A pre-processing technique for image features extraction is presented in the paper. It is based on algebraic properties of image transform ψ that are invariant to a given geometrical transformation of an image. A vector space H of digital images is introduced. Image invariant is represented by a family of linear maps R. A linear transform ψ defined on a space of images H pertained to a given im...

Many stochastic processes are defined on special geometrical objects like spheres and cones. We describe how tools from harmonic analysis, i.e. Fourier analysis on groups, can be used to investigate probability density functions (pdfs) on groups and homogeneous spaces. We consider the special case of the Lorentz group SU(1,1) and the unit disk with its hyperbolic geometry, but the procedure can...

This paper presents a novel zero-watermarking scheme, which is robust to geometric distortions and common signal processes. Zero-watemarking technique is different from traditional digital image watermarking, which constructs watermark from its host image, instead of watermark inserting. We construct watermark from low-frequency coefficients in discrete wavelet transform (DWT) domain, which is ...

A statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear Schrödinger equation with arbitrary nonlinearity. It is shown that random phase fluctuations of an incoherent plane wave lead to a Landau-like damping effect, which can st...

In the companion paper 7] a grouping strategy with a rm geometrical underpinning and without the problem of combinatorics is proposed. It is based on the exploitation of structures that remain xed under the transformations that relate corresponding contour segments in regular patterns. In this paper we present a solution for the complementary task of extracting these xed structures in an eecien...

The dual-tree complex wavelet transform (DTCWT) is a relatively recent enhancement to the discrete wavelet transform (DWT), with beneficial properties such as shift invariant, good directionality, perfect reconstruction. These properties are well utilized to obtain improved robustness and perceptibility. Principle component analysis is used as a predictive model and is an excellent technique fo...

Shape analysis has played a central role in many problems in vision and perception, being an active multidisciplinary research field. In this context, this paper introduces a new shape analysis approach using the well known wavelet transform and exploring shape representation by landmarks. This work shows how to obtain a time signal from the landmarks representation, which undergoes the wavelet...

This paper shows that the continuous shearlet transform, a novel directional multiscale transform recently introduced by the authors and their collaborators, provides a precise geometrical characterization for the boundary curves of very general planar regions. This study is motivated by imaging applications, where such boundary curves represent edges of images. The shearlet approach is able to...

This paper proposes a new method for recognition of geometrical shapes (such as lines, circles or ellipsoids) in an image. The main idea is to transform the problem into a bounded error estimation problem and then to use an interval-based method which is robust with respect to outliers. The approach is illustrated on an image taken by an underwater robot where a spheric buoy has to be detected....

in the last two decade the use of aerial laser scanner (als) or lidar (light detection and ranging) sensor in geomatics engineering and surveying application has augmented significantly . the main reason of the mentioned phenomenon is the reliability and accuracy of the data obtained by lidar sensors. the output of lidar is unclassified 3d point cloud. classification of the lidar point clouds i...