Anisotropic Diffusion Partial Differential Equations in Multi-Channel Image Processing : Framework and Applications

We review recent methods based on diffusion PDE's (Partial Differential Equations) for the purpose of multi-channel image regularization. Such methods have the ability to smooth multi-channel images anisotropically and can preserve then image contours while removing noise or other undesired local artifacts. We point out the pros and cons of the existing equations, providing at each time a local geometric interpretation of the corresponding processes. We focus then on an alternate and generic tensor-driven formulation, able to regularize images while specifically taking the curvatures of local image structures into account. This particular diffusion PDE variant is actually well suited for the preservation of thin structures and gives regularization results where important image features can be particularly well preserved compared to its competitors. A direct link between this curvature-preserving equation and a continuous formulation of the Line Integral Convolution technique (Cabral and Leedom, 1993) is demonstrated. It allows the design of a very fast and stable numerical scheme which implements the multi-valued regularization method by successive integrations of the pixel values along curved integral lines. Besides, the proposed implementation, based on a fourth-order Runge Kutta numerical integration, can be applied with a subpixel accuracy and preserves then thin image structures much better than classical finite-differences discretizations, usually chosen to implement PDE-based diffusions. We finally illustrate the efficiency of this diffusion PDE's for multi-channel image regularization - in terms of speed and visual quality - with various applications and results on color images, including image denoising, inpainting and edge-preserving interpolation

MS-PS: A Multi-Scale Network for Photometric Stereo With a New Comprehensive Training Dataset

The photometric stereo (PS) problem consists in reconstructing the 3D-surface of an object, thanks to a set of photographs taken under different lighting directions. In this paper, we propose a multi-scale architecture for PS which, combined with a new dataset, yields state-of-the-art results. Our proposed architecture is flexible: it permits to consider a variable number of images as well as variable image size without loss of performance. In addition, we define a set of constraints to allow the generation of a relevant synthetic dataset to train convolutional neural networks for the PS problem. Our proposed dataset is much larger than pre-existing ones, and contains many objects with challenging materials having anisotropic reflectance (e.g. metals, glass). We show on publicly available benchmarks that the combination of both these contributions drastically improves the accuracy of the estimated normal field, in comparison with previous state-of-the-art methods

Variational Approaches to the Estimation, Regularization and Segmentation of Diffusion Tensor Images

Diffusion magnetic resonance imaging probes and quantifies the anisotropic diffusion of water molecules in biological tissues, make it possible to non-invasively infer the architecture of the underlying structures. In this chapter, we present a set of new techniques for the robust estimation and regularization of diffusion tensor images (DTI) as well as a novel statistical framework for the segmentation of cerebral white matter structures from this type of dataset. Numerical experiments conducted on real diffusion weighted MRI illustrate the technique and exhibit promising results

Stylisation d'image basé contours et hachures par simulation de tracés de traits à géométrie tensorielle

National audienceNous abordons le problème de la transformation automatique de photographies numériques sous forme de dessins ou de croquis stylisés. Nous proposons un algorithme de rendu, simple et rapide à mettre en oeuvre, basé sur une simulation de successions de traits de crayon dirigé par un champ de tenseurs du 2ème ordre. Il permet de simuler de manière réaliste un crayonnage tel que pourrait l'exécuter un artiste souhaitant reproduire une photographie couleur sous forme de croquis. Une étape de colorisation simple, utilisant les couleurs de l'image d'entrée, permet de finaliser ce rendu non-photoréaliste

Fast Anisotropic Smoothing of Multi-Valued Images using Curvature-Preserving PDE’s

We are interested in PDE’s (Partial Differential Equations) in order to smooth multi-valued images in an anisotropic manner. Starting from a review of existing anisotropic regularization schemes based on diffusion PDE’s, we point out the pros and cons of the different equations proposed in the literature. Then, we introduce a new tensor-driven PDE, regularizing images while taking the curvatures of specific integral curves into account. We show that this constraint is particularly well suited for the preservation of thin structures in an image restoration process. A direct link is made between our proposed equation and a continuous formulation of the LIC’s (Line Integral Convolutions by Cabral and Leedom [11]). It leads to the design of a very fast and stable algorithm that implements our regularization method, by successive integrations of pixel values along curved integral lines. Besides, the scheme numerically performs with a sub-pixel accuracy and preserves then thin image structures better than classical finite-differences discretizations. Finally, we illustrate the efficiency of our generic curvature-preserving approach- in terms of speed and visual quality- with different comparisons and various applications requiring image smoothing: color images denoising, inpainting and image resizing by nonlinear interpolation

Non-Local Image Smoothing by Applying Anisotropic Diffusion PDE's in the Space of Patches

International audienceWe design a family of non-local image smoothing algorithms which approximate the application of diffusion PDE's on a specific Euclidean space of image patches. We first map a noisy image onto this high-dimensional space and estimate its geometric structure thanks to a straightforward extension of the structure tensor field. The tensors spectral elements allows us to design an oriented highdimensional smoothing process by the means of anisotropic regularization PDE's which have both local and non-local properties and whose solutions are estimated by locally oriented high-dimensional convolutions. We show that the Bilateral Filtering and Non-Local Means methods are the isotropic cases of our denoising framework

LIC-based regularization of multi-valued images

International audienceIn this paper, a general multi-valued image regularization method based on LIC's (Line Integral Convolutions \cite{cabral-leedom:93}) is proposed. From the investigation of recent approaches based on multi-valued diffusion PDE's, we show how a regularization process is naturally decomposed, first as the estimation of its underlying smoothing geometry, and then, as the application of a locally and spatially oriented smoothing. Performing this last part using LIC's significatively improves the overall regularization process both in visual quality and processing time. We illustrate three different applications of our general regularization framework : Color image denoising, inpainting and magnification