Fast High-Dimensional Bilateral and Nonlocal Means Filtering


Currently available rapid methods for bilateral and nonlocal means filtering are limited to grayscale images. High-dimensional data, such as colour and hyperspectral images, patch-based data, and flow-fields, cannot readily be applied to them. We present in this study a fast technique for bilateral and nonlocal means filtering in high dimensions. While prior methods rely primarily on approximating either data or filters (through quantization or expansion), our technique uses localised approximation utilising Gaussian weighted and shifted copies where the weights and shifts are determined from the data. Clustering and rapid convolutions are all that is required to implement the proposed approximation's algorithm. The approximation error of our approach is guaranteed by an option that is not available in previous algorithms. To highlight the speed and accuracy of our proposal, we present some findings for high-dimensional bilateral and nonlocal means filtering. Our technique also outperforms current fast approximations in terms of both accuracy and speed, as demonstrated in this paper.

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