We consider a stochastic interpretation of textures composed of textural elements that may not obey any particular ordering relation between them. Two-dimensional Markov random fields (MRF) model is proposed to describe the stochastic character of texture patterns. For a fixed lattice we show how unhomogeneous textures can be described. We discuss the evidence of phase transitions in generating such textures. Distance relation based on joint entropy is proposed to measure the statistical interdependence between random variables assigned to the nodes of the two-dimensional network. The form of this function is shown to be suitable as an objective measure of phase transitions when distinct texture regions evolve while cooling "temperature". The examples of unhomogeneous (figure-ground) type of textures which we call generalized random stereograms are used to illustrate the model. We discuss the relevance of the model for generating texture patterns for neurophysiological experiments, psychophysical experiments and pattern recognition.<>
{"title":"A Markov random fields model for describing unhomogeneous textures: generalized random stereograms","authors":"Milan Jovovic","doi":"10.1109/VMV.1994.324984","DOIUrl":"https://doi.org/10.1109/VMV.1994.324984","url":null,"abstract":"We consider a stochastic interpretation of textures composed of textural elements that may not obey any particular ordering relation between them. Two-dimensional Markov random fields (MRF) model is proposed to describe the stochastic character of texture patterns. For a fixed lattice we show how unhomogeneous textures can be described. We discuss the evidence of phase transitions in generating such textures. Distance relation based on joint entropy is proposed to measure the statistical interdependence between random variables assigned to the nodes of the two-dimensional network. The form of this function is shown to be suitable as an objective measure of phase transitions when distinct texture regions evolve while cooling \"temperature\". The examples of unhomogeneous (figure-ground) type of textures which we call generalized random stereograms are used to illustrate the model. We discuss the relevance of the model for generating texture patterns for neurophysiological experiments, psychophysical experiments and pattern recognition.<<ETX>>","PeriodicalId":380649,"journal":{"name":"Proceedings of Workshop on Visualization and Machine Vision","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122863649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Flow visualization motivates to a large extent recent research efforts in scientific visualization. The continuous improvement of resources for data generation and analysis allows researchers and engineers to produce large multivariate 3D data sets with improving speed and accuracy. Analyzing and interpreting such datasets without appropriate tools is beyond the capability of the human brain. Scientific visualization and flow visualization in particular aim to provide such tools. The approach we advocate is to follow a visualization process involving data preprocessing, visualization mapping, and rendering. We address the issues related to the second step, namely visualization mappings of vector and tensor data in flow fields. We place this process in perspective to other fields of scientific study by taking the point of view of representation theory. This allows us to classify visualization techniques and to provide a unified framework for analyzing various vector and tensor mappings.<>
{"title":"Research issues in vector and tensor field visualization","authors":"L. Hesselink","doi":"10.1109/VMV.1994.324982","DOIUrl":"https://doi.org/10.1109/VMV.1994.324982","url":null,"abstract":"Flow visualization motivates to a large extent recent research efforts in scientific visualization. The continuous improvement of resources for data generation and analysis allows researchers and engineers to produce large multivariate 3D data sets with improving speed and accuracy. Analyzing and interpreting such datasets without appropriate tools is beyond the capability of the human brain. Scientific visualization and flow visualization in particular aim to provide such tools. The approach we advocate is to follow a visualization process involving data preprocessing, visualization mapping, and rendering. We address the issues related to the second step, namely visualization mappings of vector and tensor data in flow fields. We place this process in perspective to other fields of scientific study by taking the point of view of representation theory. This allows us to classify visualization techniques and to provide a unified framework for analyzing various vector and tensor mappings.<<ETX>>","PeriodicalId":380649,"journal":{"name":"Proceedings of Workshop on Visualization and Machine Vision","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122549429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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