwise, proceed to S2.

[0019] S2. Feature extraction step: Perform color histogram statistics on the original image to be transmitted to obtain the RGB vector of each color and its frequency of occurrence, and sort them from high to low frequency.

[0020] S3, Path splitting step: Calculate the dispersion of color distribution to determine the compressed path; Input: A list of color frequencies F = {f_1, f_2, ..., f_N} obtained from S2, where N is the total number of all colors in the image, and f_1≥ f_2≥...≥f_N; Calculate the mean value μ_F of the color frequency: μ_F = (1 / N) * (f_1+ f_2+ ...+f_N) Calculate the variance Var(F) of the color frequencies: Var(F) = (1 / N) * ((f_1 - μ_F)²+(f_2 - μ_F)²+...+(f_N - μ_F)²) Var(F) quantifies the degree of deviation of all color frequency values ​​from the average value. The larger the Var(F) value, the more uneven the color distribution, with a few colors dominating.

[0021] decision making: If Var(F) > Th_var, then proceed to the compression path S4 based on color clustering; Th_var is a preset variance threshold, which is a preset empirical threshold whose value can be determined through a large number of experiments; for example, it can be calculated on a large number of power equipment images and natural landscape images, and a variance value that can best distinguish between the two types of images can be selected as the threshold. If Var(F) ≤ Th_var, then proceed to the compression path S5 based on transform domain decomposition.

[0022] S4. Compression step based on color clustering, which aims to significantly reduce the number of colors through intelligent color merging; specifically including: S41, Adaptive Weighted Clustering Algorithm: like Figure 2 The process shown includes the following steps: enter: Color list C = {c_1, c_2, ..., c_N} (sorted in descending order of frequency); Frequency list F = {f_1, f_2, ..., f_N} } ; Preset minimum and maximum RGB spatial distance thresholds T_min and T_max (e.g., T_min = 5, T_max = 30).

[0023] initialization: Initialize an empty cluster collection Clusters = {}; Initialize a boolean array `classified[1..N] = {false}` to indicate whether the colors have been classified, where `false` indicates that they are not classified and `true` indicates that they have been classified. Set the current category label to 0.

[0024] Iterative clustering process: For i = 1 to N, if classified[i] is true, skip that color; otherwise, let label = label + 1. Create a new cluster `cluster_label`, add `c_i` (the most frequent color among the unclassified colors) to it, and set `classified[i] = true`; 1 ≤ i ≤ N; l calculates the adaptive distance threshold T_i for the current color c_i: T_i = T_max - [ (f_i - f_min) / (f_max - f_min) ] * (T_max - T_min) Where f_max = f_1 (highest frequency); f_min = f_N (lowest frequency); ((f_i - f_min) / (f_max - f_min) normalizes the current frequency to the interval [0, 1], and is called the weighting factor. The higher the frequency, the larger this value is. Finding neighboring colors: For all colors c_j where j>i and classified[j] is false, calculate the distance D(c_i, c_j) between colors c_i and c_j in the RGB space: D(c_i, c_j) = max( |r_i - r_j|, |g_i - g_j|, |b_i - b_j| ) If D(c_i, c_j) ≤ T_i, then add c_j to cluster_label and set classified[j] = true; add cluster_label to Clusters; Iterate through the uncategorized colors, selecting the most frequent color in turn, until all colors are categorized.

[0025] Output: The cluster set Clusters has a size K = label, which is the final number of color categories. Each cluster can use the mean of the colors within it as the representative color rep_label for that category, forming a color palette.

