A time scale is any closed subset of the real line. Continuous time and discrete time are special cases. The unilateral Laplace transform of a signal on a time scale subsumes the continuous-time unilateral Laplace transform, and the discretetime unilateral z-transform as special cases. The regions of convergence (ROCs) time scale Laplace transforms are determined by the time scale’s graininess....

The conchoid of a plane curve C is constructed using a fixed circle B in the affine plane. We generalize the classical definition so that we obtain a conchoid from any pair of curves B and C in the projective plane. We present two definitions, one purely algebraic through resultants and a more geometric one using an incidence correspondence in P × P. We prove, among other things, that the gener...

In this paper we introduce the continuous quaternion wavelet transform (CQWT). We express the admissibility condition in terms of the (right-sided) quaternion Fourier transform. We show that its fundamental properties, such as inner product, norm relation, and inversion formula, can be established whenever the quaternion wavelets satisfy a particular admissibility condition. We present several ...

We propose the -dimensional scale invariant feature transform ( -SIFT) method for extracting and matching salient features from scalar images of arbitrary dimensionality, and compare this method’s performance to other related features. The proposed features extend the concepts used for 2-D scalar images in the computer vision SIFT technique for extracting and matching distinctive scale invarian...

This paper proposes multirate signal processing methods for realizing Gaussian scale-space filtering. We introduce new computatiolly efficient interpolated Gaussian scale-space filters. Also, the use of decimators together with interpolated Gaussian filters is considered. The proposed filtering methods require dramatically less computation than conventional Gaussian scale-space filtering especi...

The SIFT algorithm produces keypoint descriptors. This paper analyzes that the SIFT algorithm generates the number of keypoints when we increase a parameter (number of sublevels per octave). SIFT has a good hit rate for this analysis. The algorithm was tested over a specific data set, and the experiments were conducted to increase the performance of SIFT in terms of accuracy and efficiency so a...

A unitary signal transformation that is covariant by translation to scale changes (di-lations and compressions) in the signal is formulated and justiied. Unlike the Mellin transform, which is invariant to scale changes, this new transform is a true indicator of the scale content of a signal.