Thierry Gaidon

Pyramidal lattice vector quantization for multiscale image coding

Introduces a new image coding scheme using lattice vector quantization. The proposed method involves two steps: biorthogonal wavelet transform of the image, and lattice vector quantization of wavelet coefficients. In order to obtain a compromise between minimum distortion and bit rate, we must truncate and scale the lattice suitably. To meet this goal, we need to know how many lattice points lie within the truncated area. We investigate the case of Laplacian sources where surfaces of equal probability are spheres for the L(1) metric (pyramids) for arbitrary lattices. We give explicit generating functions for the codebook sizes for the most useful lattices like Z(n), D(n), E(s), wedge(16).

Optimal snake segmentation of target and background with independent Gamma density probabilities, application to speckled and preprocessed images

Abstract We propose in this paper a snake-based segmentation processor to track the shape of a target with random white intensity appearing on a random white spatially disjoint background. We study the optimal solution for Gamma laws and we discuss the relevance of such statistics for realistic situations. This algorithm, based on an active contour model (snakes), consists in correlations of a binary reference with the scene image or with pre-processed version of the scene image. This method is a generalization of correlation techniques and thus opens new applications for digital and optical correlators.

Motion estimation involving discontinuities in multiresolution scheme

A motion field estimation method for image sequence coding is presented. Motion vector field is estimated to remove the temporal redundancy between two successive images of a sequence. Motion estimation is an ill-posed inverse problem. Usually, the solution has been stabilized by regularization, as proposed by Tikhonov in 1963, i.e., by assuming a priori the smoothness of the solution. Here, discontinuities of the motion field are taken into account by using a Markov random field (MRF) model. Discontinuities, which unavoidably appear at the edges of a moving object, can be modeled by a continuous line process, as introduced by Geman and Reynolds in 1992, via a regularization function that belongs to the Φ function family. This line process leads to solutions less sensitive to noise than an all-or-nothing Boolean line process. Taking discontinuities into account leads to the minimization of a nonconvex functional to get the maximum a posteriori (MAP) optimal solution. We derive a new deterministic relaxation algorithm associated with the Φ function, to minimize the nonconvex criterion. We apply this algorithm in a coarse-to-fine multiresolution scheme, leading to more accurate results. We show results on synthetic and real-life sequences.

Motion estimation based on Markov random fields

This paper deals with a new method for estimation of motion field in image sequence coding domain. The proposed method is based on a pel-recursive technique and characterised by two fundamental points: the use of a convex function for the regularization and a deterministic relaxation algorithm for edge preserving regularization. These two points are completely new in motion estimation techniques.<<ETX>>

Edge detection using recursive biorthogonal wavelet transform

A new method of multiresolution edge detection is described. This method is based on a recursive biorthogonal wavelet transform which relates the digital filter to a continuous analysis function, the so-called wavelet. In biorthogonal wavelet analysis, there is a high-pass filter corresponding to the wavelet and a low-pass filter corresponding to the scaling function. The new idea is to compute optimal edge detection filters which yield multiresolution analysis (continuous wavelet). The high-pass filter (infinite impulse filter) is chosen in order to have first derivative properties. The family of low-pass filters is deduced from the high-pass filter using wavelet transform theory relations. The detection filters are proposed as a trade-off between detection, localization and regularity criteria.<<ETX>>

Statistical-based linear vessel structure detection in medical images

Linear structures such as blood vessels in medical images are important features for computer-aided diagnosis and follow-up of many diseases. In this letter a new tracking-based segmentation method is proposed to detect blood vessels in retinal angiorams. Bayesian segmentation with the Maximum a posteriori (MAP) Probability criterion is used for that purpose. First promising results are presented and discussed.

Adaptive entropy-constrained lattice vector quantization for multiresolution image coding

In many different fields, digitized images are replacing conventional analog images as photograph or X-rays. The volume of data required to describe such images greatly slows down transmission and makes storage prohibitively costly. The information contained in the images must therefore be compressed by extracting only the visible elements, which are then encoded. The quantity of data involved is thus substantially reduced. High compression rates can be achieved using wavelet transform and vector quantization (VQ) of wavelet coefficients subimages. In this paper, we propose a new scheme to vector quantize real Laplacian or generalized Gaussian sources using a multidimensional compandor and lattice vector quantization. We propose an approximation formula to compute the number of points contained in an n-dimensional hypercube--or truncated lattice when using uniform source data. We also propose an analytical expression for the distortion gain when a uniform source, rather than a Laplacian one, is quantized.

Non-additive noise and optimal correlation

The optimal detection and location of a target in a scene in presence of non-additive noise is studied. The optimal processors in the maximum likelihood sense are determined for different white or correlated noise statistics. It is shown that the required computations are mainly correlations, and that there is no need of iterative methods.

New Optimal Tracking Algorithms for Reference with Random Textures

The detection and location of a target in a scene is a classical problem, pervasive to many image processing applications. When the target appears on a low contrast background and the image is corrupted with additive gaussian noise, the optimal method is the matched filter [1]. However, the matched filter, as well as the improved linear filtering techniques [2] have been shown to perform poorly on many real-world images [3], because such images often do not belong to the class for which linear filtering is optimal.

Image sequence coding using quincunx wavelet transform, motion compensation, and lattice vector quantization

This paper is concerned with image sequence coding based on motion estimation-compensation using a pel-recursive technique. Motion estimation achieved by minimization of a functional is improved by the incorporation of a discontinuity constraint on the optical flow. The prediction errors are vector quantized using lattices. Recent work enabled us to use truncated lattices (D4, E8, L16, ...) in pyramidal form to construct the codebooks. The coding results were achieved on real sequence image.