Fast star map lossless compression algorithm

Abstract

The invention discloses a rapid star map lossless compression algorithm, and aims to solve the problems of large memory space and low compression efficiency of the existing lossless compression algorithm. According to the algorithm, the efficient compression of star map data is realized through the combination of a context modeling module, a predictive coding module and a run length coding module. The method specifically comprises the steps that a flat area and a non-flat area are divided according to local gradient values, run length coding is adopted in the flat area, and predictive coding is adopted in the non-flat area; the predictive coding is realized through gradient quantization merging, predictive error calculation and Rice coding; and run length coding is realized by counting the length of continuous same pixel points and performing table look-up coding. The algorithm optimizes the number of context types, reduces the storage demand, and improves the compression efficiency by dynamically correcting the predicted value. The method is suitable for application scenes with high requirements on data integrity, such as star sensors.

Description

Technical Field

[0001] The present invention relates to the technical field of image compression algorithms, and in particular to a fast lossless star image compression algorithm. Background Art

[0002] A star sensor is an attitude measurement device that uses stars as a reference frame. It can provide accurate spatial orientation and reference for satellites, missiles, and aircraft. The working principle of a star sensor's attitude determination is as follows: an image sensor captures an image of the starry sky within its current field of view. A signal processing circuit extracts star position and brightness information. A star map recognition algorithm matches the corresponding stars in the navigation star library. Finally, an attitude calculation algorithm calculates the star sensor's three-axis attitude based on the matching results.

[0003] Star maps are an important data source for star sensors, containing a large amount of stellar information. As satellite control systems place increasing demands on the accuracy of star sensors, the image arrays of star sensors are also growing larger, which puts tremendous pressure on the satellite-to-ground telemetry bandwidth. Therefore, it is necessary to effectively compress the images taken by star sensors to reduce data volume and transmission time while ensuring the integrity of stellar information.

[0004] Image compression is divided into lossy compression and lossless compression. A lossy compression algorithm is an algorithm that sacrifices some image quality when compressing an image to achieve a higher compression ratio; a lossless compression algorithm is an algorithm that can compress image data without losing any information. Since star map information is very important, a lossless compression algorithm must be used.

[0005] Common lossless compression algorithms include run-length encoding, entropy encoding, predictive encoding, and chain encoding. However, these algorithms still suffer from drawbacks such as large storage requirements and low compression efficiency. To address this, the present invention proposes a fast star map lossless compression algorithm. This algorithm comprises a context modeling module, a predictive encoding module, and a run-length encoding module, which respectively perform modeling, encoding, and compression of star map data. This reduces the storage requirements of the compression algorithm and the amount of encoded data, thereby improving compression performance. Summary of the Invention

[0006] The present invention aims to provide a fast star map lossless compression algorithm to solve the characteristics of existing lossless compression algorithms such as large storage space and low compression efficiency. The present invention proposes a fast star map lossless compression algorithm, which consists of a context modeling module, a predictive coding module and a run-length coding module, which respectively complete the functions of modeling, coding and compressing star map data, thereby reducing the storage space of the compression algorithm and the amount of encoded data, thereby improving the compression performance.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A fast lossless compression algorithm for star images, including:

[0009] Context modeling: Based on the local gradient value Q of the current pixel to be encoded i Divide the region type and select the corresponding encoding method, local gradient value Q i The calculation formula is as follows:

[0010]

[0011] When the pixel to be coded and its neighboring pixels form a flat area, the run-length coding mode is selected for compression; when the pixel to be coded and its neighboring pixels form a non-flat area, the predictive coding mode is selected for compression;

[0012] The steps of predictive coding mode are as follows:

[0013] A1. Gradient quantization and merging: Divide the local gradient value into symmetrical intervals with dense center and sparse edges. The division process is as follows, and there are 9 intervals in total:

[0014]

[0015] Q i After being concatenated into vectors (Q1, Q2, Q3) in sequence, their signs are changed. The specific steps are as follows: Check the first non-zero number that appears in Q1, Q2, and Q3 in sequence. If it is a positive number, the sign variable Sign is set to 1, and (Q1, Q2, Q3) remains unchanged; if it is a negative number, the sign variable Sign is set to -1, and (Q1, Q2, Q3) is inverted to become (-Q1, -Q2, -Q3);

