Mathematics

  2010 AUG 31 - (VerticalNews.com) -- "We describe here a method to compute the depth of a scene from a set of at least two images taken at known view-points. Our approach is based on an energy formulation of the 3D reconstruction problem which we minimize using a graph-cut approach that computes a local minimum whose energy is comparable (modulo a multiple constant) with the energy of the absolute minimum," investigators in Barcelona, Spain report ...read more

  2010 AUG 31 - (VerticalNews.com) -- According to recent research from Okayama, Japan, "A new numerical scheme is presented for computing strict maximum likelihood (ML) of geometric fitting problems having an implicit constraint. Our approach is orthogonal projection of observations onto a parameterized surface defined by the constraint."

  "Assuming a linearly separable nonlinear constraint, we show that a theoretically global solution can be obtained by iterative Sampson error minimization. Our approach is illustrated by ellipse fitting and fundamental matrix computation. Our method also encompasses optimal correction, computing, e.g., perpendiculars to an ellipse and triangulating stereo images," wrote K. Kanatani and colleagues, Okayama University ...read more

  2010 AUG 31 - (VerticalNews.com) -- "We propose and study quantitative measures of smoothness f bar right arrow A(f) which are adapted to anisotropic features such as edges in images or shocks in PDE's," researchers in Paris, France report.

  "These quantities govern the rate of approximation by adaptive finite elements, when no constraint is imposed on the aspect ratio of the triangles, the simplest example being A(p)(f) = parallel to root vertical bar det(d(2) f)vertical bar parallel to Lt which appears when approximating in the L-p norm by piecewise linear elements when 1/tau = 1/p + 1 The quantities A( f) are not semi-norms, and therefore cannot be used to define linear function spaces. We show that these quantities can be well defined by mollification when f has jump discontinuities along piecewise smooth curves," wrote J.M. Mirebeau and colleagues, University of Paris ...read more