This article discusses a method for blindly removing geometric distortions in taken images of rectangular planar patterns (such as maps, pictures, or posters) in the absence of any calibration information or explicit knowledge of the imaging device. Our approach removes lens distortion form single-view images. The method is based on Least-Square-Error (LSE) approximations and Hough transforms. ...

Affine moment invariants are widely used in pattern recognition and computer vision. The affine transform usually decomposed into a set of geometric transforms. The computation of these transforms relies on their relations with the geometric moments. Approximate computation of geometric moments produced a very large dynamic range that results in numerical instabilities. In this work, an exact m...

The use of traditional moment invariants is limited to a certain set of simple geometric transforms, such as rotation, scaling and affine transform. This paper presents a novel concept of so-called implicit moment invariants, which enable us to recognize objects under a broader set of geometric deformations.

This report present a non parametric matching method based on non parametric invariants to geometry and intensity transforms of images. The use of invariant makes it possible to match images under large geometric transforms. The use of non parametric measures makes it robust to partial occlusion. An algorithm to obtain sub-pixel precision is also shown. Results on real images validate the appro...

Geometric wavelet-like transforms for univariate and multivariate manifold-valued data can be constructed by means of nonlinear stationary subdivision rules which are intrinsic to the geometry under consideration. We show that in an appropriate vector bundle setting for a general class of interpolatory wavelet transforms, which applies to Riemannian geometry, Lie groups and other geometries, Hö...

We consider the problem of fast zeta and Möbius transforms in finite posets, particularly in lattices. It has previously been shown that for a certain family of lattices, zeta and Möbius transforms can be computed in O(e) elementary arithmetic operations, where e denotes the size of the covering relation. We show that this family is exactly that of geometric lattices. We also extend the algorit...

Intersection bodies represent a remarkable class of geometric objects associated with sections of star bodies and invoking Radon transforms, generalized cosine transforms, and the relevant Fourier analysis. We review some known facts and give them new proofs. The main focus is interrelation between generalized cosine transforms of different kinds and their application to investigation of certai...