[0026] S42, First encoding sub-step and Second encoding sub-step: If K < the preset threshold number of categories Th_k (Th_k is the preset threshold number of categories, for example, 32), then iterate through each pixel p(x, y) of the original image I, replace its RGB value with the label L (1 to K) of the category closest to it in the Clusters, and generate the index image I_index; compress the data matrix of the index image I_index using an entropy coding algorithm (such as Huffman coding or arithmetic coding) to generate the binary stream B_index; the output data stream is: preamble "01" + palette data {rep1, rep2, ..., rep_K} + B_index; If K ≥ the preset threshold number of categories Th_k, then the current image (initially the original image I) is subjected to histogram equalization to obtain I'. After increasing the distance threshold parameter in the adaptive weighted clustering algorithm (for example, set to T_min = 15, T_max = 50), the current image I' is re-performed with color histogram statistics to obtain the RGB vector color list C' = {c_1', c_2', ..., c_N'} and the frequency list F' = {f_1', f_2', ..., f_N'} of each color. }Sort the data by frequency from high to low, return to S41, repeat the process a set number of times. If K is still greater than or equal to Th_k, then iterate through each pixel p(x, y) of the current image I', replace its RGB value with the label L (1 to K) of the category closest to it in Clusters, and generate an index image I_index. Compress the data matrix of the index image I_index using an entropy coding algorithm (such as Huffman coding or arithmetic coding) to generate a binary stream B_index'. Finally, add a preamble "10" before the encoded data stream and transmit it. The output data stream is: preamble "10" + new palette data + new binary stream B_index'.

[0027] S5. Compression step based on transform domain decomposition: This step is for images with rich colors and complex textures, and compresses them from the perspective of global energy distribution; for example... Figure 3 As shown, it specifically includes: S51. Color space conversion: Convert the original image I from RGB space to YCbCr space to obtain the luminance component matrix Y and two chrominance component matrices Cb and Cr; the human eye is more sensitive to the Y component and less sensitive to the Cb and Cr components.

[0028] S52. Singular Value Decomposition (SVD) of Each Channel: Perform SVD decomposition on each of the three component matrices separately. Y = U_y * Σ_y * V_y^T Cb = U_cb * Σ_cb * V_cb^T Cr = U_cr * Σ_cr * V_cr^T; U and V are unitary matrices, and Σ is a diagonal matrix whose diagonal elements σ1, σ2, ... are singular values, arranged in descending order.

[0029] S53, Adaptive Singular Value Selection: Objective: Determine the number of singular values ​​k_y, k_cb, and k_cr that need to be retained for each component, so that the final encoded data volume is close to the target total transmission capacity TargetSize (in bytes) of the BeiDou short message.

[0030] Assuming the image size is m × n, each value after quantization occupies b bytes; Data volume estimation: To retain the first k singular values, we need to store k singular values ​​(the diagonal elements of the Σ matrix) and the first k columns of the U matrix and the first k columns of the V matrix; The amount of data that a single channel needs to store is approximately: Data(k) = k * (1 + m + n) * b; where k∈(k_y, k_cb, k_cr); Allocation strategy: Distribute the total data budget TargetSize to the three channels according to the weights, following the principle that W_y + W_cb + W_cr = 1 and W_y > W_cb = W_cr (e.g., W_y = 0.6, W_cb = 0.2, W_cr = 0.2).

[0031] Solve for the number of singular values ​​k_y, k_cb and k_cr for each channel, such that Data(k) ≈ TargetSize * Weight, Weight∈(W_y, W_cb, W_cr).

[0032] For the Y channel: k_y * (1 + m + n) * b ≈ TargetSize * W_y Solution: k_y = floor( (TargetSize * W_y) / ((1 + m + n) * b) ) Similarly, k_cb and k_cr can be obtained: For channel Cb: k_cb = floor( (TargetSize * W_cb) / ((1 + m + n) * b) ) For the Cr channel: k_cr = floor( (TargetSize * W_cr) / ((1 + m + n) * b) ) Stricter constraints are usually imposed on the chrominance components, such as setting k_cb = k_cr = min(k_cb, 10), to ensure that their data size is small enough.

[0033] S54. Quantization and Encoding: Truncating and quantization: For each channel, only the first k singular values ​​and the corresponding columns of the U and V matrices, U_k, Σ_k, and V_k, are retained. The floating-point numbers in these matrices are linearly quantized to the integer range (e.g., 0-255) and converted to uint8 type, greatly reducing the amount of data.

[0034] Entropy encoding: All the quantized data from the three channels (the values ​​of k_y, k_cb, k_cr, the quantization parameters, and the quantized data of U_k, Σ_k, V_k) are concatenated into a data stream, entropy encoded, and a binary stream B_svd is generated.

[0035] Output: The final output data stream is: preamble "11" + B_svd.

