Projective Fourier analysis for patterns

Projective Fourier analysis for patterns

Identifying PSL(2,C) as a projective group for patterns in the conformal camera model, the projective harmonic analysis on its double covering group SL(2,C) is presented in the noncompact and compact pictures–the pictures used to study different aspects of irreducible unitary representations of semisimple Lie groups. Bypassing technicalities of representation theory, but stressing the motivatio...

Projective Fourier Analysis in Computer Vision: Theory and Computer Simulations

Identifying the projective group for patterns by developing the camera model, the projective Fourier transform and its inverse are obtained in analogy with the classical, that is, Euclidean Fourier analysis. Projectively adapted properties are demonstrated in a numerical test. Using the expression of the projective Fourier integral by a standard Fourier integral in the coordinates given by the ...

Analysis and synthesis of motion patterns using the projective plane

We first review theoretical results for the problem of estimating single and multiple transparent motions. For N motions we obtain a M×M generalized structure tensor JN with M = 3 for one, M = 6 for two, and M = 10 for three motions. The analysis of motion patterns is based on the ranks of JN and is thus not only conceptual but provides computable confidence measures for the different types of ...

Fourier Analysis of Conservation Patterns in Protein Secondary Structure

Residue conservation is a common observation in alignments of protein families, underscoring positions important in protein structure and function. Though many methods measure the level of conservation of particular residue positions, currently we do not have a way to study spatial oscillations occurring in protein conservation patterns. It is known that hydrophobicity shows spatial oscillation...

Projective Geometry for Image Analysis