There are many applications that are not naturally based on the orthogonal co-ordinate systems, like ultrasound imaging, astronomy, mechanical computations etc. In many cases it is necessary to transform the problem formulation to the orthogonal co-ordinate system, where the problem is solved, transform the solution back and visualize the solution. The polar, spherical or cylindrical co-ordinat...

The conformal geometry of spacelike surfaces in 4-dimensional Lorentzian space forms has been studied by the authors in a previous paper, where the so-called polar transform was introduced. Here it is shown that this transform preserves spacelike conformal isothermic surfaces. We relate this new transform with the known transforms (Darboux transform and spectral transform) of isothermic surface...

Polar Cosine Transform (PCT) is one of the Polar Harmonic Transforms that those kernels are basic waves and harmonic in nature. They are proposed to represent invariant patterns for two dimensional image description and are demonstrated to show superiorities comparing with other methods on extracting rotation invariant patterns for images. However in order to increase the computation speed, fas...

This paper describes a hierarchical image registration algorithm for affine motion recovery. The algorithm estimates the affine transformation parameters necessary to register any two digital images misaligned due to rotation, scale, shear, and translation. The parameters are computed iteratively in a coarse-to-fine hierarchical framework using a variation of the Levenberg-Marquadt nonlinear le...

In this paper, polar and spherical Fourier Analysis are defined as the decomposition of a function in terms of eigenfunctions of the Laplacian with the eigenfunctions being separable in the corresponding coordinates. Each eigenfunction represents a basic pattern with the wavenumber indicating the scale. The proposed transforms provide an effective radial decomposition in addition to the well-kn...

Image registration has great significance in medicine, astrophotography and satellite imaging, so a lot of techniques have been developed within its perspective of one or the other discipline. This paper presents a method for medical image registration of multimodal brain images using Modified Adaptive Polar Transform (MAPT). This algorithm can be used to register images of the same or differen...

Space-variant sensing is the architectural basis of all higher vertebrate visual systems (Schwartz, 1994). One evident motivation for this is that the spacecomplexity of the human visual system is reduced by up to four orders of magnitude (Rojer and Schwartz, 1990) via the use of space-variant architecture (jar a given ratio of field width to maximum resolution). This observation has obvious pr...

This paper through Comparative analysis of This Discrete Polar Complex Exponential Transform approach is improved from traditional Polar Complex Exponential Transform (PCET) and this transform also encompasses the features of orthogonality and rotation invariance. We introduce a new 9×9 circle instead of a unit circle in DPCET to calculate features of image more precision. And various experimen...

In a wide range of applied problems of 2-D and 3-D imaging a continuous formulation of the problem places great emphasis on obtaining and manipulating the Fourier transform in Polar coordinates. However, the translation of continuum ideas into practical work with data sampled on a Cartesian grid is problematic. In this article we develop a fast high accuracy Polar FFT. For a given two-dimension...