[0036] Example 1: Taking the transmission of images during the inspection of power poles as an example Suppose an inspection drone captures a 256×256 pixel image of an insulator on a power pole and needs to transmit it back to the command center, but there is no 4G signal at the site.

[0037] S1, Mode Decision: No 4G signal, image size approximately 196KB, far exceeding the carrying capacity of a single BeiDou short message (229B for a BeiDou Level 2 card), compression is necessary. Proceed to compression process.

[0038] S2. Feature Extraction: Analyze the color histogram of the image. Assume there are 5000 different RGB colors. The blue of the sky ((50, 100, 200)) and the gray of the tower ((120, 120, 120)) have the highest frequencies, f1 = 18000 times and f2 = 15000 times respectively. The remaining colors have lower frequencies. Sort the colors in descending order of frequency.

[0039] S3, Path Splitting: Calculate the variance Var(F) of color frequencies. Due to the presence of high-frequency colors such as f1 and f2 and a large number of low-frequency colors, the variance is very large (far exceeding the preset threshold Th_var). Therefore, the path is compressed based on color clustering.

[0040] S4. Compression based on color clustering: S41, Adaptive Weighted Clustering: Set T_min = 5, T_max = 30.

[0041] Starting with the highest frequency color c_1 ((50,100,200), f_1=18000), its normalized weight Weight1 = (18000 - f_min) / (18000 - f_min) ≈ 1.0. Therefore, its clustering distance threshold T_1 = 30 - 1.0*(30-5) = 5. This means that only colors with an RGB Euclidean distance of less than 5 from c_1 (very similar colors) are classified into class 1.

[0042] Next, process the next highest frequency color c_2 ((120,120,120), f_2=15000). Weight2 is very high, and T_2 is also very small, so perform fine clustering.

[0043] When processing a low-frequency color c_5000 ((133, 135, 137), f_5000=5), its Weight5000≈ 0 and T_5000 ≈ 30. This means that all unclassified colors whose distance to this color is within 30 can be classified into the same category, realizing rough merging.

[0044] After clustering, it is assumed that 5000 kinds of colors are merged into K=18 kinds of colors.

[0045] S42, the first sub-step of encoding: determine that K=18<Th_k (assuming Th_k=32). Therefore, the color of each pixel in the original image is replaced by its corresponding category index (0-17). The generated index matrix is then compressed using Huffman coding. Finally, a preamble "01" is added before the compressed data. Assuming that the final data size is 6KB, it can be transmitted through 27 Beidou short messages.

[0046] Decoding at the receiving end: after receiving the data, read the preamble "01", then it is known that decoding needs to be performed in the "color index-palette" mode. First, the palette of 18 colors is parsed, then the subsequent Huffman encoded data is decoded to obtain the index matrix, and finally the colors are filled according to the indexes to reconstruct the image. The reconstructed image retains the main colors of the tower and the insulator, and there may be a slight color block feeling in the sky area, but the key equipment information is clearly distinguishable.

[0047] Example 2: Aerial image of disaster site Assuming that another image is a post-disaster aerial image with rich colors and uniform color distribution (small Var(F)), then the process proceeds to S5, the compression path based on transform domain decomposition.

[0048] Convert the image from RGB to YCbCr space.

[0049] Perform SVD decomposition on the Y, Cb and Cr components respectively.

[0050] Set the target data volume TargetSize=11KB. Allocate weights: W_y=0.6, W_cb=0.2, W_cr=0.2.

[0051] Assuming that the image size is 256×256, and the unit size of the quantized data is 1 byte. Calculate the number of retained singular values k_y for the Y component: k_y×(256+256+1)×1≈11×1024×0.6 =>k_y = 13. Similarly, k_cb=k_cr=4 can be calculated.

[0052] Only these main singular values and their corresponding singular vectors are retained, quantized, then entropy encoded, and transmitted after adding the preamble "11".

[0053] The receiving end initiates the SVD reconstruction process based on the preamble "11", reconstructs the YCbCr image using the received singular values ​​and vectors, and then converts it back to RGB. The reconstructed image loses a lot of detail and becomes blurry, but the outlines of mountains, rivers, and roads are preserved, which is sufficient for the initial assessment of the disaster area.

