This paper makes use of the continuous eccentricity transform to perform shape matching. The eccentricity transform has already been proven useful in a discrete graph-theoretic setting. We show how these ideas extend naturally to the continuous setting thus bringing a higher geometrical fidelity. The continuous eccentricity transform is used to compute multiscale descriptors for shapes. These d...

A special member of the emerging family of multiscale geometric transforms is the curvelet transform which was developed in the last few years in an attempt to overcome inherent limitations of traditional multistage representations such as wavelets. Mathematical is a set and lattice theoretic methodology for image analysis, which aims at quantitatively describing the geometrical structure of im...

A method for derivation of inversion formulas for the Radon transform of f (x) is given. This method allows one to construct functions ψ(x) which are easy to compute and which have the same wave fronts as f (x). This, in turn, allows one to calculate the singular support S of f (x) by computing ψ(x) given tomographic data. A simple geometrical relation between the singular supports of f andˆf ,...

The continuous curvelet and shearlet transforms have recently been shown to be much more effective than the traditional wavelet transform in dealing with the set of discontinuities of functions and distributions. In particular, the continuous shearlet transform has the ability to provide a very precise geometrical characterization of general discontinuity curves occurring in images. In this pap...

The contourlet transform has the benefit of efficiently capturing the oriented geometrical structures of images. In this paper, by incorporating the ideas of Stein’s Unbiased Risk Estimator (SURE) approach in Nonsubsampled Contourlet Transform (NSCT) domain, a new image denoising technique is devised. We utilize the characteristics of NSCT coefficients in high and low subbands and apply SURE sh...

The paper presents a registration algorithm based on the Analytical Fourier-Mellin Transform (AFMT). In the Fourier Mellin registration algorithm, the estimation of the geometrical transformation is only done in the Fourier Transform phase domain which is known by containing the shape information. The proposed algorithm will be used to estimate homography since in the vicinity of key points, we...

The most existing digital watermarking methods were robust to general attacks such as additive noise, image filtering, JPEG compression and so on, but resisting to geometric attacks is still a difficult challenge. This paper proposed a watermarking algorithm resisting to geometrical attacks. The Radon transform was employed to project two dimension image onto projection space. Then the rotation...

A new image denoising method based on curvelet transform is proposed. The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. Here, we pursue "true" two-dimensional transform that can capture the intrinsic geometrical structure that is key in visual information. Deno...