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S. K. Katiyar

Publications and source records attributed to S. K. Katiyar.

12 recordsLinked to original sources
arXiv2025

Constrained Quantization for Uniform Distributions with Two Constraint Families

In this paper, we first consider a family of constraints given by straight lines. For a uniform probability distribution, we determine the constrained optimal sets of $n$-points and the corresponding $n$th constrained quantization errors for all positive integers $n$. In addition, we calculate the constrained quantization dimension and the constrained quantization coefficient with respect to this family of constraints. Next, we turn to another family of constraints, consisting of concentric circles. For the same probability distribution, we present a methodology to compute the constrained optimal sets of $n$-points and the corresponding $n$th constrained quantization errors for all positive integers $n$. Finally, we conclude the paper with a summary of the results and a discussion of future research directions.

math.PR↗
arXiv2025

Optimal Sets and Quantization Errors under Geometric Constraints for Discrete Distributions

This paper presents a detailed study of constrained quantization for both finite and infinite discrete probability distributions supported on subsets of the real line. Under specific geometric constraints - namely, a semicircular arc and the union of two sides of an equilateral triangle - we compute constrained optimal sets of $n$-points and the corresponding $n$th constrained quantization errors. For finite discrete distributions, we consider both uniform and nonuniform cases with support on $\{-3, -2, \dots, 3\}$. For infinite discrete distributions, two cases are analyzed: one supported on $\left\{ \frac{1}{n} : n \in \mathbb{N} \right\}$ and the other on the set of natural numbers $\mathbb{N}$. Explicit constructions and numerical computations of optimal quantizers and errors are provided. Furthermore, for the infinite discrete distribution supported on $\mathbb{N}$, we develop a general framework for constrained quantization under the linear constraint $y = mx + c$ and prove that the constrained quantization dimension in this setting is zero. Our results highlight how geometric constraints influence the structure and existence of optimal quantizers and pave the way for further investigations into constrained quantization theory.

math.PR↗
arXiv2019

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].

math.NA↗
arXiv2018

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 $Φ\in \mathcal{C}^3(I)$ 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.

math.DS↗
arXiv2018

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 examples

math.NA↗
arXiv2014

Comparative analysis of common edge detection techniques in context of object extraction

Edges characterize boundaries and are therefore a problem of practical importance in remote sensing.In this paper a comparative study of various edge detection techniques and band wise analysis of these algorithms in the context of object extraction with regard to remote sensing satellite images from the Indian Remote Sensing Satellite (IRS) sensors LISS 3, LISS 4 and Cartosat1 as well as Google Earth is presented.

cs.CV↗
arXiv2014

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.

cs.CV↗
arXiv2014

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.

cs.CV↗
arXiv2014

An enhanced neural network based approach towards object extraction

The improvements in spectral and spatial resolution of the satellite images have facilitated the automatic extraction and identification of the features from satellite images and aerial photographs. An automatic object extraction method is presented for extracting and identifying the various objects from satellite images and the accuracy of the system is verified with regard to IRS satellite images. The system is based on neural network and simulates the process of visual interpretation from remote sensing images and hence increases the efficiency of image analysis. This approach obtains the basic characteristics of the various features and the performance is enhanced by the automatic learning approach, intelligent interpretation, and intelligent interpolation. The major advantage of the method is its simplicity and that the system identifies the features not only based on pixel value but also based on the shape, haralick features etc of the objects. Further the system allows flexibility for identifying the features within the same category based on size and shape. The successful application of the system verified its effectiveness and the accuracy of the system were assessed by ground truth verification.

cs.CV↗
arXiv2013

An intelligent approach towards automatic shape modeling and object extraction from satellite images using cellular automata based algorithm

Automatic feature extraction domain has witnessed the application of many intelligent methodologies over past decade; however detection accuracy of these approaches were limited as object geometry and contextual knowledge were not given enough consideration. In this paper, we propose a frame work for accurate detection of features along with automatic interpolation, and interpretation by modeling feature shape as well as contextual knowledge using advanced techniques such as SVRF, Cellular Neural Network, Core set, and MACA. 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 CNN approach. CNN has been effective in modeling different complex features effectively and complexity of the approach has been considerably reduced using corset optimization. The system has dynamically used spectral and spatial information for representing contextual knowledge using CNN-prolog approach. System has been also proved to be effective in providing intelligent interpolation and interpretation of random features.

cs.CV↗
arXiv2013

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.

cs.CV↗