Discrete Winner-take-all Competition Model And Its Application

Competition is a phenomenon widely existing in nature and society.Different fields focus on different research issues.The winner-take-all problem is widely used as a representative phenomenon in competition.At present,there are many complicated mathematical models at home and abroad for studying this phenomenon.Various neural networks are designed to implement this phenomenon and are applied to various fields,such as different engineering fields such as biological sciences,hardware circuits,and intelligent robots.However,we noticed that the image field is a field that is rarely involved in winner-take-all,and we can combine the competitive phenomenon with the image.This field is more worthy of our study.This paper first introduces the background and significance of the study of winner-takeall,the existing problems and our research topics,and elaborates on the phenomenon of winnertake-all and several different kinds of winner-take-all.Then the classic winner-take-all mathematical model and its significance,the winner-take-all phenomenon produced in different engineering fields,extracts a common problem from the existing problems in different fields,and finally we propose a discrete type of winner-take-all model represented by differential equation,which has multi-model options.Next,the validity and feasibility of the mathematical model are carefully proved from the balance point of the model,the local and global stability of the balance point.For this model,we design a numerical simulation experiment of static input competition and dynamic input competition to realize the winner-take-all phenomenon to verify the model,on the basis of this model,we design the model to be applied to the image experiment,we have carried out a number of different single-image experiments and multilayer edit-take-all image experiments to solve the problem of matrix segmentation of large images.Theoretical proof and experiments with a large amount of detailed data confirm the correctness and validity of our model.The main research results of this paper include discrete winner-take-all mathematical models and numerical simulation experiments under static and dynamic matrix data input,comparative experiments under different norms,single image processing,and multilayer winner-take-all processing.The large images are compared with the original algorithm's experiments.The results of numerical simulation and image experiments confirm the feasibility and correctness of the proposed model and better performance.