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: Procrustes Analysis (PA) has been a popular technique to align and build 2-D statistical models of shapes. Given a set of 2-D shapes PA is applied to remove rigid transformations. Then, a non-rigid 2-D model is computed by modeling (e.g., PCA) the residual. Although PA has been widely used, it has several limitations for modeling 2-D shapes: occluded landmarks and missing data can result in local minima solutions, and there is no guarantee that the 2-D shapes provide a uniform sampling of the 3-D space of rotations for the object. To address previous issues, this paper proposes Subspace PA (SPA). Given several
instances of a 3-D object, SPA computes the mean and a 2-D subspace that can simultaneously model all rigid and non-rigid deformations of the 3-D object. We propose a discrete (DSPA) and continuous (CSPA) formulation for SPA, assuming that 3-D samples of an object are provided. DSPA extends the traditional PA, and produces unbiased 2-D models by uniformly sampling different views of the 3-D object. CSPA provides a continuous approach to uniformly sample the space of 3-D rotations, being more efficient in space and time. Experiments using SPA to learn 2-D models of bodies from motion capture data illustrate the benefits of our approach.

Abstract: Magnetic resonance imaging (MRI) is unique in its ability to noninvasively and selectively alter tissue magnetization, and create tag planes intersecting image slices. The resulting grid of signal voids allows for tracking deformations of tissues in otherwise homogeneous-signal myocardial regions. In this paper, we propose a specific spatial modulation of magnetization (SPAMM) imaging protocol together with efficient techniques for measurement of three-dimensional (3-D) motion of material points of the human heart (referred to as myocardial beads) from images collected with the SPAMM method. The techniques make use of tagged images in orthogonal views by explicitly reconstructing 3-D B-spline surface representation of tag planes (tag planes in two orthogonal orientations intersecting the short-axis (SA) image slices and tag planes in an orientation orthogonal to the short-axis tag planes intersecting long-axis (LA) image slices). The developed methods allow for viewing deformations of 3-D tag surfaces, spatial correspondence of long-axis and short-axis image slice and tag positions, as well as nonrigid movement of myocardial beads as a function of time.