CN113674371A - Three-dimensional element image array coding method based on five-dimensional secondary kernel modeling - Google Patents
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Abstract
A three-dimensional element image array coding method based on five-dimensional secondary kernel modeling belongs to the technical field of computer image processing, and comprises the following steps: deducing and establishing a theoretical system of a five-dimensional secondary kernel model; executing a five-dimensional quadratic kernel mixed expert algorithm initialized by five-dimensional Gaussian regression; executing a five-dimensional adaptive model selection algorithm; and (4) executing the coding framework. The invention provides a coding method adaptive to human eyes based on the theory of a five-dimensional secondary kernel model and the characteristics of a three-dimensional element image. Compared with the traditional HEVC and JPEG2000 coding algorithms based on transformation, the method has good coding effect at low bit rate compared with the two traditional coding methods.
Description
Technical Field
The invention belongs to the technical field of computer image processing, and particularly relates to a three-dimensional element image array coding method based on five-dimensional secondary kernel modeling.
Background
The light field imaging technology, as a next generation display technology, requires a much larger amount of data to be transmitted than a conventional image, so that it is very important to research on the light field image encoding technology. Since the light field image is acquired by the lens array, it is expressed as a voxel image array in the transmission process. The key point for breaking through the coding problem is to reasonably utilize the correlation of the stereo volume image array to code the image.
Most of the existing methods for solving the coding problem are transform-based methods, such as HEVC, JPEG2000, and the like. The correlation of stereo element image arrays is utilized, and the HEVC video coding by arranging stereo elements into a pseudo video sequence is a very common technical means. However, the hybrid expert model based on the gaussian kernel breaks through the conventional method, and the optimal parameters are obtained by applying the gaussian hybrid model to carry out regression and are used for representing light field image information, so that the advantage of the coding effect on low bit rate is realized. After the breakthrough of the coding method based on modeling, the theoretical development of non-gaussian models and the application of non-gaussian models in image coding are concerned, and the excessive noise phenomenon of the transformation method at low bit rate can be improved by the modeling method.
Disclosure of Invention
The invention aims to provide a three-dimensional element image array coding method based on a five-dimensional quadratic mixture model, aiming at the problems that the coding effect noise of light field image coding at low bit rate is too large and is not suitable for human eyes in the existing method. The algorithm based on the quadratic kernel model is superior to the traditional Gaussian modeling in effect.
In order to achieve the purpose, the invention adopts the following technical scheme:
a three-dimensional element image array coding method based on five-dimensional quadratic kernel modeling comprises the following steps:
1.1 deducing and establishing a theoretical system of a five-dimensional secondary kernel model, and setting variables:
wherein: x is the abscissa of the three-dimensional element image, y is the ordinate of the three-dimensional element image, and z, u and v are gray values of three channels of the color image respectively;
1.1.1 solving the distribution function of the five-dimensional quadratic kernel function:
using the basic principle of kernel functions: after the global integral is 1 and the function is not less than 0, after the normalization coefficient is solved, the standard expression is translated and rotated to obtain a general expression as follows:
wherein: mu.sjIs the mean of five-dimensional variables; sigmajA covariance matrix of five-dimensional variables;
1.1.2 by double integration of a five-dimensional quadratic kernel function, the joint distribution function of δ ═ x, y and z is found as:
1.1.4 reconstruction of images with a hybrid expert model, where two important variables are the mean function and the gate function:
the gate function is:
the mean function is:
wherein: the mean and covariance matrix of the five-dimensional variables contain relevant parameters
1.2 five-dimensional quadratic kernel mixed expert algorithm based on five-dimensional Gaussian regression initialization:
in the algorithm regression process, a stereo image block is represented as an Nx 5 matrix, 5 columns represent the abscissa, the ordinate and the gray value of a color image three channel; the information of the N rows is data corresponding to N pixel points in the three-dimensional pixel; the ith pixel point in the t iteration is represented as (x)ti,yti,zti,uti,vti);
1.2.1 initializing parameter values as a result of t ═ 1 parameters
