Feature Keypoint-Based Image Compression Technique Using a Well-Posed Nonlinear Fourth-Order PDE-Based Model

Tudor Barbu
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Tudor Barbu: Institute of Computer Science of the Romanian Academy—Iași Branch, 700481 Iași, Romania

Mathematics, 2020, vol. 8, issue 6, 1-16

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.

Keywords: lossy image (de)compression; scale-invariant feature keypoint; image sparsification; scattered data point interpolation; nonlinear PDE-based structural inpainting; well-posed PDE model; variational solution; finite-difference-based numerical approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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