Parametric Regression on the Grassmannian

We address the problem of fitting parametric curves on the Grassmann manifold for the purpose of intrinsic parametric regression. As customary in the literature, we start from the energy minimization formulation of linear least-squares in Euclidean spaces and generalize this concept to general nonflat Riemannian manifolds, following an optimal-control point of view. We then specialize this idea to the Grassmann manifold and demonstrate that it yields a simple, extensible and easy-to-implement solution to the parametric regression problem. In fact, it allows us to extend the basic geodesic model to (1) a time-warped variant and (2) cubic splines. We demonstrate the utility of the proposed solution on different vision problems, such as shape regression as a function of age, traffic-speed estimation and crowd-counting from surveillance video clips. Most notably, these problems can be conveniently solved within the same framework without any specifically-tailored steps along the processing pipeline.Comment: 14 pages, 11 figure

Side-View Face Recognition

Side-view face recognition is a challenging problem with many applications. Especially in real-life scenarios where the environment is uncontrolled, coping with pose variations up to side-view positions is an important task for face recognition. In this paper we discuss the use of side view face recognition techniques to be used in house safety applications. Our aim is to recognize people as they pass through a door, and estimate their location in the house. Here, we compare available databases appropriate for this task, and review current methods for profile face recognition

Tidal Torquing of Elliptical Galaxies in Cluster Environments

Observational studies of galaxy isophotal shapes have shown that galaxy orientations are anisotropic: a galaxy's long axis tends to be oriented toward the center of its host. This radial alignment is seen across a wide range of scales, from galaxies in massive clusters to small Milky Way type satellite systems. Recently, this effect has also been detected in dark matter simulations of cosmological structure, but the degree of alignment of dark matter substructures in these studies is significantly stronger than seen in observations. In this paper we attempt to reconcile these two results by performing high-resolution numerical experiments on N-body multi-component models of triaxial galaxies orbiting in an external analytical potential. The large number of particles employed allows us to probe deep into the inner structure of the galaxy: we show that the discrepancy between observed galaxies and simulated dark matter halos is a natural consequence of induced radial shape twisting in the galaxy by the external potential. The degree of twisting depends strongly on the orbital phase and eccentricity of the satellite, and it can, under certain conditions, be significant at radii smaller than the dark matter scale radius. Such internal misalignments will have important consequences, both for the dynamical evolution of the galaxy itself, and for mass modeling of galaxies in clustered environments.Comment: 19 pages, 22 figures, published in Ap