Smoothed Shock Filtering: Algorithm and Applications.

Antoine Vacavant

doi:10.3390/jimaging7030056

Abstract

This article presents the smoothed shock filter, which iteratively produces local segmentations in image’s inflection zones with smoothed morphological operators (dilations, erosions). Hence, it enhances contours by creating smoothed ruptures, while preserving homogeneous regions. After describing the algorithm, we show that it is a robust approach for denoising, compared to related works. Then, we expose how we exploited this filter as a pre-processing step in different image analysis tasks (medical image segmentation, fMRI, and texture classification). By means of its ability to enhance important patterns in images, the smoothed shock filter has a real positive impact upon such applications, for which we would like to explore it more in the future.

Highlights

Image enhancement and denoising consists of improving digital images by reducing inherent noise, which has been addressed by a wide variety of approaches [1,2,3,4]
In [18], we proposed to improve this PDE scheme by integrating smoothed morphological operators inspired by the work of Kass and Solomon [19]
In [22], we proposed a first original and foundational definition of robustness dedicated to image processing algorithms, by getting inspiration from what has been introduced in computer vision

Summary

Introduction

Image enhancement and denoising consists of improving digital images by reducing inherent noise, which has been addressed by a wide variety of approaches [1,2,3,4]. Shock filters locally “shock” an image by erosion and dilation to create ruptures between local maxima and minima, by applying morphological operators depending on the sign of the Laplacian calculated on each pixel This algorithm has several relevant theoretical properties: the range of output image’s values stays between the limits of the input image, contrary to other approaches such as Fourier transform- or wavelet-based ones; border effects such as Gibbs phenomenon cannot occur [14]; and it preserves the total variation of the processed signal and approximates deconvolution [15]. Even if this PDE scheme is not originally able to process noisy signals, several authors have proposed extended versions [15,17,18]

Objectives

Methods

Conclusion