Shape deformation analysis from the optimal control viewpoint

A crucial problem in shape deformation analysis is to determine a deformation of a given shape into another one, which is optimal for a certain cost. It has a number of applications in particular in medical imaging. In this article we provide a new general approach to shape deformation analysis, within the framework of optimal control theory, in which a deformation is represented as the flow of diffeomorphisms generated by time-dependent vector fields. Using reproducing kernel Hilbert spaces of vector fields, the general shape deformation analysis problem is specified as an infinite-dimensional optimal control problem with state and control constraints. In this problem, the states are diffeomorphisms and the controls are vector fields, both of them being subject to some constraints. The functional to be minimized is the sum of a first term defined as geometric norm of the control (kinetic energy of the deformation) and of a data attachment term providing a geometric distance to the target shape. This point of view has several advantages. First, it allows one to model general constrained shape analysis problems, which opens new issues in this field. Second, using an extension of the Pontryagin maximum principle, one can characterize the optimal solutions of the shape deformation problem in a very general way as the solutions of constrained geodesic equations. Finally, recasting general algorithms of optimal control into shape analysis yields new efficient numerical methods in shape deformation analysis. Overall, the optimal control point of view unifies and generalizes different theoretical and numerical approaches to shape deformation problems, and also allows us to design new approaches. The optimal control problems that result from this construction are infinite dimensional and involve some constraints, and thus are nonstandard. In this article we also provide a rigorous and complete analysis of the infinite-dimensional shape space problem with constraints and of its finite-dimensional approximations

Multiple Shape Registration using Constrained Optimal Control

Lagrangian particle formulations of the large deformation diffeomorphic metric mapping algorithm (LDDMM) only allow for the study of a single shape. In this paper, we introduce and discuss both a theoretical and practical setting for the simultaneous study of multiple shapes that are either stitched to one another or slide along a submanifold. The method is described within the optimal control formalism, and optimality conditions are given, together with the equations that are needed to implement augmented Lagrangian methods. Experimental results are provided for stitched and sliding surfaces

Deriving large-scale glacier velocities from a complete satellite archive : Application to the Pamir-Karakoram-Himalaya

International audienceMountain glaciers are pertinent indicators of climate change and their dynamics, in particular surface velocity change, is an essential climate variable. In order to retrieve the climatic signature from surface velocity, large-scale study of temporal trends spanning multiple decades is required. Satellite image feature-tracking has been successfully used to derive mountain glacier surface velocities, but most studies rely on manually selected pairs of images, which is not adequate for large datasets. In this paper, we propose a processing strategy to exploit complete satellite archives in a semi-automated way in order to derive robust and spatially complete glacier velocities and their uncertainties on a large spatial scale. In this approach, all available pairs within a defined time span are analysed, preprocessed to improve image quality and features are tracked to produce a velocity stack; the final velocity is obtained by selecting measures from the stack with the statistically higher level of confidence. This approach allows to compute statistical uncertainty level associated with each measured image pixel.This strategy is applied to 1536 pairs of Landsat 5 and 7 images covering the 3000 km long Pamir–Karakoram–Himalaya range for the period of 1999–2001 to produce glacier annual velocity fields. We obtain a velocity estimate for 76,000 km2 or 92% of the glacierized areas of this region. We then discuss the impact of coregistration errors and variability of glacier flow on the final velocity. The median 95% confidence interval ranges from 2.0 m/year on the average in stable areas and 4.4 m/year on the average over glaciers with variability related to data density, surface conditions and strain rate. These performances highlight the benefits of processing of a complete satellite archive to produce glacier velocity fields and to analyse glacier dynamics at regional scales

SCHATTEN MATRIX NORM BASED POLARIMETRIC SAR DATA REGULARIZATION. APPLICATION OVER CHAMONIX MONT-BLANC

International audienceThe paper addresses the filtering of Polarimetry Synthetic Aperture Radar (PolSAR) images. The filtering strategy is based on a regularizing cost function associated with matrix norms called the Schatten p-norms. These norms apply on matrix singular values. The proposed approach is illustrated upon scattering and coherency matrices on RADARSAT-2 PolSAR images over the Chamonix Mont-Blanc site. Several p values of Schatten p-norms are surveyed and their capabilities on filtering PolSAR images is provided in comparison with conventional strategies for filtering PolSAR data

Multi-Date Divergence Matrices for the Analysis of SAR Image Time Series

International audienceThe paper provides a spatio-temporal change detection framework for the analysis of image time series. In this framework, the detection of changes in time is addressed at the image level by using a matrix of cross-dissimilarities computed upon wavelet and curvelet image features. This makes possible identifying the acquisitions-of-interest: the acquisitions that exhibit singular behavior with respect to their neighborhood in the time series and those that are representatives of some stationary behavior. These acquisitions-of-interest are compared at the pixel level in order to detect spatial changes characterizing the evolution of the time series. Experiments carried out over ERS and TerraSAR-X time series highlight the relevancy of the approach for analyzing SAR image time series

