arXiv subjects

Adrien Wohrer

Publications and source records attributed to Adrien Wohrer.

3 recordsLinked to original sources

arXiv2025

Diffeomorphic ICP Registration for Single and Multiple Point Sets

We propose a generalization of the iterative closest point (ICP) algorithm for point set registration, in which the registration functions are non-rigid and follow the large deformation diffeomorphic metric mapping (LDDMM) framework. The algorithm is formulated as a well-posed probabilistic inference, and requires to solve a novel variation of LDDMM landmark registration with an additional term involving the Jacobian of the mapping. The algorithm can easily be generalized to construct a diffeomorphic, statistical atlas of multiple point sets. The method is successfully validated on a first set of synthetic data.

eess.SP↗

arXiv2019

Ising distribution as a latent variable model

During the past decades, the Ising distribution has attracted interest in many applied disciplines, as the maximum entropy distribution associated to any set of correlated binary (`spin') variables with observed means and covariances. However, numerically speaking, the Ising distribution is unpractical, so alternative models are often preferred to handle correlated binary data. One popular alternative, especially in life sciences, is the Cox distribution (or the closely related dichotomized Gaussian distribution and log-normal Cox point process), where the spins are generated independently conditioned on the drawing of a latent variable with a multivariate normal distribution. This article explores the conditions for a principled replacement of the Ising distribution by a Cox distribution. It shows that the Ising distribution itself can be treated as a latent variable model, and it explores when this latent variable has a quasi-normal distribution. A variational approach to this question reveals a formal link with classic mean-field methods, especially Opper and Winther's adaptive TAP approximation. This link is confirmed by weak coupling (Plefka) expansions of the different approximations and then by numerical tests. Overall, this study suggests that an Ising distribution can be replaced by a Cox distribution in practical applications, precisely when its parameters lie in the `mean-field domain'.

cond-mat.dis-nn↗

arXiv2013

Percept formation from neural populations in sensory decision-making tasks

We study a standard linear readout model of perceptual integration from a population of sensory neurons. We show that the readout can be associated to a set of characteristic equations which summarize the joint trial-to-trial covariance structure of neural activities and animal percept. These characteristic equations implicitly determine the readout parameters that were used by the animal to create its percept. In particular, they implicitly constrain the temporal integration window w and the typical number of neurons K which give rise to the percept. Comparing neural and behavioral sensitivity alone cannot disentangle these two sources of perceptual integration, so the characteristic equations also involve a measure of choice signals, like those assessed by the classic experimental measure of choice probabilities. We then propose a statistical method of analysis which allows to recover the typical scales of integration w and K from finite numbers of recorded neurons and recording trials, and show the efficiency of this method on an artificial encoding network. We also study the statistical method theoretically, and relate its laws of convergence to the underlying structure of neural activity in the population, as described through its singular value decomposition. Altogether, our method provides the first thorough interpretation of feedforward percept formation from a population of sensory neurons. It can readily be applied to experimental recordings in classic sensory decision-making tasks, and hopefully provide new insights into the nature of perceptual integration.

q-bio.NC↗