Bernard Rougé

A Variational Model for P+XS Image Fusion

We propose an algorithm to increase the resolution of multispectral satellite images knowing the panchromatic image at high resolution and the spectral channels at lower resolution. Our algorithm is based on the assumption that, to a large extent, the geometry of the spectral channels is contained in the topographic map of its panchromatic image. This assumption, together with the relation of the panchromatic image to the spectral channels, and the expression of the low-resolution pixel in terms of the high-resolution pixels given by some convolution kernel followed by subsampling, constitute the elements for constructing an energy functional (with several variants) whose minima will give the reconstructed spectral images at higher resolution. We discuss the validity of the above approach and describe our numerical procedure. Finally, some experiments on a set of multispectral satellite images are displayed.

TV Based Image Restoration with Local Constraints

The problem of recovering an image that has been blurred and corrupted with additive noise is ill-posed. Among the methods that have been proposed to solve this problem, one of the most successful ones is that of constrained Total Variation (TV) image restoration, proposed by L. Rudin, S. Osher, and E. Fatemi. In its original formulation, to ensure the satisfaction of constraints, TV restoration requires the estimation of a global parameter λ (a Lagrange multiplier). We observe that if λ is global, the constraints of the method are also satisfied globally, but not locally. The effect is that the restoration is better achieved in some regions of the image than in others. To avoid this, we propose a variant of the TV restoration model including, instead of a single constraint λ, a set of constraints λi, each one corresponding to a region Oi of the image. We discuss the existence and uniqueness of solutions of the proposed model and display some numerical experiments.

Small Baseline Stereovision

Abstract This paper presents a study of small baseline stereovision. It is generally admitted that because of the finite resolution of images, getting a good precision in depth from stereovision demands a large angle between the views. In this paper, we show that under simple and feasible hypotheses, small baseline stereovision can be rehabilitated and even favoured. The main hypothesis is that the images should be band limited, in order to achieve sub-pixel precisions in the matching process. This assumption is not satisfied for common stereo pairs. Yet, this becomes realistic for recent spatial or aerian acquisition devices. In this context, block-matching methods, which had become somewhat obsolete for large baseline stereovision, regain their relevance. A multi-scale algorithm dedicated to small baseline stereovision is described along with experiments on small angle stereo pairs at the end of the paper.

Interpolation of digital elevation models using AMLE and related methods

Interpolation of digital elevation models becomes necessary in many situations, for instance, when constructing them from contour lines (available e.g., from nondigital cartography), or from disparity maps based on pairs of stereoscopic views, which often leaves large areas where point correspondences cannot be found reliably. The absolutely minimizing Lipschitz extension (AMLE) model is singled out as the simplest interpolation method satisfying a set of natural requirements. In particular, a maximum principle is proven, which guarantees not to introduce unnatural oscillations which is a major problem with many classical methods. The authors then discuss the links between the AMLE and other existing methods. In particular, they show its relation with geodesic distance transformation. They also relate the AMLE to the thin-plate method, that can be obtained by a prolongation of the axiomatic arguments leading to the AMLE, and addresses the major disadvantage of the AMLE model, namely its inability to interpolate slopes as it does for values. Nevertheless, in order to interpolate slopes, they have to give up the maximum principle and authorize the appearance of oscillations. They also discuss the possible link between the AMLE and Kriging methods that are the most widely used in the geoscience literature.

Measuring the Global Phase Coherence of an image

The Fourier phase spectrum of an image is well known to contain crucial information about the image geometry, in particular its contours. In this paper, we show that it is also strongly related to the image quality, in particular its sharpness. We propose a way to define the Global Phase Coherence (GPC) of an image, by comparing the likelihood of the image to the likelihood of all possible images sharing the same Fourier power spectrum. The likelihood is measured with the total variation (Rudin-Osher-Fatemi implicit prior), and the numerical estimation is realized by a Monte-Carlo simulation. We show that the obtained GPC measure decreases with blur, noise, and ringing, and thus provides a new interesting sharpness indicator, that can be used for parametric blind deconvolution, as demonstrated by experiments.

SPOT5 THR mode

SPOT Earth observation satellites are based upon the PUSH- BROOM acquisition principle whereby a CCD linear array acquires images row by row, perpendicularly to the satellite track, with columnwise displacement being generated by the satellites motion on its orbit.

Image deconvolution in mirror wavelet bases

Deconvolution in presence of additive noise is an inverse problem that often occurs in image processing. We introduce a restoration algorithm which is regularized with a thresholding technique, in an optimally designed mirror wavelet basis. We prove the asymptotic optimality and the superiority of this procedure over linear methods in the set of signals with bounded variations. Besides, this restoration procedure is fast, provides excellent metric and perceptual results and has been chosen as the best method by satellite images photointerpreters from the French space agency (CNES), among several different competing algorithms.

Restoration and Zoom of Irregularly Sampled, Blurred, and Noisy Images by Accurate Total Variation Minimization with Local Constraints

We propose an algorithm to solve a problem in image restoration which considers several different aspects of it, namely irregular sampling, denoising, deconvolution, and zooming. Our algorithm is b...

The Flutter Shutter Paradox

Photography is the art of acquiring as many photons as possible of a given scene. In classic cameras, the aperture time is irremediably limited by the risk of a motion blur when the camera and the scene are in relative motion. Nevertheless, two recent camera concepts, the Agrawal et al. flutter shutter and the Levin et al. motion-invariant photography permit one to extend indefinitely the exposure time while guaranteeing an invertible motion blur. In this paper, a complete mathematical theory of these new technologies is proposed. Modeling the capture noise, the theory furnishes explicit formulas for the signal to noise ratio

Constrained Anisotropic Diffusion and some Applications.

(SNR)