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Randomness and Geometric Features in Computer Vision

Xavier Pennec 1 Nicholas Ayache
1 EPIDAURE - Medical imaging and robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : It is often necessary to handle randomness and geometry in computer vision, for instance to match and fuse together noisy geometric features such as points, lines or 3D frames, or to estimate a geometric transformation from a set of matched features. However, the proper handling of these geometric features is far more difficult than for points, and a number of paradoxes can arise. We try to establish in this article the basic mathematical framework required to avoid them and analyze more specifically three basic problems: \begin{itemize} \item what is a random distribution of features, \item how to define a distance between features, \item and what is the «mean feature» of a number of feature measurements~? \end{itemize} We insist on the importance of an invariance hypothesis for these definitions relative to a group of transformations. We develop general methods to solve these three problems and illustrate them with 3D frame features under rigid transformations. The first problem has a direct application in the computation of the prior probability of false match in classical model-based object recognition algorithms, and we present experimental results of the two others for a data fusion problem: the statistical analysis of anatomical features (extremal points) automatically extracted on 24 three dimensional images of the head of a single patient. These experiments successfully confirm the importance of the rigorous requirements presented in this article.
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https://hal.inria.fr/inria-00073871
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Submitted on : Wednesday, May 24, 2006 - 1:57:22 PM
Last modification on : Friday, February 4, 2022 - 3:18:53 AM
Long-term archiving on: : Sunday, April 4, 2010 - 9:23:26 PM

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  • HAL Id : inria-00073871, version 1

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Xavier Pennec, Nicholas Ayache. Randomness and Geometric Features in Computer Vision. RR-2820, INRIA. 1996. ⟨inria-00073871⟩

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