Affine Non-Local Means Image Denoising

Abstract

This paper presents an extension of the Non-Local Means denoising method, that effectively exploits the affine invariant self-similarities present in the images of real scenes. Our method provides a better image denoising result by grounding on the fact that in many occasions similar patches exist in the image but have undergone a transformation. The proposal uses an affine invariant patch similarity measure that performs an appropriate patch comparison by automatically and intrinsically adapting the size and shape of the patches. As a result, more similar patches are found and appropriately used. We show that this image denoising method achieves top-tier performance in terms of PSNR, outperforming consistently the results of the regular Non-Local Means, and that it provides state-of-the-art qualitative results.

Image Denoising with Recurrent Polak-Ribière-Polyak Conjugate Gradient-Based Neuro-Fuzzy Edge-Preserving Segmentation Based on OAMNHA

“…Fedorov & Ballester [10] proposed an enhanced non-local means denoising method for effectively achieving the affine invariant self-similarities present in the real-scene images. In this method, an affine invariant patch similarity measure was used that performs an appropriate patch comparison by automatically and intrinsically adapting the size and shape of the patches.…”

An Affine Invariant Patch Similarity

“…Notice that, in our examples, p = 0 or p = −1. Lemma 2.2 permits to iterate the above construction (10) and redefine for k ≥ 1 where k is the index of iteration, and…”

“…The choice of r might depend also on the application. For instance, in [22,23] a thorough analysis was made to experimentally show the robustness of a patch-based variational segmentation method that considers the same adaptive patches depending on the values of t and r. It was also analyzed in [10] for image denoising where, on the other hand, a patch size constraint limiting the maximum patch size was introduced. It was developed by slightly modifying the tensors adding an appropriate constant to its diagonal [10].…”

“…For instance, in [22,23] a thorough analysis was made to experimentally show the robustness of a patch-based variational segmentation method that considers the same adaptive patches depending on the values of t and r. It was also analyzed in [10] for image denoising where, on the other hand, a patch size constraint limiting the maximum patch size was introduced. It was developed by slightly modifying the tensors adding an appropriate constant to its diagonal [10]. Obviously, this modification breaks the affine covariant property of the structure tensors and associated neighborhoods but limiting the maximum patch size to capture only small pieces of visual information, with the limit depending on the noise level, has proven to be beneficial in the context of denoising.…”

“…The main intuition is simple: the similarity measure compares elliptical patches (defined as spatially varying balls of the underlying metric previously defined in the image domain) by normalizing them to a common disk domain. Potential applications of such similarity measure are numerous, for example, a novel image inpainting method was presented recently in [8], a variational segmentation method in [23], and an image denoising method achieving top-tier performance in [10]. The similarity measure was originally introduced and studied in [9] (see also [7]), whereas this work is focused on the numerical implementation.…”