Claims

1. An adaptive image compression and transmission method based on BeiDou short message communication, characterized in that, Includes the following steps: S1. If the detected 4G / 5G signal strength is greater than the set threshold, or the image data volume is less than the set threshold, or the user specifies that lossless transmission is required, then the original image data is transmitted directly after adding the preamble "00"; otherwise, proceed to S2. S2. Perform color histogram statistics on the original image to be transmitted to obtain the RGB vector of each color and its frequency of occurrence, and sort them from high to low frequency. S3. Calculate the variance Var(F) of all color frequencies and compare it with the preset variance threshold Th_var; if Var(F) > Th_var, proceed to S4; if Var(F) ≤ Th_var, proceed to S5. S4. Starting with the color that appears most frequently in the image, dynamically calculate the clustering distance threshold based on its frequency value; perform iterative clustering on each color according to the clustering distance threshold until all colors are classified, and obtain the total number of categories K; if K is less than the preset threshold Th_k, generate an index image and perform entropy encoding, and output a data stream with a preamble "01"; if K is greater than or equal to Th_k, perform histogram equalization on the image and relax the distance threshold to re-cluster and encode, and finally output a data stream with a preamble "10". S5. Convert the original image to the YCbCr color space, perform singular value decomposition on the three components Y, Cb and Cr obtained after conversion, and select the number of singular values ​​k_y, k_cb and k_cr to retain for each component according to the set total data volume of the Beidou short message target; then quantize and entropy encode the matrix composed of the singular values ​​of each component, and add a preamble "11" before transmission.

2. The adaptive image compression and transmission method based on BeiDou short message communication according to claim 1, characterized in that, The S4 process includes: S41. Select the most frequent color from the unclassified colors. Dynamically calculate the clustering distance threshold T_i of the currently selected color based on its frequency value and the maximum and minimum distance thresholds. Calculate the distance D between other unclassified colors and the currently selected color in the RGB space. Group unclassified colors with a distance less than or equal to T_i into the same class. Where D = max(∣ΔR∣,∣ΔG∣,∣ΔB∣), ΔR, ΔG, and ΔB are the differences between the R, G, and B components of two vectors, respectively. S42. Return to S41 until all colors have been classified, obtain the total number of categories K, and assign an index number to each category; S43. If K < the preset threshold number of categories Th_k, then each pixel in the original image is replaced with the index number of its category to obtain an index image and entropy encoding is performed. Finally, a preamble "01" is added before the encoded data stream and then transmitted. If K ≥ the preset threshold number of categories Th_k, then histogram equalization is performed on the current image, and the distance threshold parameter in the adaptive weighted clustering algorithm is increased. Then, color histogram statistics are performed on the current image to obtain the RGB vectors of each color and their frequency of occurrence. The colors are sorted from high to low frequency, and the process returns to S41. After repeating the process a set number of times, each pixel in the original image is replaced with the index number of its category to obtain an index image and entropy encoding is performed. Finally, a preamble "10" is added before the encoded data stream and then transmitted.

3. The adaptive image compression and transmission method based on BeiDou short message communication according to claim 2, characterized in that, The clustering distance threshold T_i in S41 is calculated as follows: T_i = T_max - [(f_i - f_min) / (f_max - f_min)] * (T_max - T_min) Where f_i is the frequency of the currently selected color, f_max and f_min are the maximum and minimum frequencies of all colors, respectively, and T_max and T_min are the preset maximum and minimum distance thresholds.

4. The adaptive image compression and transmission method based on BeiDou short message communication according to claim 1, characterized in that, The number of singular values ​​k_y, k_cb, and k_cr retained for each component in S5 are calculated as follows: For the Y channel: k_y = floor( (TargetSize * W_y) / ((1 + m + n) * b) ) For channel Cb: k_cb = floor( (TargetSize * W_cb) / ((1 + m + n) * b) ) For the Cr channel: k_cr = floor( (TargetSize * W_cr) / ((1 + m + n) * b) ) Where m and n are the dimensions of the original image, b is the number of bytes occupied by each value in the final matrix, TargetSize is the target data volume, W_y, W_cb and W_cr are the data volume weights assigned to the corresponding components, W_y + W_cb + W_cr = 1 and Wy > Wcb = Wcr.

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