Virginie Uhlmann

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We study the issue of localization in the context of isotropic wavelet frames. We define a variance-type measure of lo-calization and propose an algorithm based on calculus of variations to minimize this criterion under the constraint of a tight wavelet frame. Based on these calculations, we design the variance-optimal wavelet (VOW). Finally, we demonstrate(More)
We present a new exponential B-spline basis that enables the construction of active contours for the analysis of biomedical images. Our functions generalize the well-known polynomial Hermite B-splines and provide us with a direct control over the tangents of the parameterized contour, which is absent in traditional spline-based active contours. Our basis(More)
BACKGROUND The Human Protein Atlas (HPA) is an effort to map the location of all human proteins ( It contains a large number of histological images of sections from human tissue. Tissue micro arrays (TMA) are imaged by a slide scanning microscope, and each image represents a thin slice of a tissue core with a dark brown(More)
We propose a framework for the detection of junctions in images. Although the detection of edges and key points is a well examined and described area, the multiscale detection of junction centers, especially for odd orders, poses a challenge in pattern analysis. The goal of this paper is to build optimal junction detectors based on 2D steerable wavelets(More)
We propose a novel active contour for the analysis of filament-like structures and boundaries—features that traditional snakes based on closed curves have difficulties to delineate. Our method relies on a parametric representation of an open curve involving Hermite-spline basis functions. This allows us to impose constraints both on the contour and on its(More)
—Hermite splines are commonly used for interpolating data when samples of the derivative are available, in a scheme called Hermite interpolation. Assuming a suitable statistical model, we demonstrate that this method is actually optimal for reconstructing random signals in Papoulis' generalized sampling framework. We focus on second-order Lévy processes—the(More)
A crucial component of steerable wavelets is the radial profile of the generating function in the frequency domain. In this paper, we present an infinite-dimensional optimization scheme that helps us find the optimal profile for a given criterion over the space of tight frames. We consider two classes of criteria that measure the localization of the(More)