Perception of Motion and Architectural Form: Computational Relationships between Optical Flow and Perspective

Perceptual geometry refers to the interdisciplinary research whose objectives focuses on study of geometry from the perspective of visual perception, and in turn, applies such geometric findings to the ecological study of vision. Perceptual geometry attempts to answer fundamental questions in perception of form and representation of space through synthesis of cognitive and biological theories of visual perception with geometric theories of the physical world. Perception of form, space and motion are among fundamental problems in vision science. In cognitive and computational models of human perception, the theories for modeling motion are treated separately from models for perception of form.Comment: 10 pages, 13 figures, submitted and accepted in DoCEIS'2012 Conference: http://www.uninova.pt/doceis/doceis12/home/home.ph

3D Reconstruction with Uncalibrated Cameras Using the Six-Line Conic Variety

We present new algorithms for the recovery of the Euclidean structure from a projective calibration of a set of cameras with square pixels but otherwise arbitrarily varying intrinsic and extrinsic parameters. Our results, based on a novel geometric approach, include a closed-form solution for the case of three cameras and two known vanishing points and an efficient one-dimensional search algorithm for the case of four cameras and one known vanishing point. In addition, an algorithm for a reliable automatic detection of vanishing points on the images is presented. These techniques fit in a 3D reconstruction scheme oriented to urban scenes reconstruction. The satisfactory performance of the techniques is demonstrated with tests on synthetic and real data

Reconstruction of algebraic-exponential data from moments

Let $G$ be a bounded open subset of Euclidean space with real algebraic boundary $\Gamma$. Under the assumption that the degree $d$ of $\Gamma$ is given, and the power moments of the Lebesgue measure on $G$ are known up to order $3d$, we describe an algorithmic procedure for obtaining a polynomial vanishing on $\Gamma$. The particular case of semi-algebraic sets defined by a single polynomial inequality raises an intriguing question related to the finite determinateness of the full moment sequence. The more general case of a measure with density equal to the exponential of a polynomial is treated in parallel. Our approach relies on Stokes theorem and simple Hankel-type matrix identities