[0016] Finally, the vector (Q1, Q2, Q3) is mapped to an integer Q in the interval [0, 364]. The mapping formula is as follows:

[0017] Q=81Q1+9Q2+Q3

[0018] A2. Prediction error calculation: The prediction period in the prediction coding selects the median edge detection prediction period with small calculation amount. The prediction value P X It is expressed by the following formula:

[0019]

[0020] The prediction error is the difference between the grayscale value and the predicted value:

[0021]

[0022] A3. Rice encoding of prediction errors: Before Rice encoding, the prediction errors are mapped so that they obey a geometric distribution, as follows:

[0023]

[0024] After the mapping is completed, Rice encoding is performed. First, the parameters k and q required for the encoding process are calculated. The calculation process is as follows:

[0025]

[0026] The parameter k is used to remove the length of each field in the Rice code, the parameter q represents the quotient in the Rice code calculation process, N[Q] and A[Q] are both context parameters, N[Q] represents the number of occurrences of the current context type, and A[Q] represents the sum of the absolute values ​​of the prediction errors;

[0027] A4. Context parameter update: The context parameters need to be updated after each encoding. The update process is as follows:

[0028]

[0029] Where errval is the prediction error, Q is the index value, which ranges from [0,364] to 365 context types, A[Q] is the sum of the absolute values ​​of the prediction errors, which is used to estimate the parameter k of the Rice code; B[Q] is the sum of the prediction errors, which is used to assist in calculating the average prediction error C[Q]; C[Q] is the average prediction error, which is used to correct the prediction value of the pixel; N[Q] is the number of occurrences of the current context type;

[0030] The run-length encoding mode is as follows: first, count the number of pixels with the same grayscale value that appear continuously, and perform different processing according to the reason for scanning termination; if the end pixel of the row is not scanned, the run-length encoding mode is exited after encoding the run-length; if it is due to scanning pixels with different grayscale values, the run-length encoding mode is exited after encoding the run-length, and return to the prediction encoding mode to perform prediction encoding on the difference pixels.

[0031] Furthermore, in the run-length encoding mode, in order to avoid memory overflow caused by excessive run length, a method of run-length encoding using a lookup table is designed: the encoder scans each element along the index in turn, and accumulates the run length represented by each element. The scanning stops when the accumulated value is greater than or equal to the actual run length.

[0032] Furthermore, in step A2 of the predictive coding mode, in order to prevent the subsequent prediction error from being too large, the prediction value is corrected after calculation. The correction process is as follows:

[0033]

[0034] Where sign is the sign variable for judging flipping, and C[Q] is the average prediction error.

[0035] The principles and beneficial effects of this technical solution: The method of the present invention utilizes a combination of predictive coding and run-length coding. The compression algorithm includes a context modeling module, a predictive coding module, and a run-length coding module. These modules implement star chart data modeling, encoding, and compression. This algorithm effectively eliminates redundant information, reduces star chart storage space, and thus improves compression efficiency. Compared to traditional single encoding methods, the present invention utilizes context modeling to determine the encoding mode and combines predictive coding with run-length coding algorithms. This effectively reduces the storage requirements of the compression algorithm, reduces the amount of encoded data, and improves compression performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 2 is a framework diagram of a lossless compression encoder according to the present invention;

[0037] Figure 2 A flow chart of the upper and lower modeling process of the present invention;

[0038] Figure 3 Calculate template for local gradient value;

[0039] Figure 4 Schematic diagram of image boundary extension;

[0040] Figure 5 is a flow chart of a predictive coding mode of the present invention;

[0041] Figure 6 Schematic diagram of interval division in the gradient quantization merging process of the present invention;

[0042] Figure 7 Flowchart of the run-length encoding mode of the present invention;

[0043] Figure 8 Schematic diagram of the lookup table in the run-length encoding mode of the present invention;

[0044] Figure 9 Four different types of star images are used to test the performance of the lossless compression algorithm: a) a star image with a single background, b) a star image with a complex background, c) a star image with interference in the background, and d) a star image with pure black. DETAILED DESCRIPTION

