[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120144-en":3,"doc-seo-120144-105":30,"detail-sidebar-cat-0-en-105":92},{"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":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},120144,8796095461610,"Oliver","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Graph representations of 3D data for machine learning","Overview of combinatorial representations for 3D data—graphs, meshes, point clouds, and simplicial complexes—evaluated through their suitability for machine learning analysis. The discussion compares advantages and limitations of different representation choices and outlines methods for generating or switching between them. Two applied cases are presented in life science and industry. Although theoretical, the motivation focuses on practical real-world challenges in Geometric Machine Learning.","arXiv :2408 .08336v1 [ cs .LG] 15 Aug 2024  \nGraph representations of 3D data for machine learning  \nTomasz Prytula  \nSeptember 27, 2024  \nAbstract  \nWe give an overview of combinatorial methods to represent 3D data, such as graphsand meshes, from the viewpoint of their amenability to analysis using machine learning algorithms. We highlight pros and cons of various representations and we discuss some methods of generating/switching between the representations. We finally present two concrete applications in life science and industry. Despite its theoretical nature, our discussion is in general motivated by, and biased towards real-world challenges.  \n1 Introduction  \n3D data appears naturally in science and industry, and covers a wide range of domains, from bioimaging (microscopy images, CT scans), through molecular chemistry, to 3D modeling and design plans [GZW+20] . A 3D representation is often advantageous as it describes a real world (hence 3D) object more accurately, compared to e.g., 2D projections or slices. However, a drawback of the 3-dimensional representation is the computational cost of the analysis, as the extra dimension, together with scarcity typical for 3D data, makes it very challenging to apply learning algorithms that scale effectively-to the extreme where already analysis of a single sample can be on a verge of capability of a single machine.  \nIn our work we have investigated whether this challenge can be overcome, or at least partially alleviated by employing lighter representations of 3D data - graphs, meshes, point clouds, and simplicial complexes, and  \nthe corresponding deep learning algorithms that operate on those representations. Our findings suggest that in many real-world situations it is the case, and we hope that practitioners of machine learning can adapt some of our learnings to their work with 3D data. Our approach is backed by recent developments in the field Geometric Machine Learning, both theoretical [BBC+21] and softwareoriented [FL19] .  \nIn the specific domain of preclinical research and biomedical imaging, we are plannig to release a set of guidelines for analyzing 3D data using a variety of combinatorial methods, in cases where classical 3D deep learning is not feasible.  \nAnother benefit of using combinatorial representations is their potential for explainability. Since such representations usually come at a higher level of abstraction (e.g. , a graph modeling a human pose), their elements (edges, vertices) naturally carry semantic meaning, and thus it may be easier to  \nextract the ‘logic’ behind a machine learning model’s predictions.  \n2 3D data  \nIn this section we present an overview of some representations of 3D data, and we compare them from a viewpoint of analysis using deep learning methods. The overview is biased by the specific problems we encountered, and by the overarching theme of studying combinatorial representations.  \nVolumetric  \nThe main challenge with 3D data compared with 2D data is the computational complexity of algorithms to analyze this data. This stems from the fact the most common representation of 3D data is by voxels (3D analogue of pixels), which means that a volume is represented by a dense grid of 3-dimensional cubes, each of the cubes storing information about e.g., RGB color or intensity. This is a standard format used in many imaging techniques, and thus can be considered as a ‘fundamental’ or ‘raw’ format for 3D data. It is a trivial observation that the number of voxels grows exponentially with the dimension, and thus already a jump from 2D to 3D has severe consequences for compute requirements.  \nAnother issue, which is somehow more a characteristic of 3D data in general, is its sparsity. Whether it is a microscopy image of a neuron cell, or a 3D design for manufacturing, a lot of voxels are unoccupied, and the actual object of interest fills only a small portion of the volume, see Figure 2. However, one does not know it in advance, and ther","cbCaivp6a84CxINX","https://ap.wps.com/l/cbCaivp6a84CxINX","pdf",4811961,1,14,"English","en",105,"# Introduction\n## 3D data and computational challenges\n## Combinatorial representations\n# 3D data representations\n## Volumetric representations\n## Mesh representations","[{\"question\":\"Why are 3D data representations harder to analyze than 2D ones?\",\"answer\":\"3D analysis is more computationally complex, and 3D data is often sparse and comes from expensive procedures, leading to smaller datasets. Standard methods may process full volumes even when only a small region contains the object of interest.\"},{\"question\":\"What are volumetric representations and what drawbacks do they have?\",\"answer\":\"Volumetric representations typically use voxels, storing values on a dense 3D grid. They suffer from exponential growth in voxel count when moving from 2D to 3D and from sparsity, where many voxels are unoccupied.\"},{\"question\":\"How do mesh representations help with 3D learning?\",\"answer\":\"Meshes tessellate a 3D surface using triangles or polygons, which better captures geometry and avoids the sparsity burden of dense voxel grids. Mesh data stores vertex positions and connectivity, enabling deep learning architectures tailored to geometric features.\"}]","Graph representations of 3D data for machine learning | PDF",1785728426,35,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"graph-representations-of-3d-data-for-machine-learning","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"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":53},"https://docshare.wps.com/document/graph-representations-of-3d-data-for-machine-learning/120144/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04","2026-08-03",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"Why are 3D data representations harder to analyze than 2D ones?","Question",{"text":76,"@type":77},"3D analysis is more computationally complex, and 3D data is often sparse and comes from expensive procedures, leading to smaller datasets. Standard methods may process full volumes even when only a small region contains the object of interest.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What are volumetric representations and what drawbacks do they have?",{"text":81,"@type":77},"Volumetric representations typically use voxels, storing values on a dense 3D grid. They suffer from exponential growth in voxel count when moving from 2D to 3D and from sparsity, where many voxels are unoccupied.",{"name":83,"@type":74,"acceptedAnswer":84},"How do mesh representations help with 3D learning?",{"text":85,"@type":77},"Meshes tessellate a 3D surface using triangles or polygons, which better captures geometry and avoids the sparsity burden of dense voxel grids. Mesh data stores vertex positions and connectivity, enabling deep learning architectures tailored to geometric features.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,124,129,132,136],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":46,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":46,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":46,"category_name":138,"show_sort_weight":107,"slug":139},19,"General","general"]