Initializing parameters by using a kmeans algorithm, and initializing the three-dimensional metadata information into K clusters, wherein the parameters of each cluster are as follows: mean, covariance matrix, and weight values of the clusters; the initial parameters for the K clusters are: omega1=(μj1,Σj1,αj1) J ═ 1,2,. K; solving initial modeling through initial parameters, reconstructing three-channel gray values of small blocks, and recording mean square error MSE (1) of three channels and original data;
1.2.2 parameter iteration posterior probability through posterior probability of Gaussian mixture model is:
wherein: 1,2, N, j 1,2, K;
for 7 iterations (t ═ 2:8), the results of each iteration of the parameters are:
1.2.3 recording the iteration parameters and the data mean square error values corresponding to each group of parameters
Set t iterative parametersΩt=(μjt,Σjt,αjt) And substituting the t 2, the 8, the j 1, the 2, the K into the mean value of the five-dimensional quadratic kernel expert modelAndin the solution formula (2), the corresponding:
1.2.4 picking the best results
Searching iteration times t corresponding to minimum MSE value0Corresponding parameterAnd reconstructing a corresponding voxel image block; reconstructing the three channels to correspond to the optimal gray value of
1.3 five-dimensional adaptive model selection algorithm
Selecting an optimal balance from bit consumption and modeling distortion to realize the selection of the corresponding parameter group under the optimal model number, wherein the rate distortion optimization formula is as follows:
J=D+λR
wherein: d is mean square error distortion, R is bit rate consumption, and lambda is a Lagrange coefficient;
1.3.1 initial model number Range for judged optimal coding
For the specified stereo image blocks and λ, the algorithm in step 1.2 is respectively executed by using 1, 8, 16, 24, 32, 40, 48, 56 and 64 models, and J values are respectively calculated for the reconstructed images; finding out the model number corresponding to the minimum J and the corresponding parameters;
1.3.2 finding the optimal direction of the initial optimal model number recorded in step 1.3.1
Traversing the directions of the suboptimal model numbers on the two sides of the optimal model number recorded in the step 1.3.1;
1.4 coding framework execution
1.4.1 extracting stereo element image array information
Extracting row parallax offset and column parallax offset between adjacent stereo elements of a stereo element image array, recording the row parallax offset and the column parallax offset as two offset matrixes, and encoding the two offset matrixes;
extracting the information of the imaging shadow of the image blocks at different positions of the stereo image array, and modeling the first-order function parameter a of the shadow in the ith area of the stereo image arrayi1,bi1,ai2,bi2I is 1,2,3, 4;
1.4.2 extraction of submatrix modeling
Determining the maximum extraction interval as s according to the row parallax offset and the column deviation offset extracted in the step 1.4.1, and extracting one stereo element from each s rows and s columns to form a sub-matrix; according to the definition requirement, selecting a lambda value to perform 1.3-dimensional quadratic kernel adaptive selection modeling on each stereo element in the submatrix, and coding model parameters;
1.4.3 predictive reconstruction of entire anay of stereoscopic images
According to the shadow information extracted in the step 1.4.1, reconstructing the decoding parameters into a sub-matrix through a formula in the step 1.1.4, and fusing the stereo elements of adjacent columns; intercepting an image block which is not coded in the middle in the fusion image through the two offset matrixes extracted in the step 1.4.1; and after the non-coding blocks between the columns are reconstructed, performing the same operation between the rows, and finally predicting the whole stereoscopic element image array.
The invention has the beneficial effects that: under the condition of low bit rate, the coding effect superior to that of the traditional HEVC and JPEG2000 can be realized by using less bit consumption, and the method has extremely low noise and good sensory effect.
Drawings
FIG. 1 is a graph comparing a five-dimensional quadratic kernel mixture expert model based on Gaussian initialization and modeling results using only Gaussian regression,
wherein: (a) a Gaussian model result and (b) a five-dimensional secondary kernel modeling result;
FIG. 2 is a schematic diagram of a codec frame structure;
FIG. 3 is a diagram illustrating extraction of line parallax offset information;
figure 4 is a schematic diagram of information extraction from shadows,
wherein: parameter a of region EIAii1,bi1,ai2,bi2,i=1,2,3,4;
Figure 5 is a schematic diagram of an array of predictively reconstructed voxel images,
wherein: (a) for adjacent voxels in the original submatrix, (b) for the de-shadowing process, (c) for calculating rd 75-rdAB-rdBC-rdCDThe (d) is the fusion result, (e) is the interception process, (f) is the interception result, and (g) is the shadow recovery;
FIG. 6 is a drawing image effect diagram of a central image block of a reconstructed voxel image array at 0.05bpp,
wherein: (a1) for the light field image coding system result based on the five-dimensional quadratic kernel model, (b2) is the HEVC Low Delay P (GOP ═ 4) coding result, and (c3) is the JPEG2000 coding result.
