Abstract
A digital image compression framework based on nonlinear partial differential equations (PDEs) is proposed in this research article. First, a feature keypoint-based sparsification algorithm is proposed for the image coding stage. The interest keypoints corresponding to various scale-invariant image feature descriptors, such as SIFT, SURF, MSER, ORB, and BRIEF, are extracted, and the points from their neighborhoods are then used as sparse pixels and coded using a lossless encoding scheme. An effective nonlinear fourth-order PDE-based scattered data interpolation is proposed for solving the decompression task. A rigorous mathematical investigation of the considered PDE model is also performed, with the well-posedness of this model being demonstrated. It is then solved numerically by applying a consistent finite difference method-based numerical approximation algorithm that is next successfully applied in the image compression and decompression experiments, which are also discussed in this work.
Highlights
The digital image compression represents an important image processing and analysis task whose purpose is to reduce the image file size without losing much information and while conserving its visual quality, so as to facilitate the image storing and transmission operations
More performant partial differential equations (PDEs)-based image compression frameworks are those based on edge-enhancing diffusion (EED)
It uses an edge-enhancing diffusion-based interpolation and an adaptive B-tree triangular coding-based image sparsification [10].The BTTC-EED compression method outperforms JPEG standard, when the two are compared at the same high compression rate, but it is outperformed by JPEG 2000 coder
Summary
The digital image compression represents an important image processing and analysis task whose purpose is to reduce the image file size without losing much information and while conserving its visual quality, so as to facilitate the image storing and transmission operations. More performant PDE-based image compression frameworks are those based on edge-enhancing diffusion (EED) Such a compression solution is the BTTC-EED image encoder introduced by. Weickert et al in 2005 [21] It uses an edge-enhancing diffusion-based interpolation and an adaptive B-tree triangular coding-based image sparsification [10].The BTTC-EED compression method outperforms JPEG standard, when the two are compared at the same high compression rate, but it is outperformed by JPEG 2000 coder. The most successful EED-based compression technique is the rectangular subdivision with edge-enhancing diffusion (R-EED) codec developed by Schmaltz et al [11] It clearly outperforms the BTTC-EED schemes and other PDE-based compression algorithms, as well as the JPEG codec. While the conclusions of this research are drawn in the final section of this article
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