A New Class of Monotone/Convex Rational Fractal Function

This paper presents a description and analysis of a rational cubic spline FIF (RCSFIF) that has two shape parameters in each subinterval when it is defined implicitly. To be precise, we consider the iterated function system (IFS) with $q_n=\frac{P_n}{Q_n}$, $n \in \mathbb{N}_{N-1}$, where $P_n(x)$ are cubic polynomials to be determined through interpolatory conditions of the corresponding FIF and $Q_n(x)$ are preassigned quadratic polynomials each containing two free shape/rationality parameters. We establish the convergence of the proposed RCSFIF $g$ to the original function $\Phi \in \mathcal{C}^3(I)$ with respect to the uniform norm. We also provide the sufficient conditions for an automatic selection of the rational IFS parameters to preserve monotonicity and convexity of a prescribed set of data points. We consider some examples to illustrate the developed fractal interpolation scheme and its shape preserving aspects.Comment: 18 Pages, 18 Figures. arXiv admin note: text overlap with arXiv:1809.0820

An evolutionary computational based approach towards automatic image registration

Image registration is a key component of various image processing operations which involve the analysis of different image data sets. Automatic image registration domains have witnessed the application of many intelligent methodologies over the past decade; however inability to properly model object shape as well as contextual information had limited the attainable accuracy. In this paper, we propose a framework for accurate feature shape modeling and adaptive resampling using advanced techniques such as Vector Machines, Cellular Neural Network (CNN), SIFT, coreset, and Cellular Automata. CNN has found to be effective in improving feature matching as well as resampling stages of registration and complexity of the approach has been considerably reduced using corset optimization The salient features of this work are cellular neural network approach based SIFT feature point optimisation, adaptive resampling and intelligent object modelling. Developed methodology has been compared with contemporary methods using different statistical measures. Investigations over various satellite images revealed that considerable success was achieved with the approach. System has dynamically used spectral and spatial information for representing contextual knowledge using CNN-prolog approach. Methodology also illustrated to be effective in providing intelligent interpretation and adaptive resampling.Comment: arXiv admin note: substantial text overlap with arXiv:1303.671

An N-dimensional approach towards object based classification of remotely sensed imagery

Remote sensing techniques are widely used for land cover classification and urban analysis. The availability of high resolution remote sensing imagery limits the level of classification accuracy attainable from pixel-based approach. In this paper object-based classification scheme based on a hierarchical support vector machine is introduced. By combining spatial and spectral information, the amount of overlap between classes can be decreased; thereby yielding higher classification accuracy and more accurate land cover maps. We have adopted certain automatic approaches based on the advanced techniques as Cellular automata and Genetic Algorithm for kernel and tuning parameter selection. Performance evaluation of the proposed methodology in comparison with the existing approaches is performed with reference to the Bhopal city study area

A review over the applicability of image entropy in analyses of remote sensing datasets

Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability preference of these versions to specific operations.Comment: arXiv admin note: substantial text overlap with arXiv:1303.692

Cellular Automata based adaptive resampling technique for the processing of remotely sensed imagery

Resampling techniques are being widely used at different stages of satellite image processing. The existing methodologies cannot perfectly recover features from a completely under sampled image and hence an intelligent adaptive resampling methodology is required. We address these issues and adopt an error metric from the available literature to define interpolation quality. We also propose a new resampling scheme that adapts itself with regard to the pixel and texture variation in the image. The proposed CNN based hybrid method has been found to perform better than the existing methods as it adapts itself with reference to the image features

An investigation towards wavelet based optimization of automatic image registration techniques

Image registration is the process of transforming different sets of data into one coordinate system and is required for various remote sensing applications like change detection, image fusion, and other related areas. The effect of increased relief displacement, requirement of more control points, and increased data volume are the challenges associated with the registration of high resolution image data. The objective of this research work is to study the most efficient techniques and to investigate the extent of improvement achievable by enhancing them with Wavelet transform. The SIFT feature based method uses the Eigen value for extracting thousands of key points based on scale invariant features and these feature points when further enhanced by the wavelet transform yields the best results

A Comparative Analysis on the Applicability of Entropy in remote sensing

Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability preference of these versions to specific operations. Methodologies were implemented in Matlab and were enhanced with entropy variations. Evaluation of various implementations was based on different statistical parameters with reference to the study area The popular available versions like Tsalli's, Shanon's, and Renyi's entropies were analysed in context of various remote sensing operations namely thresholding, clustering and registration

Parameter Identification of Constrained Data by a New Class of Rational Fractal Function

This paper sets a theoretical foundation for the applications of the fractal interpolation functions (FIFs). We construct rational cubic spline FIFs (RCSFIFs) with quadratic denominator involving two shape parameters. The elements of the iterated function system (IFS) in each subinterval are identified befittingly so that the graph of the resulting $\mathcal{C}^1$-RCSFIF lies within a prescribed rectangle. These parameters include, in particular, conditions on the positivity of the $\mathcal{C}^1$-RCSFIF. The problem of visualization of constrained data is also addressed when the data is lying above a straight line, the proposed fractal curve is required to lie on the same side of the line. We illustrate our interpolation scheme with some numerical examplesComment: 16 pages, 9 Figures. Presented by Sangita Jha at International Conference on Mathematics and Computing, Haldia, January 17-21, 201

Bicubic partially blended rational quartic surface

This paper investigates some univariate and bivariate constrained interpolation problems using rational quartic fractal interpolation functions, which has been submitted long back in a reputed journal and revised as per the journal requirement. This research is extension of the work [S. K. Katiyar and A. K. B. Chand, Shape Preserving Rational Quartic Fractal Functions, Fractal, in Press]

One-magnon (electromagnon) light scattering in BiFeO3 single crystals

We observed Raman scattering from magnon in frequency range from 10 to 65 cm-1 in BiFeO3 single crystals at cryogenic temperatures; the temperature dependence of the magnon frequency at 18.2 cm-1 approximates an S=5/2 Brillouin function up to the temperature (280 K) at which the magnon becomes overdamped. The diverging cross-section and the frequency-shift at 140K and 200 K implies a magnon-reorientation transition as in orthoferrites. Magnons in polar materials such as BiFeO3 are often termed electromagnons meaning that they possess an electric dipole moment due to magnetoelectric coupling.Comment: 6 pages, 4 figure