Randomness and Geometric Features in Computer Vision - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports Year : 1996

Randomness and Geometric Features in Computer Vision

Xavier Pennec
Nicholas Ayache
  • Function : Author
  • PersonId : 833436


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.
Fichier principal
Vignette du fichier
RR-2820.pdf (838.13 Ko) Télécharger le fichier

Dates and versions

inria-00073871 , version 1 (24-05-2006)


  • HAL Id : inria-00073871 , version 1


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


Gmail Facebook Twitter LinkedIn More