[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-156470-105":59,"doc-detail-156470-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","heat-mapping-a-robust-approach-toward-perceptually-consistent-mesh-segmentation","Heat-Mapping: A Robust Approach Toward Perceptually Consistent Mesh Segmentation","","3D mesh segmentation is a foundational low-level task used across computer vision, computer-aided design, bio-informatics, and 3D medical imaging. The paper defines perceptually consistent mesh segmentation (PCMS) as segmentation invariant to isometric surface transforms, robust to surface perturbations, stable under numerical noise, and closely aligned with human perception. It introduces Heat-Mapping using heat kernels and a three-step pipeline: segment number estimation via Laplacian spectrum behavior, heat center discovery by a proposed algorithm, and heat-center-driven segmentation. Experiments on diverse models validate consistent segmentation of articulated bodies, topological changes, and varying noise levels.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/heat-mapping-a-robust-approach-toward-perceptually-consistent-mesh-segmentation/156470/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/heat-mapping-a-robust-approach-toward-perceptually-consistent-mesh-segmentation/156470.png","ImageObject",300,407,{"name":92,"@type":93},"Emma Wilson","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-09-19","2026-08-28",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does perceptually consistent mesh segmentation (PCMS) require?","Question",{"text":112,"@type":113},"PCMS satisfies invariance to isometric transformations, robustness to surface perturbations, robustness to numerical noise, and close conformation to human perception.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does Heat-Mapping estimate the number of segments?",{"text":117,"@type":113},"It analyzes the behavior of the Laplacian spectrum to estimate the segment count before performing the remaining steps.",{"name":119,"@type":110,"acceptedAnswer":120},"What are the main steps in the Heat-Mapping pipeline?",{"text":121,"@type":113},"Heat-Mapping (1) estimates segment numbers from the Laplacian spectrum, (2) finds a heat center per segment using a heat center hunting algorithm, and (3) performs a heat center driven segmentation to achieve PCMS.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},156470,1787959517,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":39,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":46},3848291630094,"https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Heat-Mapping: A Robust Approach Toward Perceptually Consistent Mesh  \nSegmentation  \nYi Fang Purdue University West Lafayette, IN 47907  \n[fang4@purdue.edu](fang4@purdue.edu)  \nMengtian Sun Purdue University West Lafayette, IN 47907  \n[sun84@purdue.edu](sun84@purdue.edu)  \nMinhyong Kim University of College London Gower Street, London WCIE, UK  \n[minhyong.kim@ucl.ac.uk](minhyong.kim@ucl.ac.uk)  \nKarthik Ramani Purdue University West Lafayette, IN 47907  \n[ramani@purdue.edu](ramani@purdue.edu)  \nAbstract  \n3D mesh segmentation is a fundamental low-level task with applications in areas as diverse as computer vision, computer-aided design, bio-informatics, and 3D medical imaging. A perceptually consistent mesh segmentation (PCMS), as de􀀂ned in this paper is one that satis􀀂es 1) invariance to isometric transformation of the underlying surface, 2) robust to the perturbations of the surface, 3) robustness to numerical noise on the surface, and 4) close conformation to human perception. We exploit the intelligence of the heat as a global structure-aware message on ameshed surface and develop a robust PCMS scheme, called Heat-Mapping based on the heat kernel. There are three main steps in Heat-Mapping. First, the number of the segments is estimated based on the analysis of the behavior of the Laplacian spectrum. Second, the heat center, which is de􀀂ned as the most representative vertex on each segment, is discovered by a proposed heat center hunting algorithm. Third, a heat center driven segmentation scheme reveals the PCMS with a high consistency towards human perception. Extensive experimental results on various types of models verify the performance of Heat-Mapping with respect to the consistent segmentation of articulated bodies, the topological changes, and various levels of numerical noise.  \n1. Introduction  \n1.1. Background  \nIn recent years, we have seen an explosive growth of the available 3D model data across a variety of 􀀂elds, such as reverse engineering and 3D medical imaging, with the development of the acquisition techniques [1, 23, 20, 16, 15, 8,  \n7, 5, 10, 18] . We are therefore faced with an ever-increasing demand for approaches towards automatic model processing, understanding and analysis. As a 􀀂rst important step of mesh model processing, the segmentation of a model into a small number of meaningful components is dif􀀂cult. A segmentation approach likely confronts the problems of 1) isometrically-variant segmentation of the surface, 2) sensitivity to topological perturbations of the surface, 3) sensitivity to numerical noise inherently embedded within observed models, and 4) inconsistency with human understanding of segmentation. We de􀀂ne a segmentation, which can robustly provide a solution to the above four challenges above, as the perceptually consistent mesh segmentation (PCMS) . Over the past several years, the integrated characteristics of PCMS has become more important for advanced mesh processing and understanding as it provides more insights into mesh models [8, 16, 23, 25] . PCMS facilitates the interpretation of 3D surface meshes in terms of either a pure geometric sense, semantic information or both through the representation of an intrinsically hidden geometric structure of the meshes. The intrinsic interpretation of the structure is able to partition the objects into a number of functional components in a way close to human understanding. Compared to ongoing 3D segmentation, PCMS is much more adequate to analyze the features of models, enabling diverse applications to modeling. This includes 3D shape (or partial shape) matching, skeleton extraction, texture mapping, simpli􀀂cation, parameterization and shape retrieval [7, 13, 8, 24] .  \n1.2. Brief review of related works  \nSome studies have addressed how the mesh surface can be decomposed into perceptually meaningful units in an au-  \ntomatic or semi-automatic way [8, 16, 23, 25] . The outreaching goal of a robust PCMS is to perform it on a model in ","cbCaioRJZV7mB5IS","https://ap.wps.com/l/cbCaioRJZV7mB5IS","pdf",5006887,"English","# Abstract\n# Introduction\n## Background\n## Brief review of related works","[{\"question\":\"What does perceptually consistent mesh segmentation (PCMS) require?\",\"answer\":\"PCMS satisfies invariance to isometric transformations, robustness to surface perturbations, robustness to numerical noise, and close conformation to human perception.\"},{\"question\":\"How does Heat-Mapping estimate the number of segments?\",\"answer\":\"It analyzes the behavior of the Laplacian spectrum to estimate the segment count before performing the remaining steps.\"},{\"question\":\"What are the main steps in the Heat-Mapping pipeline?\",\"answer\":\"Heat-Mapping (1) estimates segment numbers from the Laplacian spectrum, (2) finds a heat center per segment using a heat center hunting algorithm, and (3) performs a heat center driven segmentation to achieve PCMS.\"}]","Heat-Mapping: A Robust Approach Toward Perceptually Consistent Mesh Segmentation | PDF"]