Detailed Description
The invention establishes a three-dimensional element image array coding method based on five-dimensional secondary kernel modeling, as shown in figure 2. The core content of the invention is as follows: a brand-new model theory is proposed, and the algorithm uses a traditional Gaussian model; and proposes a reconstruction framework established by using the correlation between stereo meta-image elements. Compared with the traditional algorithm, the coding effect of the system is more suitable for human eyes under low bit rate and has better structural similarity.
For the purpose of making the objects, technical solutions and advantages of the present invention clearer, the following detailed description is made with reference to the accompanying drawings and examples:
1.1 extracting stereo element image array information
In a stereo element image array having 72 x 96 rows and columns, the resolution of each stereo element is 75 x 75. As shown in fig. 2 and 3, a row parallax matrix and a column parallax matrix of the stereoscopic element image array are extracted and encoded. Extraction ofShaded areas, as shown in FIG. 4, a11=0.64,b11=-37,a12=-0.5,b12=18,a21=0.64,b21=-37,a22=-0.35,b22=18,a31=-0.64,b31=37,a32=0.35,b32=-18,a41=-0.73,b41=37,a42=0.3,b42These data are encoded-18.
1.2 extracting sub-matrices for modeling
If the input λ is 40, the decimation interval of the sub-matrix is determined to be 3. The final extracted sub-matrix is 25 x 33 with each voxel resolution of 75 x 75. And (3) performing a five-dimensional adaptive model selection algorithm on each solid element in the sub-matrix:
1.2.1 Secondary Nuclear hybrid expert model performing Gaussian hybrid model initialization
The quadratic kernel mixture expert model for gaussian mixture model initialization is first performed on 1, 8, 16, 24, 32, 40, 48, 56, and 64 models (i.e., K ═ 1, 8, 16, 24, 32, 40, 48, 56, and 64), respectively. Each voxel resolution is 75 × 75, so N5625.
1.2.2 cases where modeling is done with 16 models (K16) are taken as an example
The posterior probability is:
wherein i 1, 2.,. 5625, j 1, 2.,. 16.
For 7 iterations (t ═ 2:8), the result of each iteration of the parameters is
1.2.3 recording the iteration parameters and the data mean square error values corresponding to each group of parameters
T sets of iteration parameters omegat=(μjt,Σjt,αjt),t=2,...8, j 1,2, 16 substituted into solving the five-dimensional quadratic kernel expert model meanAndin the solution formula (2). Record correspondence
1.2.4 picking the best results
Searching iteration times t corresponding to minimum MSE value0Corresponding parameterAnd reconstructs the corresponding voxel image block. Reconstructing the three channels to correspond to the optimal gray value ofThe optimal parameters at the current lambda are encoded and the parameters are encoded.
1.3 reconstruction of the submatrix prediction into the entire stereoscopic element image array
And decoding the parallax matrix and the shading parameters coded in the 1.1. As in fig. 5, will passAndthe reconstruction formula decodes the reconstructed stereo elements of the adjacent columns of the submatrix for fusion. Intercepting the middle uncoded image block in the fusion image through the offset matrix extracted in the step 1.1; and after the non-coding blocks between the columns are reconstructed, performing the same operation between the rows, and finally predicting the whole stereoscopic element image array.
1.4 Effect presentation
A central 8 × 8 patch is extracted from each stereo volume element of the stereo element image array, and the patches are spliced together in an inverted manner to form a drawing image, as shown in fig. 6.
1. The working conditions are as follows:
the experimental platform adopts Intel Core i74.2 GHz CPU @4.20GHz 4.20GHz, the memory is 16GB, a PC running Windows 7 is adopted, and the programming language is MATLAB language.
2. And (3) analyzing an experimental result:
from the above experiments, it can be seen that the image result similarity of the system at low bit rate (0.05bpp) is better than that of other methods. The imaging effect is low in noise and accords with the vision of human eyes.
