arXiv subjects

Manoj Sahni

Publications and source records attributed to Manoj Sahni.

3 recordsLinked to original sources

arXiv2022

A Trio-Method for Retinal Vessel Segmentation using Image Processing

Inner Retinal neurons are a most essential part of the retina and they are supplied with blood via retinal vessels. This paper primarily focuses on the segmentation of retinal vessels using a triple preprocessing approach. DRIVE database was taken into consideration and preprocessed by Gabor Filtering, Gaussian Blur, and Edge Detection by Sobel and Pruning. Segmentation was driven out by 2 proposed U-Net architectures. Both the architectures were compared in terms of all the standard performance metrics. Preprocessing generated varied interesting results which impacted the results shown by the UNet architectures for segmentation. This real-time deployment can help in the efficient pre-processing of images with better segmentation and detection.

eess.IV↗

arXiv2021

Novel Results on Series of Floor and Ceiling Functions

In the following work, we first propose two (partial summation) formulas involving the floor and ceiling functions. We use principle of mathematical induction to prove the propositions. Another formula relating to the difference of floor and ceiling functions is deduced using aforementioned pair. Finally, in the same section, we propose generalisation of Faulhaber's formula without proof and deduce certain new results using the generalised results. Thereafter, we introduce F-Hurwitz and C-Hurwitz Zeta functions (infinite series involving floor and ceiling functions respectively) which can be considered as the generalizations of Hurwitz Zeta function. For both infinite series, there exist equivalent series and two distinct methods are used to prove the same. Certain new relations are deduced using new Zeta functions. Thereafter, it is shown that even if new deductions have poles at s=q, their differences at the same are convergent. Further some special cases are given for particular values of the Zeta functions. Lastly, certain open problems are provided which might be helpful for further advancements in the field.

math.GM↗

arXiv2018

Pythagorean fuzzy graphs: Some results

Graph theory has successfully used to solve a wide range of problems encountered in diverse fields such as medical sciences, neural networks, control theory, transportation, clustering analysis, expert systems, image capturing, and network security. In past few years, a number of generalizations of graph theoretical concepts have developed to model the impreciseness and uncertainties in graphical network problems. A Pythagorean fuzzy set is a powerful tool for describing the vague concepts more precisely. The Pythagorean fuzzy set-based models provide more flexibility in handling the human judgment information as compared to other fuzzy models. The objective of this paper is to apply the concept of Pythagorean fuzzy sets to graph theory. This work introduces the notion of Pythagorean fuzzy graphs (PFGs) and describes a number of methods for their construction. We then define some basic operations on PFGs and prove some of their important properties. The work also discusses the notion of isomorphism between Pythagorean fuzzy graphs with a numerical example. Further, we introduce the concept of the strong Pythagorean fuzzy graph and the complete Pythagorean fuzzy graph. In addition, the paper also proves some results on self-complementary, self-weak complementary with Pythagorean fuzzy strong graphs and Pythagorean fuzzy complete graphs.

math.GM↗