Abstract: In this work, we propose a probabilistic approach for the detection and the
tracking of particles on biological images. In presence of very noised and poor
quality data, particles and trajectories can be characterized by an a-contrario
model, that estimates the probability of observing the structures of interest
in random data. This approach, first introduced in the modeling of human visual
perception and then successfully applied in many image processing tasks, leads
to algorithms that do not require a previous learning stage, nor a tedious
parameter tuning and are very robust to noise. Comparative evaluations against
a well established baseline show that the proposed approach outperforms the
state of the art.

Abstract: Otolith end organs of vertebrates sense linear accelerations of the head and gravitation. The hair cells on their epithelia are responsible for transduction. In mammals, the striola, parallel to the line where hair cells reverse their polarization, is a narrow region centered on a curve with curvature and torsion. It has been shown that the striolar region is functionally different from the rest, being involved in a phasic vestibular pathway. We propose a mathematical and computational model that explains the necessity of this amazing geometry for the striola to be able to carry out its function. Our hypothesis, related to the biophysics of the hair cells and to the physiology of their afferent neurons, is that striolar afferents collect information from several type I hair cells to detect the jerk in a large domain of acceleration directions. This predicts a mean number of two calyces for afferent neurons, as measured in rodents. The domain of acceleration directions sensed by our striolar model is compatible with the experimental results obtained on monkeys considering all afferents. Therefore, the main result of our study is that phasic and tonic vestibular afferents cover the same geometrical fields, but at different dynamical and frequency domains.

Abstract: Cone regression is a particular case of quadratic programming that minimizes a weighted sum of squared residuals under a set of linear inequality constraints. Several important statistical problems such as isotonic, concave regression or ANOVA under partial orderings, just to name a few, can be considered as particular instances of the cone regression problem. Given its relevance in Statistics, this paper aims to address the fundamentals of cone regression from a theoretical and practical point of view. Several formulations of the cone regression problem are considered and, focusing on the particular case of concave regression as an example, several algorithms are analyzed and compared both qualitatively and quantitatively through numerical simulations. Several improvements to enhance numerical stability and bound the computational cost are proposed. For each analyzed algorithm, the pseudo-code and its corresponding code in Matlab are provided. The results from this study demonstrate that the choice of the optimization approach strongly impacts the numerical performances. It is also shown that methods are not currently available to solve efficiently cone regression problems with large dimension (more than many thousands of points). We suggest further research to fill this gap by exploiting and adapting classical multi-scale strategy to compute an approximate solution.