Research On The Theory Of Epanechnikov Kernel Modeling And Its Application In Image Coding

Image coding technology has become an indispensable technology in modern information field.More importantly,the demand and development scale of emerging stereoscopic display technology has seen explosive growth.3D display can express higher dimensional information,and solving its compression problem has become the key breakthrough direction of image coding.This paper innovates from mathematical modeling,which not only improves the kernel theory system,but also provides a new idea for image coding framework.Starting from the derivation of the high dimensional Epanechnikov kernel function and its statistics for mixture model,this paper innovatively puts forward the Epanechnikov mixture regression,which has obvious advantages compared with the Gaussian mixture model in the application of image modeling.At the same time,starting from the research of modeling-based coding framework,this paper proposes an adaptive model or mode selection coding structure based on rate-distortion optimization by combining Gaussian mixture regression and Epanechnikov mixture regression.For light field image,we also propose a light field image reconstruction frame based on the similarity of its elementary image blocks.Our new theoretical framework not only has better performance than the traditional algorithm at bit rates,but also opens up a new idea of image coding by breaking through the theoretical bottleneck.The main contributions and innovative work of this thesis are summarized as the following four parts:1.Aiming at the problem of poor performance of Gaussian mixture model in image coding,the 3D Epanechnikov kernel theory and the 3D Epanechnikov kernel based image coding algorithm are proposed.In this paper,the expression of three-dimensional Epanechnikov kernel in matrix form is derived,which contains the scale,rotation,and transformation information,among which the three-dimensional variable contains the horizontal coordinates,vertical coordinates,and gray value of a single-channel image block.And the marginal distribution,conditional mean,and other statistics required by the regression model are derived.These statistics are key to the application of 3D Epanechnikov kernel regression theory in the modeling-based image coding for single-channel image.Under the condition of the same bit consumption,the modeling performance of three-dimensional Epanechnikov kernel regression is better than the traditional Gaussian regression model for small size single-channel image.Therefore,this paper realizes the optimization design of modeling-based coding combining Gaussian and Epanechnikov kernel regression model for the three channels of a color image.Furthermore,the parameters of the mixed regression model are encoded by referring to the parameter characteristics of the model to maximize the compression efficiency.The algorithm has good visual adaptability at low bit rates,and its objective quality is better than that of JPEG based on DCT.2.In order to make the decoded image of light field image have better visual effect,this paper applies the modeling-based coding method to light field image,and proposes an elementary image array reconstruction framework based on linear function.At the encoder,based on the correlation between adjacent elementary images of light field images,the row and column offset information is extracted and encoded according to the parallax offset between adjacent elementary images,and the sub-elementary image array is extracted according to the maximum offset.At the same time,the shadow corners of the elementary images are modeled by linear function and its coefficients are encoded.A modeling-based adaptive model selection algorithm was used for the extracted sub-array elementary image combined Epanechnikov with Gaussian mixture regression algorithm,and its optimal parameter group was encoded.At the decoder,the decoded parameters are used to predict and reconstruct the elementary image array.This method is efficient and fast,and achieves better coding performance than HE VC for video sequence with a higher speed at low bit rates.3.In order to make better use of the correlation of elementary images to improve the modeling-based light field image coding,this paper proposes the four-dimensional Epanechnikov kernel theory and its application to the 4D Epanechnikov kernel based coding of elementary image array.Compared with the three-dimensional Epanechnikov kernel function,the variable of the general matrix form expression of the four-dimensional Epanechnikov kernel function contains a one-dimensional time variable.In this paper,the time variable refers to the frame number of the pseudo-video sequence formed by the arrangement of elementary image blocks.Further,the correlated statistics of the four-dimensional Epanechnikov kernel mixture model are derived and the four-dimensional Epanechnikov kernel mixture regression is proposed.Compared with the four-dimensional modeling performance of Gaussian regression,four-dimensional Epanechnikov kernel regression has obvious advantages for the modeling effect of the elementary image sequence with complex texture and small size.Using the elementary image array reconstruction framework based on linear function,the sub-elementary image array is extracted.The elementary image blocks in each channel of the subarray are serpentine arranged into pseudo video sequence,and the adaptive modeling coding is carried out to make use of the correlation between elementary images again and make it tightly expressed.At the decoder,the sub-elementary images are arranged and restored by decoded pseudo-sequence,and the elementary image array is reconstructed by the decoded parameters.The experimental results show that in the elementary image array reconstruction framework based on linear function,the use of four-dimensional function based modeling for sub-elementary image array can limit the modeling effect,but the pseudo-video sequence modeling can enhance the modeling stability by enhancing the association between elementary images.This method not only develops a new model theory,but also further studies the adaptability of light field image coding framework.4.In order to solve the problem that the three-dimensional and four-dimensional Epanechnikov kernel mixture regression theory cannot directly model a three-channel image,this paper proposes an elementary image array coding algorithm using the five-dimensional Epanechnikov kernel mixture regression to directly model the horizontal and vertical coordinates of elementary image and the gray values of Y,U and V channels.The formal expression of matrix form five-dimensional Epanechnikov kernel and the correlated statistics of five-dimensional Epanechnikov mixture model are derived,and a five-dimensional Epanechnikov mixture regression based on Gaussian initialization is proposed.The algorithm also uses the elementary image array reconstruction framework based on linear function,and model the whole elementary image of each sub-array extracted.This algorithm can avoid block effect effectively and get better subjective effect,and expand the range of good effect of modeling-based coding algorithm.