[0045] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments:

[0046] like Figure 1The figure shows the framework of the lossless compression encoder proposed in this invention, which is mainly divided into two parts: modeling and encoding. In the figure, the encoder reads the pixel data of the source image row by row from left to right in a raster scan order. After the pixel data enters the encoder, the gradient value is calculated based on its adjacent scanned pixels to complete the modeling process. After the modeling is completed, the encoder selects different encoding methods based on the size of the gradient value, including predictive coding and run-length coding. Predictive coding uses a predictor to predict the current pixel and then performs Rice coding on the prediction error after the prediction is completed. Run-length coding counts consecutive identical pixel values ​​and encodes the statistical results. After the encoding process is completed, the encoder outputs the obtained compressed code stream.

[0047] 1. Context Modeling Process

[0048] like Figure 2 The figure shows the context modeling flow chart of the method of the present invention. There are different areas in the actual image, such as flat areas with very close pixel values, texture areas with rich edge details, etc. In order to adapt to the compression requirements of different areas, it is necessary to divide the area type according to the local gradient value of the current pixel and select the corresponding encoding method. This process is called the context modeling process.

[0049] like Figure 3 The figure shows a template for calculating the local gradient value. The local gradient value is calculated based on the pixel values ​​of the current pixel to be encoded X and its four adjacent pixels A, B, C, and D. The calculation formula for the local gradient value is as follows:

[0050]

[0051] For edge pixels of an image, since the adjacent pixels around them are not all present, boundary extension is required to ensure the correctness and integrity of image operations: if the current pixel to be encoded X is located in the first row of the image, the pixel values ​​at positions A, B, and C are all 0, that is, I A =I B =I C =0; if the current pixel to be encoded X is located in the first column of the image, the pixel value at position D is equal to the pixel value at position B, that is, I D =I B ; If the current pixel to be encoded X is located in the last column of the image, the pixel value at position C is equal to the pixel value at position B, that is, I C =I B .like Figure 4 As shown, the solid line part is the image area, and the dotted line part is the extension area.

[0052] The local gradient value reflects the flatness around the current pixel to be encoded. When the three gradient values ​​D1, D2, and D3 are all 0, it means that the current pixel to be encoded and its neighboring pixels form a flat area, and the run-length coding mode is used for compression. When the three gradient values ​​D1, D2, and D3 are not 0, it means that the current pixel to be encoded and its neighboring areas form a non-flat area, and the predictive coding mode is used for compression.

[0053] 2. Predictive Coding Mode

[0054] like Figure 5 The figure shows a flowchart of the predictive coding mode. The predictive coding mode uses predictive coding for compression, which mainly includes two processes: prediction and coding. It utilizes the correlation between adjacent pixels of the image, and achieves lossless compression by predicting each pixel in the non-flat area and performing Rice coding on the prediction error.

[0055] 2.1 Gradient Quantization Merging

[0056] During the context modeling process, different local gradient values ​​(D1, D2, and D3) classify pixels into different context types. The prediction errors corresponding to the pixels in each context type are assumed to follow the same statistical distribution. When the image to be compressed is an 8-bit grayscale image, the image is divided into a total of 511×511×511 context types. While more context types can improve prediction accuracy, they also have the following drawbacks: First, the large number of divisions results in a small or even zero number of pixels belonging to each type, resulting in parameter redundancy. Second, during algorithm implementation, more storage space is required to store the different types, increasing the algorithm's resource usage. Therefore, appropriate quantization and merging of gradient values ​​is necessary.

[0057] First, the local gradient value is divided into a symmetrical interval of "dense in the middle and sparse on both sides", as shown in the following diagram: Figure 6 As shown, it is divided into 9 intervals, and the division process is shown as follows:

[0058]

[0059] Secondly, in order to further reduce the context types, Q i After concatenating them into the vector (Q1, Q2, Q3), the signs are changed. The specific steps are as follows: Check the first non-zero number in Q1, Q2, and Q3 in order. If it is positive, set the sign variable Sign to 1, and (Q1, Q2, Q3) remains unchanged. If it is negative, set the sign variable Sign to -1, and invert (Q1, Q2, Q3) to (-Q1, -Q2, -Q3). Compared to the original data type, the number of types after the transformation is reduced from 729 to 365.

