Implementing a multi-model estimation method

This work is realized within the scope of a general attempt to understand parametric adaptation, regarding visual perception. The key idea is to analyze how we may use multi-model parametric estimation as a 1st step towards categorization. More generally, the goal is to formalize how the notion of ``objects'' or ``events'' in an application may be reduced to a choice in a hierarchy of parametric models used to estimate the underlying data categorization. These mechanisms are to be linked with what occurs in the cerebral cortex where object recognition corresponds to a parametric neuronal estimation (see for instanced Page 2000 for a discussion and Freedman et al 2001 for an example regarding the primate visual cortex). We thus hope to bring here an algorithmic element in relation with the ``grand-ma'' neuron modelization. We thus revisit the problem of parameter estimation in computer vision, presented here as a simple optimization problem, considering (i) non-linear implicit measurement equations and parameter constraints, plus (ii) robust estimation in the presence of outliers and (iii) multi-model comparisons. Here, (1) a projection algorithm based on generalizations of square-root decompositions allows an efficient and numerically stable local resolution of a set of non-linear equations. On the other hand, (2) a robust estimation module of a hierarchy of non-linear models has been designed and validated. A step ahead, the software architecture of the estimation module is discussed with the goal of being integrated in reactive software environments or within applications with time constraints.