This paper reports algorithms for computing the log-polar transform (LPT) of a digital image using optimal parameters for use in an active vision system. The LPT is a space-variant mapping similar in form to the human retina, with a central high-resolution fovea and a periphery of radially decreasing resolution. In the past, only cursory attention has been given to the selection of transform pa...

Problems of effective rapid and reliable CBIR (Content Based Image Retrieval) are discussed in the paper, generally concerning the so called “primary” CBIR, i.e. the image query by example into a large database of images of hallmark type. A novel Polar-Fourier-Wavelet transform (PFWT) is proposed herein, allowing both high invariance towards accidental input image rotation and low correlation a...

We consider the behavior of entropy of data elements as they are operated on by polar transforms. The data elements under consideration are pairs (X,Y ) where X is a binary random variable and Y is some side information about X . The entropy random variable for such a data element is defined as h(X|Y ) = − log pX|Y (X|Y ). The variance of entropy (varentropy) is defined as Var(h(X|Y )). A polar...

A critical examination is made of the somewhat loose and incomplete statement that a polar diagram is the Fourier transform of an aperture distribution. By aperture distribution it is necessary to understand, in the two-dimensional case, distribution across the aperture of the component along the aperture plane of the electromagnetic field in the plane of propagation. Furthermore, the concept o...

The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional informati...

There are many applications that are not naturally based on the orthogonal co-ordinate systems, like ultrasound imaging, astronomy, mechanical computations etc. In those 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-ordina...

Deep learning models have a large number of free parameters that must be estimated by efficient training of the models on a large number of training data samples to increase their generalization performance. In real-world applications, the data available to train these networks is often limited or imbalanced. We propose a sampling method based on the radial transform in a polar coordinate syste...

In this work, a novel robust image hashing scheme for image authentication is proposed based on the combination of the quaternion discrete Fourier transform (QDFT) with the log-polar transform. QDFT offers a sound way to jointly deal with the three channels of color images. The key features of the present method rely on (i) the computation of a secondary image using a log-polar transform; and (...

Symmetry detection in 3D images is an important task in many fields such as computer vision, pattern recognition to name a few. An algebraic based 3D symmetry detection algorithm is presented. The 3D volume is transformed to the Fourier domain by using the pseudo-polar Fourier transform. The pseudo-polar representation enables to analyze angular properties such as finite symmetric properties th...