[0060] Finally, in order to facilitate subsequent context parameter update steps, the vector (Q1, Q2, Q3) is mapped to an integer Q in the interval [0, 364]. The mapping formula is as follows:

[0061] Q=81Q1+9Q2+Q3

[0062] 2.2 Prediction error calculation

[0063] In order to facilitate hardware implementation, the predictor in the predictive coding selects the median edge detection predictor with a small amount of calculation. This predictor completes the prediction by detecting the edge information around the current pixel. A ≥max(I B ,I D ), if I B ≥I D This means that there is a horizontal edge near the current pixel. At this time, the predicted value is the gray value to the left of the current pixel, that is, P X =I D ;if I B D This means that there is a vertical edge near the current pixel. At this time, the predicted value is the grayscale value above the current pixel, that is, P X =I B . When I A ≤min(I B ,I D ) is the same. If there is no edge near the current pixel, then P X =I B +I D -I A . Prediction value P X It is expressed by the following formula:

[0064]

[0065] In order to prevent the subsequent prediction errors from being too large, the predicted values ​​are corrected after calculation. The correction process is as follows:

[0066]

[0067] Where sign is the sign variable for judging flipping, and C[Q] is the average prediction error, which is used here as a prediction correction value and is a kind of context parameter.

[0068] When the predicted value is corrected, the prediction error is the difference between the grayscale value and the predicted value:

[0069]

[0070] 2.3 Prediction Error Rice Coding

[0071] ​Rice coding is suitable for lossless compression of non-negative integer sequences that conform to the geometric distribution. The prediction error follows a bilateral geometric distribution. Therefore, before Rice coding, the prediction error needs to be mapped to make it conform to the geometric distribution, as follows:

[0072]

[0073] After the mapping is completed, Rice encoding is performed. First, the parameters k and q required for the encoding process are calculated. The calculation process is as follows:

[0074]

[0075] The parameter k is used to remove the length of each field in the Rice code, the parameter q represents the quotient in the Rice code calculation process, and N[Q] and A[Q] are both context parameters. N[Q] represents the number of occurrences of the current context type, and A[Q] represents the sum of the absolute values ​​of the prediction errors.

[0076] 2.4 Context Parameter Update

[0077] Each context type has a corresponding set of context parameters, which are used to correct prediction errors and select appropriate encoding methods. Context parameters mainly include the following:

[0078] (1) A[Q]: The sum of the absolute values ​​of the prediction errors, used to estimate the parameter k of Rice coding.

[0079] (2) B[Q]: The sum of the prediction errors, used to assist in calculating the average prediction error C[Q].

[0080] (3) C[Q]: Average prediction error, used to correct the predicted value of the pixel.

[0081] (4) N[Q]: The number of occurrences of the current context type.

[0082] The context parameters need to be updated after each encoding. The update process is as follows:

[0083]

[0084] Among them, errval is the prediction error, Q is the index value, and the value is [0,364] corresponding to 365 context types.

[0085] 3. Run-length encoding mode

[0086] like Figure 7The following is a flow chart of the run-length encoding mode. When pixels are located in a flat area of ​​the image, the encoder uses run-length encoding to compress them. First, the pixels to be encoded are scanned for their run length, which counts the number of consecutive pixels with the same grayscale value. Then, different processing is performed based on the reason for the scan termination. If the scan terminates due to reaching the end of a row, the run length is encoded and run-length encoding mode is exited. If the scan terminates due to reaching a pixel with a different grayscale value, run-length encoding is performed and run-length encoding mode is exited, returning to prediction mode to perform predictive encoding on the difference pixels.

[0087] When encoding the run length, in order to avoid the occurrence of memory overflow caused by the run length being too large, the present invention designs a method for encoding the run length using a lookup table:

[0088] like Figure 8 As shown, each element in the table represents a run length, recorded as 2 rk The encoder scans each element along the index and accumulates the run length represented by each element. Scanning stops when the accumulated value is greater than or equal to the actual run length.

