{"id":343757,"date":"2016-12-29T21:28:54","date_gmt":"2016-12-30T05:28:54","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=343757"},"modified":"2018-10-16T21:35:32","modified_gmt":"2018-10-17T04:35:32","slug":"computing-locally-injective-mappings-advanced-mips","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/computing-locally-injective-mappings-advanced-mips\/","title":{"rendered":"Computing Locally Injective Mappings by Advanced MIPS"},"content":{"rendered":"<p><span class=\"tx\">Computing locally injective mappings with low distortion in an<\/span><span class=\"tx\">ef\ufb01cient way is a fundamental task in computer graphics.\u00a0By re-<\/span><span class=\"tx\">visiting the well-known MIPS (Most-Isometric ParameterizationS)<\/span><span class=\"tx\">method, we introduce an advanced MIPS method that inherits the<\/span><span class=\"tx\">local injectivity of MIPS, achieves as low as possible distortions<\/span><span class=\"tx\">compared to the state-of-the-art locally injective mapping techniques,<\/span><span class=\"tx\">and performs one to two orders of magnitude faster in computing<\/span><span class=\"tx\">a mesh-based mapping.\u00a0The success of our method relies on two<\/span><span class=\"tx\">key components. The \ufb01rst one is an enhanced MIPS energy function<\/span><span class=\"tx\">that penalizes the maximal distortion signi\ufb01cantly and distributes<\/span><span class=\"tx\">the distortion evenly over the domain for both mesh-based and mesh-<\/span><span class=\"tx\">less mappings. The second is a use of the inexact block coordinate<\/span><span class=\"tx\">descent method in mesh-based mapping in a way that ef\ufb01ciently min-<\/span><span class=\"tx\">imizes the distortion with the capability not to be trapped early by<\/span><span class=\"tx\">the local minimum. We demonstrate the capability and superiority of<\/span><span class=\"tx\">our method in various applications including mesh parameterization,<\/span><span class=\"tx\">mesh-based and meshless deformation, and mesh improvemen<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Computing locally injective mappings with low distortion in anef\ufb01cient way is a fundamental task in computer graphics.\u00a0By re-visiting the well-known MIPS (Most-Isometric ParameterizationS)method, we introduce an advanced MIPS method that inherits thelocal injectivity of MIPS, achieves as low as possible distortionscompared to the state-of-the-art locally injective mapping techniques,and performs one to two orders of magnitude [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13562],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-343757","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-computer-vision","msr-locale-en_us"],"msr_publishername":"ACM","msr_edition":"ACM Transactions on Graphics (TOG) - 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