Three-dimensional Epanechnikov mixture regression in image coding

•A 3-D Epanechnikov Kernel (EK) is deduced.•Statistic Theories of 3-D Epanechnikov Mixture Regression (EMR) is proposed.•Improving the EM algorithm using Mean Square Error (MSE) based optimization.•Using the 3-D EMR we proposed in image coding and it outperforms Guassian Mixture Regression in some cases.•A coding framework based on Adaptive Mode Selection (AMS) using GMR and EMR. Kernel methods have been studied extensively in recent years. We propose a three-dimensional (3-D) Epanechnikov Mixture Regression (EMR) based on our Epanechnikov Kernel (EK) and realize a complete framework for image coding. In our research, we deduce the covariance-matrix form of 3-D Epanechnikov kernels and their correlated statistics to obtain the Epanechnikov mixture models. To apply our theories to image coding, we propose the 3-D EMR which can better model an image in smaller blocks compared with the conventional Gaussian Mixture Regression (GMR). The regressions are all based on our improved Expectation-Maximization (EM) algorithm with mean square error optimization. Finally, we design an Adaptive Mode Selection (AMS) algorithm to realize the best model pattern combination for coding. Our recovered image has clear outlines and superior coding efficiency compared to JPEG below 0.25bpp. Our work realizes an unprecedented theory application by: (1) enriching the theory of Epanechnikov kernel, (2) improving the EM algorithm using MSE optimization, (3) exploiting the EMR and its application in image coding, and (4) AMS optimal modeling combined with Gaussian and Epanechnikov kernel.