[0089] Experimental process:

[0090] In order to cover different star map types, four typical star maps with different backgrounds were selected for the performance test of the lossless compression algorithm, namely, star map with a single background, star map with a complex background, star map with interference in the background, and star map with pure black. Figure 9 shown.

[0091] First, a lossless compression algorithm was implemented through software, and lossless compression and decompression experiments were carried out on each star map; secondly, the values ​​of various indicators were analyzed; finally, the differences in the experimental results of different star maps were compared, and corresponding conclusions were drawn.

[0092] 1. Experimental results of star images with a single background

[0093] The experimental data obtained after compressing and decompressing the star image with a single background using the lossless compression algorithm of the present invention is shown in Table 1.

[0094] Table 1 Evaluation indicators of lossless compression algorithms (background single star image)

[0095]

[0096] The experimental data in Table 1 shows that the star image is not very complex. Using the lossless compression algorithm, we achieve a compression ratio of 2.7355:1, indicating that the original image contains significant information redundancy. The coding efficiency is 0.8158, indicating that the compressed data is close to the theoretical minimum compression code length. These results demonstrate that the lossless compression algorithm effectively removes information redundancy from the original image.

[0097] 2. Experimental results of star maps with complex backgrounds

[0098] The experimental data obtained after compressing and decompressing the star map with complex background using the lossless compression algorithm of the present invention is shown in Table 2.

[0099] Table 2 Evaluation indicators of lossless compression algorithm (star map with complex background)

[0100]

[0101] The experimental data in Table 2 show that the compression ratio and relative redundancy of star images with complex backgrounds are lower than those with simple backgrounds. This indicates that images with complex backgrounds have less internal information redundancy and smaller potential for lossless compression.

[0102] The coding efficiency is very close to 1, which indicates that the average code length of the compressed data is almost equal to the theoretical shortest compression code length. This also reflects that it is difficult to achieve a high lossless compression ratio for images with complex backgrounds.

[0103] 3. Star map experiment results with background interference

[0104] The experimental data obtained after compressing and decompressing the star map with background interference using the lossless compression algorithm of the present invention is shown in Table 3.

[0105] Table 3 Evaluation indicators of lossless compression algorithm (with interfering star map in the background)

[0106]

[0107] The experimental data in Table 3 shows that the image complexity of star images with background noise is higher than that of images with a simple background, but lower than that of images with a complex background. This indicates that, despite some interference in the background, the overall image is relatively smooth. Using a lossless compression algorithm on star images with noise yields a high compression ratio of 2.5654:1, indicating that these images have more internal information redundancy and therefore more room for lossless compression. However, compared to images with a simple background, the compression ratio is lower, indicating that the compression effect is not as good as that of images with a simple background.

[0108] 4. Pure Black Star Map Experiment Results

[0109] The experimental data obtained after compression and decompression operations on the pure black star map using the lossless compression algorithm of the present invention are shown in Table 4.

[0110] Table 4 Evaluation indicators of lossless compression algorithm (pure black star map)

[0111]

[0112] Experimental data shows that the background complexity of a pure black image is zero, indicating that its interior is very smooth and its pixel values ​​are uniform. Using a lossless compression algorithm, we achieve an extremely high compression ratio of 18927.3616:1, demonstrating that pure black images have a lot of internal information redundancy and a vast potential for lossless compression. This compression effect is more significant than any other star image.

[0113] However, for a pure black image, the ideal compression code length is 0, and the coding efficiency is also 0. This is because, from the perspective of information theory, an information source that outputs only a single element has no information content, because the probability of each output element appearing is 100%, there is no uncertainty, and therefore no amount of uncertainty can be eliminated. Therefore, using coding efficiency metrics for pure color images is meaningless.

[0114] Experimental results analysis

[0115] The compression ratio and relative redundancy of an image decrease as image complexity increases. Images with higher complexity have less information redundancy and less potential for lossless compression. Therefore, for images with smooth, clean backgrounds, the lossless compression algorithm of the present invention has better compression effects.