Amplitude-Driven-Adaptive-Neighbourhood Filtering of High-Resolution Pol-InSAR Information

International audienceIn this paper a new method for fltering coherency matrices issued from Synthetic Aperture Radar (SAR) polarimetric interferometric data is presented. For each pixel of the interferogram, an adaptive neighborhood is determined by a region growing technique driven exclusively by the amplitude image information. All the available amplitude images of the interferometric couple are fused in the region growing process to ensure the stationarity hypothesis of the derived statistical population. In addition, for preserving local stationarity requirement of the interferogram, a phase compensation step is performed. Afterwards, all the pixels within the obtained adaptive neighborhood are complex averaged to yield the fltered values of the polarimetric and interferometric coherency matrices. The method has been tested on airborne high-resolution polarimetric interferometric SAR images (Oberpfaffenhofen area - German Space Agency). For comparison purposes, the standard phase compensated fixed multi-look flter and the linear adaptive coherence flter proposed by Lee at al. were also implemented. Both subjective and objective performance analysis, including coherence edge detection, ROC graph and bias reduction tables, recommends the proposed algorithm as a powerful post-processing POL-InSAR tool

Détection automatique de réseaux enterrés par imagerie géoradar

National audienceAfin d’améliorer la connaissance de l’existant et d’éviter l’endommagement d’ouvrages tiers au cours de travaux de voirie, la localisation des canalisations de gaz de manière non destructive est devenue un important domaine de recherche ces dernières années. Pour répondre à cette problématique, nous utilisons un géoradar. La forme de l’ensemble des réflexions ainsi que leurs intensités donnent une indication sur la nature de l’objet. Une forme hyperbolique indique la présence d’un objet "ponctuel" situé au niveau de son aplomb. Ainsi la détection d’hyperbolesdans le radargramme permet de localiser des canalisations. Dans ces travaux, nous proposons une méthode pour détecter automatiquement les hyperboles des données géoradar à partir d'un dictionnaire de formes théoriques et de deux modèles obtenus par apprentissage supervisé.Cette méthode montre des résultats quantitatifs intéressants et a été testée sur des données réelles

Application of the curvelet transform for pipe detection in GPR images

International audienceThis paper is dedicated to the detection of buried pipeswith a ground penetrating radar (GPR). The imagesfrom GPR acquisitions also called B-scan are corruptedby clutter and noise. In order to remove these undesirableitems we propose to use the properties of the curvelettransform. Were using this method as a first step of theautomatic detection of hyperbola in a B-scan

TEMPORAL ADAPTIVE FILTERING OF SAR IMAGE TIME SERIES BASED ON THE DETECTION OF STABLE AND CHANGE AREAS

International audienceThis paper presents a novel multitemporal filtering approach for Synthetic Aperture Radar (SAR) images. This is a temporal adaptive filter for a time series of SAR images based on coefficient of variation test to detect stable areas and change areas. The proposed approach is illustrated on a time series of 25 ascending TerraSAR-X images acquired from 11/06/2009 to 09/25/2011 over Chamonix-MontBlanc test-site which includes different kind of changes: parking occupation, glacier surface evolution, etc

Wavelet Operators and Multiplicative Observation Models -Application to SAR Image Time Series Analysis

International audienceThis paper first provides statistical properties of wavelet operators when the observation model can be seen as the product of a deterministic piece-wise regular function (signal) and a stationary random field (noise). This multiplicative observation model is analyzed in two standard frameworks by considering either (1) a direct wavelet transform of the model or (2) a log-transform of the model prior to wavelet decomposition. The paper shows that, in Framework (1), wavelet coefficients of the time series are affected by intricate correlation structures which blur signal singularities. Framework (2) is shown to be associated with a multiplicative (or geometric) wavelet transform and the multiplicative interactions between wavelets and the model highlight both sparsity of signal changes near singularities (dominant coefficients) and decorre-lation of speckle wavelet coefficients. The paper then derives that, for time series of synthetic aperture radar data, geometric wavelets represent a more intuitive and relevant framework for the analysis of smooth earth fields observed in the presence of speckle. From this analysis, the paper proposes a fast-and-concise geometric wavelet based method for joint change detection and regularization of synthetic aperture radar image time series. In this method, geometric wavelet details are first computed with respect to the temporal axis in order to derive generalized-ratio change-images from the time series. The changes are then enhanced and speckle is attenuated by using spatial block sigmoid shrinkage. Finally, a regularized time series is reconstructed from the sigmoid shrunken change-images. Some applications highlight relevancy of the method for the analysis of SENTINEL-1A and TerraSAR-X image time series over Chamonix-Mont-Blanc