Frédéric Champagnat

Dense optical flow by iterative local window registration

We study dense optical flow estimation using iterative registration of local window, also known as iterative Lucas-Kanade (LK) [B. Lucas et al, 1981]. We show that the usual iterative-warping scheme encounters divergence problems and propose a modified scheme with better behavior. It yields good results with a much lower cost than the exact dense LK algorithm, on simulated and real sequences.

A connection between half-quadratic criteria and EM algorithms

Iteratively Reweighted Least Squares (IRLS) and Residual Steepest descent (RSD) algorithms of robust statistics arise as special cases of half-quadratic schemes . Here, we adopt a statistical framework and we show that both algorithms are instances of the EM algorithm. The augmented dataset respectively involves a scale and a location mixture of Gaussians. The sufficient conditions for the construction cover a broad class of already known robust statistics.

Dense height map estimation from oblique aerial image sequences

We are concerned with dense height map reconstruction from aerial oblique image sequences. This configuration occurs when estimating a DSM (digital surface model) of areas where flying over is not allowed or for updating an on-board DSM, for instance, in trajectory planning with obstacle avoidance. We present a complete process starting from a partially calibrated sequence and leading to an estimated height map. The calibration step consists in refining the extrinsic parameters given by on-board ego-motion sensors (GPS and inertial measurement unit, IMU) by means of interest points tracking and bundle adjustment. We then propose a dense matching process based on the minimization of a multi-view pixelwise similarity criterion combined with a discretized L1-norm or total variation (TV) regularization term. Minimization is conducted thanks to an optimal graph-cut approach. Occlusions are accounted for without additional computational cost by a modification of the similarity criterion based on a dictionary of visibility patterns. Finally, two ways of refinement of the height map are proposed. The first one uses a local similarity minimization followed by non-linear Gaussian smoothing. The second relies on a novel approach to increase the height map resolution which combines multi-view 3-D reconstruction and image super-resolution. This method is validated on various synthetic and real aerial sequences, on either side-looking or forward-looking configurations.

Time-space regularization of the inverse problem of electrocardiography

Our goal is to reconstruct the epicardial potentials (EPs) from measured body surface potentials. This non-invasive technique is useful for the diagnostics of cardio-vascular diseases. In our approach, the time-correlation between EPs is used as the regularizing a priori information. This information is introduced via the state-space representation previously proposed. Our contribution is the derivation of maximum likelihood estimators for identification of the parameters of the state-space model, and in a second stage, for determination of the EPs. Therefore, all unknown quantities are determined from the only available data: the body surface potentials.

Point target detection and subpixel position estimation in optical imagery

We address the issue of distinguishing point objects from a cluttered background and estimating their position by image processing. We are interested in the specific context in which the objects signature varies significantly relative to its random subpixel location because of aliasing. The conventional matched filter neglects this phenomenon and causes a consistent degradation of detection performance. Thus alternative detectors are proposed, and numerical results show the improvement brought by approximate and generalized likelihood-ratio tests compared with pixel-matched filtering. We also study the performance of two types of subpixel position estimator. Finally, we put forward the major influence of sensor design on both estimation and point object detection.

Stationary Markov random fields on a finite rectangular lattice

This paper provides a complete characterization of stationary Markov random fields on a finite rectangular (non-toroidal) lattice in the basic case of a second-order neighborhood system. Equivalently, it characterizes stationary Markov fields on Z/sup 2/ whose restrictions to finite rectangular subsets are still Markovian (i.e., even on the boundaries). Until now, Pickard random fields formed the only known class of such fields. First, we derive a necessary and sufficient condition for Markov random fields on a finite lattice to be stationary. It is shown that their joint distribution factors in terms of the marginal distribution on a generic (2/spl times/2) cell which must fulfil some consistency constraints. Second, we solve the consistency constraints and provide a complete characterization of such measures in three cases. Symmetric measures and Gaussian measures are shown to necessarily belong to the Pickard class, whereas binary measures belong either to the Pickard class, or to a new nontrivial class which is further studied. In particular, the corresponding fields admit a simple parameterization and may be simulated in a simple, although nonunilateral manner.

Deconvolution of sparse spike trains accounting for wavelet phase shifts and colored noise

The problem of the restoration of spiky sequences when the usual convolution model is corrupted by nonstationary wavelet phase-shifts is addressed. To this end, an extended convolution model driven by a Bernoulli-Gaussian (BG)-like process is introduced. This setting lends itself to easy extension of algorithms designed for BG deconvolution. A comparison of practical results obtained with this new method and BG deconvolution is provided. Numerical experiments indicate an increased robustness compared with standard BG methods.<<ETX>>

Statistical performance modeling for superresolution: a discrete data-continuous reconstruction framework

We address performance modeling of superresolution (SR) techniques. Superresolution consists in combining several images of the same scene to produce an image with better resolution and contrast. We propose a discrete data-continuous reconstruction framework to conduct SR performance analysis and derive a theoretical expression of the reconstruction mean squared error (MSE) as a compact, computationally tractable function of signal-to-noise ratio (SNR), scene model, sensor transfer function, number of frames, interframe translation motion, and SR reconstruction filter. A formal expression for the MSE is obtained that allows a qualitative study of SR behavior. In particular we provide an original outlook on the balance between noise and aliasing reduction in linear SR. Explicit account for the SR reconstruction filter is an original feature of our model. It allows for the first time to study not only optimal filters but also suboptimal ones, which are often used in practice.

Passive depth estimation using chromatic aberration and a depth from defocus approach

In this paper, we propose a new method for passive depth estimation based on the combination of a camera with longitudinal chromatic aberration and an original depth from defocus (DFD) algorithm. Indeed a chromatic lens, combined with an RGB sensor, produces three images with spectrally variable in-focus planes, which eases the task of depth extraction with DFD. We first propose an original DFD algorithm dedicated to color images having spectrally varying defocus blurs. Then we describe the design of a prototype chromatic camera so as to evaluate experimentally the effectiveness of the proposed approach for depth estimation. We provide comparisons with results of an active ranging sensor and real indoor/outdoor scene reconstructions.

Single image local blur identification

We present a new approach for spatially varying blur identification using a single image. Within each local patch in the image, the local blur is selected between a finite set of candidate PSFs by a maximum likelihood approach. We propose to work with a Generalized Likelihood to reduce the number of parameters and we use the Generalized Singular Value Decomposition to limit the computing cost, while making proper image boundary hypotheses. The resulting method is fast and demonstrates good performance on simulated and real examples originating from applications such as motion blur identification and depth from defocus.