Claims (1)
1. A three-dimensional element image array coding method based on five-dimensional quadratic kernel modeling is characterized by comprising the following steps:
1.1 deducing and establishing a theoretical system of a five-dimensional secondary kernel model, and setting variables:
wherein: x is the abscissa of the three-dimensional element image, y is the ordinate of the three-dimensional element image, and z, u and v are gray values of three channels of the color image respectively;
1.1.1 solving the distribution function of the five-dimensional quadratic kernel function:
using the basic principle of kernel functions: after the global integral is 1 and the function is not less than 0, after the normalization coefficient is solved, the standard expression is translated and rotated to obtain a general expression as follows:
wherein: mu.sjIs the mean of five-dimensional variables; sigmajA covariance matrix of five-dimensional variables;
1.1.2 by double integration of a five-dimensional quadratic kernel function, the joint distribution function of δ ═ x, y and z is found as:
1.1.4 reconstruction of images with a hybrid expert model, where two important variables are the mean function and the gate function:
the gate function is:
the mean function is:
wherein: the mean and covariance matrix of the five-dimensional variables contain relevant parameters
1.2 five-dimensional quadratic kernel mixed expert algorithm based on five-dimensional Gaussian regression initialization:
in the algorithm regression process, a stereo image block is represented as an Nx 5 matrix, 5 columns represent the abscissa, the ordinate and the gray value of a color image three channel; the information of the N rows is data corresponding to N pixel points in the three-dimensional pixel; the ith pixel point in the t iteration is represented as (x)ti,yti,zti,uti,vti);
1.2.1 initializing parameter values as a result of t ═ 1 parameters
Initializing parameters by using a kmeans algorithm, and initializing the three-dimensional metadata information into K clusters, wherein the parameters of each cluster are as follows: mean, covariance matrix, and weight values of the clusters; the initial parameters for the K clusters are: omega1=(μj1,Σj1,αj1) J ═ 1,2,. K; solving initial modeling through initial parameters, reconstructing three-channel gray values of small blocks, and recording mean square error MSE (1) of three channels and original data;
1.2.2 parameter iteration posterior probability through posterior probability of Gaussian mixture model is:
wherein: 1,2, N, j 1,2, K;
for 7 iterations (t ═ 2:8), the results of each iteration of the parameters are:
1.2.3 recording the iteration parameters and the data mean square error values corresponding to each group of parameters
T sets of iteration parameters omegat=(μjt,Σjt,αjt) And substituting the t 2, the 8, the j 1, the 2, the K into the mean value of the five-dimensional quadratic kernel expert modelAndin the solution formula of (1); record correspondence
1.2.4 picking the best results
Searching iteration times t corresponding to minimum MSE value0Corresponding parameterAnd reconstructing a corresponding voxel image block; reconstructing the three channels to correspond to the optimal gray value of
1.3 five-dimensional adaptive model selection algorithm
Selecting an optimal balance from bit consumption and modeling distortion to realize the selection of the corresponding parameter group under the optimal model number, wherein the rate distortion optimization formula is as follows:
J=D+λR
wherein: d is mean square error distortion, R is bit rate consumption, and lambda is a Lagrange coefficient;
1.3.1 initial model number Range for judged optimal coding
For the specified stereo image blocks and λ, the algorithm in step 1.2 is respectively executed by using 1, 8, 16, 24, 32, 40, 48, 56 and 64 models, and J values are respectively calculated for the reconstructed images; finding out the model number corresponding to the minimum J and the corresponding parameters;
1.3.2 finding the optimal direction of the initial optimal model number recorded in step 1.3.1
Traversing the directions of the suboptimal model numbers on the two sides of the optimal model number recorded in the step 1.3.1;
1.4 coding framework execution
1.4.1 extracting stereo element image array information
Extracting row parallax offset and column parallax offset between adjacent stereo elements of a stereo element image array, recording the row parallax offset and the column parallax offset as two offset matrixes, and encoding the two offset matrixes;
extracting the information of the imaging shadow of the image blocks at different positions of the stereo image array, and modeling the first-order function parameter a of the shadow in the ith area of the stereo image arrayi1,bi1,ai2,bi2I is 1,2,3,4Code;
1.4.2 extraction of submatrix modeling
Determining the maximum extraction interval as s according to the row parallax offset and the column deviation offset extracted in the step 1.4.1, and extracting one stereo element from each s rows and s columns to form a sub-matrix; according to the definition requirement, selecting a lambda value to perform 1.3-dimensional quadratic kernel adaptive selection modeling on each stereo element in the submatrix, and coding model parameters;
1.4.3 predictive reconstruction of entire anay of stereoscopic images
According to the shadow information extracted in the step 1.4.1, reconstructing the decoding parameters into a sub-matrix through a formula in the step 1.1.4, and fusing the stereo elements of adjacent columns; intercepting an image block which is not coded in the middle in the fusion image through the two offset matrixes extracted in the step 1.4.1; and after the non-coding blocks between the columns are reconstructed, performing the same operation between the rows, and finally predicting the whole stereoscopic element image array.
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