[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82526-en":3,"doc-seo-82526-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},82526,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1782698725881665579",8,"Research & Report","GenSP Consistent Spherical Parameterization via Learning Shape Generative Models","GenSP presents a data-driven framework for learning consistent spherical parameterizations across a dataset of genus-0 shapes. Instead of computing parameterizations independently for each shape, GenSP trains a neural generative model that predicts a continuous mapping from the unit sphere to shapes, with spherical parameterizations derived from the inverse of the learned generator. The method uses a continuous neural deformation model, intermediate shape augmentation, and latent-space spanning-tree correspondence propagation. Experiments on ShapeNet show reduced geometric distortion and improved cross-shape consistency versus existing approaches.","arXiv :2607 .00492v 1 [ cs .CV] 1 Jul 2026  \nGenSP: Consistent Spherical Parameterization via Learning Shape Generative Models  \nSai Karthikey Pentapati 1⋆, Shashank Gupta 1⋆, Rajesh Sureddi 1 , Yuezhi Yang 1 ,  \nAlan C. Bovik2 , and Qixing Huang 1  \n1 The University of Texas at Austin  \n{ps.karthik,[shashank.gupta}@utexas.edu](shashank.gupta}@utexas.edu)  \n2 University of Colorado Boulder  \nAbstract. We introduce GenSP, a data-driven framework that learns consistent spherical parameterizations across a collection of genus-0 shapes.  \nInstead of optimizing the parameterization of each shape independently, our method learns a neural generative model that predicts a continuous mapping from the unit sphere to shapes in a dataset. Under this formulation, spherical parameterizations are obtained through the inverse mappings of the learned generator, which encourages similar shapes to share consistent parameterizations. To make this formulation practical, we address several key challenges in learning such a generative model.  \nFirst, we introduce a continuous neural deformation model that predicts surface points from sphere coordinates and latent shape codes, avoiding discretization artifacts common in mesh-based formulations. Second, we augment the training space with intermediate shapes that bridge the sphere and input shapes, allowing the model to learn meaningful deformations across a heterogeneous shape collection. Third, we compute reliable initial correspondences by propagating mappings along a spanning tree of training shapes in the latent space. Experiments on the ShapeNet [10] dataset demonstrate that our approach significantly reduces geometric distortion and improves cross-shape consistency compared with state-of-the-art spherical parameterization methods.  \nKeywords: Spherical Parameterization, Neural Geometry Processing, Generative Models.  \n1 Introduction  \nComputing spherical parameterizations of genus-0 surfaces is a fundamental problem in geometry processing and visual computing [27, 44, 52, 62] . Given agenus-0 surface, spherical parameterization computes a bijective mapping between the surface and the unit sphere, providing a canonical domain for applications such as texture transfer, shape correspondence, and geometric analysis. Compared with planar parameterization methods that map surfaces to the UV plane, spherical parameterization does not require cutting the surface. Such cuts introduce discrete optimization decisions that are difficult to solve and often lead  \n⋆ Equal contribution.  \n2 S.K. Pentapati et al.  \nFig. 1: Comparison of spherical parameterizations with existing approaches.  \nA texture defined on an icosphere is mapped onto each shape through the spherical parameterization to visualize the consistency of the mappings across shapes. Existing approaches either produce inconsistent parameterizations across shapes (SMAT [50], AHSP [28]) or exhibit high geometric distortion in thin or high-curvature regions (CMCF [33]) . In contrast, GenSP produces consistent, feature-preserving and accurate parameterizations across the shape collection.  \nto additional distortion in the parameterization. Most existing approaches [22,47] compute spherical parameterizations for each surface independently. However, a fundamental challenge is that there exist infinitely many spherical parameterizations for a genus-0 surface. Even when the mapping is restricted to be conformal, the space of valid parameterizations forms a Möbius group [37] . As a result, two geometrically similar shapes may obtain very different parameterizations when using existing methods, as shown in Figure 1 .  \nIn this paper, we introduce a data-driven approach for computing consistent spherical parameterizations across a collection of genus-0 shapes. Our approach learns a generative model that continuously deforms the unit sphere to each shape in the dataset. Under this formulation, spherical parameterizations arise naturally as the inverse mapping","cbCaidM8RYsqEKL3","https://ap.wps.com/l/cbCaidM8RYsqEKL3","pdf",19025716,4,1,29,"English","en",105,"# Introduction\n## Spherical parameterization as a canonical domain\n## Motivation: inconsistency and geometric distortion\n## GenSP approach and core challenges","[{\"question\":\"What problem does GenSP address?\",\"answer\":\"GenSP addresses the need for consistent spherical parameterizations across multiple genus-0 shapes, avoiding shape-by-shape inconsistency and distortion.\"},{\"question\":\"How does GenSP produce spherical parameterizations for each shape?\",\"answer\":\"GenSP learns a neural generative model mapping the unit sphere to shapes, then obtains spherical parameterizations as the inverse mappings of the generator.\"},{\"question\":\"What challenges does GenSP solve to make the framework practical?\",\"answer\":\"GenSP tackles generative-model representation via continuous neural deformation, expands training with intermediate shapes to enable meaningful latent trajectories, and computes reliable initial correspondences by propagating mappings along a latent-space spanning tree.\"}]",1784181245,73,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"gensp-consistent-spherical-parameterization-via-learning-shape-generative-models","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":20},"https://docshare.wps.com/document/gensp-consistent-spherical-parameterization-via-learning-shape-generative-models/82526/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-23","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does GenSP address?","Question",{"text":75,"@type":76},"GenSP addresses the need for consistent spherical parameterizations across multiple genus-0 shapes, avoiding shape-by-shape inconsistency and distortion.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does GenSP produce spherical parameterizations for each shape?",{"text":80,"@type":76},"GenSP learns a neural generative model mapping the unit sphere to shapes, then obtains spherical parameterizations as the inverse mappings of the generator.",{"name":82,"@type":73,"acceptedAnswer":83},"What challenges does GenSP solve to make the framework practical?",{"text":84,"@type":76},"GenSP tackles generative-model representation via continuous neural deformation, expands training with intermediate shapes to enable meaningful latent trajectories, and computes reliable initial correspondences by propagating mappings along a latent-space spanning 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