An algebraic approach to Hough transforms

Recognition of feature curves on 3D shapes using an algebraic approach to Hough transforms

Feature curves are largely adopted to highlight shape features, such as sharp lines, or to divide surfaces into meaningful segments, like convex or concave regions. Extracting these curves is not sufficient to convey prominent and meaningful information about a shape. We have first to separate the curves belonging to features from those caused by noise and then to select the lines, which descri...

Representing Directions for Hough Transforms

Many algorithms in computer vision operate with directions, i. e. with representations of 3D-points by ignoring their distance to the origin. Even though minimal parametrizations of directions may contain singularities, they can enhance convergence in optimization algorithms and are required e. g. for accumulator spaces in Hough transforms. There are numerous possibilities for parameterizing di...

An algebraic approach to discrete dilations. Application to discrete wavelet transforms

We investigate the connections between continuous and discrete wavelet transforms on the basis of algebraic arguments. The discrete approach is formulated abstractly in terms of the action of a semidirect product A × Γ on `2(Γ), with Γ a lattice and A an abelian semigroup acting on Γ. We show that several such actions may be considered, and investigate those which may be written as deformations...

Generalized Hough Transforms with Flexible Templates

A Probabilistic Algorithm for Computing Hough Transforms

The Hough transform is a common technique in computer vision and pattern recognition for recognizing patterns of points. We describe an efficient probabilistic algorithm for a Monte-Carlo approximation to the Hough transform. Our algorithm requires substantially less computation and storage than the standard Hough transform when applied to patterns that are easily recognized by humans. The prob...