[0116] Coding efficiency increases with image complexity. The lossless compression algorithm of the present invention can better utilize the compression space for complex images, bringing them closer to the theoretically optimal compression state. However, it also shows that for star images with complex backgrounds, the theoretical compression space is inherently small, making it difficult to achieve a high compression ratio. On the other hand, for star images with a simple background, the theoretical compression space is larger, and the lossless compression algorithm of the present invention needs to process more information redundancy. Although the coding efficiency is lower, a higher compression ratio can be achieved.

[0117] The above is only an embodiment of the present invention, and common knowledge such as the specific technical solutions or characteristics in the solution is not described in detail here. For those skilled in the art, without departing from the technical solution of the present invention, several variations and improvements can be made, which should also be regarded as the scope of protection of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the description can be used to interpret the content of the claims.

Claims

1. A fast lossless compression algorithm for star images, characterized in that: include: Context modeling: Based on the local gradient value Q of the current pixel to be encoded i Divide the region type and select the corresponding encoding method, local gradient value Q i The calculation formula is as follows: When the pixel to be coded and its neighboring pixels form a flat area, the run-length coding mode is selected for compression; when the pixel to be coded and its neighboring pixels form a non-flat area, the predictive coding mode is selected for compression; The steps of predictive coding mode are as follows: A1. Gradient quantization and merging: Divide the local gradient value into symmetrical intervals with dense center and sparse edges. The division process is as follows, and there are 9 intervals in total: Q i After being concatenated into vectors (Q1, Q2, Q3) in sequence, their signs are changed. The specific steps are as follows: Check the first non-zero number that appears in Q1, Q2, and Q3 in sequence. If it is a positive number, the sign variable Sign is set to 1, and (Q1, Q2, Q3) remains unchanged; if it is a negative number, the sign variable Sign is set to -1, and (Q1, Q2, Q3) is inverted to become (-Q1, -Q2, -Q3); Finally, the vector (Q1, Q2, Q3) is mapped to an integer Q in the interval [0, 364]. The mapping formula is as follows: Q=81Q1+9Q2+Q3 A2. Prediction error calculation: The prediction period in the prediction coding selects the median edge detection prediction period with small calculation amount. The prediction value Px is expressed by the following formula: The prediction error is the difference between the gray value and the predicted value: A3. Rice encoding of prediction errors: Before Rice encoding, the prediction errors are mapped so that they obey a geometric distribution, as follows: After the mapping is completed, Rice encoding is performed. First, the parameters k and q required for the encoding process are calculated. The calculation process is as follows: The parameter k is used to remove the length of each field in the Rice code, the parameter q represents the quotient in the Rice code calculation process, N[Q] and A[Q] are both context parameters, N[Q] represents the number of occurrences of the current context type, and A[Q] represents the sum of the absolute values ​​of the prediction errors; A4. Context parameter update: The context parameters need to be updated after each encoding. The update process is as follows: Where errval is the prediction error, Q is the index value, which ranges from [0,364] to 365 context types, A[Q] is the sum of the absolute values ​​of the prediction errors, which is used to estimate the parameter k of the Rice code; B[Q] is the sum of the prediction errors, which is used to assist in calculating the average prediction error C[Q]; C[Q] is the average prediction error, which is used to correct the prediction value of the pixel; N[Q] is the number of occurrences of the current context type; The run-length encoding mode is as follows: first, count the number of pixels with the same grayscale value that appear continuously, and perform different processing according to the reason for scanning termination; if the end pixel of the row is not scanned, the run-length encoding mode is exited after encoding the run-length; if it is due to scanning pixels with different grayscale values, the run-length encoding mode is exited after encoding the run-length, and return to the prediction encoding mode to perform prediction encoding on the difference pixels.

2. A fast star image lossless compression algorithm according to claim 1, characterized in that: In the run-length encoding mode, in order to avoid memory overflow caused by excessive run length, a method of run-length encoding using a lookup table is designed: the encoder scans each element along the index in turn, and accumulates the run length represented by each element. When the accumulated value is greater than or equal to the actual run length, the scanning stops.

3. A fast star image lossless compression algorithm according to claim 1, characterized in that: In step A2 of the predictive coding mode, in order to prevent the subsequent prediction error from being too large, the prediction value is corrected after calculation. The correction process is as follows: Where sign is the sign variable for judging flipping, and C[Q] is the average prediction error.

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