MSGID: 1:317/3 646ee489   
   PID: hpt/lnx 1.9.0-cur 2019-01-08   
   TID: hpt/lnx 1.9.0-cur 2019-01-08   
    A better way to match 3D volumes    
      
     Date:   
         May 24, 2023   
     Source:   
         Massachusetts Institute of Technology   
     Summary:   
         Researchers developed an algorithm that can align two 3D shapes by   
         mapping their volumes, which is more effective than other methods   
         that align shapes by only mapping their surfaces.   
      
      
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   FULL STORY   
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   In computer graphics and computer-aided design (CAD), 3D objects are   
   often represented by the contours of their outer surfaces. Computers   
   store these shapes as "thin shells," which model the contours of the   
   skin of an animated character but not the flesh underneath.   
      
   This modeling decision makes it efficient to store and manipulate 3D   
   shapes, but it can lead to unexpected artifacts. An animated character's   
   hand, for example, might crumple when bending its fingers -- a motion   
   that resembles how an empty rubber glove deforms rather than the motion   
   of a hand filled with bones, tendons, and muscle. These differences   
   are particularly problematic when developing mapping algorithms, which   
   automatically find relationships between different shapes.   
      
   To address these shortcomings, researchers at MIT have developed   
   an approach that aligns 3D shapes by mapping volumes to volumes,   
   rather than surfaces to surfaces. Their technique represents shapes   
   as tetrahedral meshes that include the mass inside a 3D object. Their   
   algorithm determines how to move and stretch the corners of tetrahedra   
   in a source shape so it aligns with a target shape.   
      
   Because it incorporates volumetric information, the researchers' technique   
   is better able to model fine parts of an object, avoiding the twisting   
   and inversion typical of surface-based mapping.   
      
   "Switching from surfaces to volumes stretches the rubber glove over   
   the whole hand. Our method brings geometric mapping closer to physical   
   reality," says Mazdak Abulnaga, an electrical engineering and computer   
   science (EECS) graduate student who is lead author of the paper on this   
   mapping technique.   
      
   The approach Abulnaga and his collaborators developed was able to align   
   shapes more effectively than baseline methods, leading to high-quality   
   shape maps with less distortion than competing alternatives. Their   
   algorithm was especially well-suited for challenging mapping problems   
   where the input shapes are geometrically distinct, such as mapping a   
   smooth rabbit to LEGO-style rabbit made of cubes.   
      
   The technique could be useful in a number of graphics applications. For   
   instance, it could be used to transfer the motions of a previously   
   animated 3D character onto a new 3D model or scan. The same algorithm   
   can transfer textures, annotations, and physical properties from one   
   3D shape to another, with applications not just in visual computing but   
   also for computational manufacturing and engineering.   
      
   Joining Abulnaga on the paper are Oded Stein, a former MIT postdoc who   
   is now on the faculty at the University of Southern California; Polina   
   Golland, a Sunlin and Priscilla Chou Professor of EECS, a principal   
   investigator in the MIT Computer Science and Artificial Intelligence   
   Laboratory (CSAIL), and the leader of the Medical Vision Group; and   
   Justin Solomon, an associate professor of EECS and the leader of the   
   CSAIL Geometric Data Processing Group. The research will be presented   
   at the ACM SIGGRAPH conference.   
      
   Shaping an algorithm Abulnaga began this project by extending   
   surface-based algorithms so they could map shapes volumetrically, but each   
   attempt failed or produced implausible maps. The team quickly realized   
   that new mathematics and algorithms were needed to tackle volume mapping.   
      
   Most mapping algorithms work by trying to minimize an "energy," which   
   quantifies how much a shape deforms when it is displaced, stretched,   
   squashed, and sheared into another shape. These energies are often   
   borrowed from physics, which uses similar equations to model the motion   
   of elastic materials like gelatin.   
      
   Even when Abulnaga improved the energy in his mapping algorithm to better   
   model volume physics, the method didn't produce useful matchings. His team   
   realized one reason for this failure is that many physical energies --   
   and most mapping algorithms -- lack symmetry.   
      
   In the new work, a symmetric method doesn't care which order the shapes   
   come in as input; there is no distinction between a "source" and "target"   
   for the map.   
      
   For example, mapping a horse onto a giraffe should produce the same   
   matchings as mapping a giraffe onto a horse. But for many mapping   
   algorithms, choosing the wrong shape to be the source or target leads to   
   worse results. This effect is even more pronounced in the volumetric case.   
      
   Abulnaga documented how most mapping algorithms don't use symmetric   
   energies.   
      
   "If you choose the right energy for your algorithm, it can give you maps   
   that are more realizable," Abulnaga explains.   
      
   The typical energies used in shape alignment are only designed to map   
   in one direction. If a researcher tries to apply them bidirectionally to   
   create a symmetric map, the energies no longer behave as expected. These   
   energies also behave differently when applied to surfaces and volumes.   
      
   Based on these findings, Abulnaga and his collaborators created a   
   mathematical framework that researchers can use to see how different   
   energies will behave and to determine which they should choose to create   
   a symmetric map between two objects. Using this framework, they built   
   a mapping algorithm that combines the energy functions for two objects   
   in a way that guarantees symmetry throughout.   
      
   A user feeds the algorithm two shapes that are represented as tetrahedral   
   meshes. Then the algorithm computes two bidirectional maps, from one   
   shape to the other and back. These maps show where each corner of each   
   tetrahedron should move to match the shapes.   
      
   "The energy is the cornerstone of this mapping process. The model tries to   
   align the two shapes, and the energies prevent it from making unexpected   
   alignments," he says.   
      
   Achieving accurate alignments When the researchers tested their   
   approach, it created maps that better aligned shape pairs and which   
   were higher quality and less distorted than other approaches that work   
   on volumes. They also showed that using volume information can yield   
   more accurate maps even when one is only concerned with the map of the   
   outer surface.   
      
   However, there were some cases where their method fell short. For   
   instance, the algorithm struggles when the shape alignment requires   
   a great deal of volume changes, such as mapping a shape with a filled   
   interior to one with a cavity inside.   
      
   In addition to addressing that limitation, the researchers want to   
   continue optimizing the algorithm to reduce the amount of time it   
   takes. The researchers are also working on extending this method to   
   medical applications, bringing in MRI signals in addition to shape. This   
   can help bridge the mapping approaches used in medical computer vision   
   and computer graphics.   
      
   This research is funded, in part, by the National Institutes of Health,   
   Wistron Corporation, the U.S. Army Research Office, the Air Force Office   
   of Scientific Research, the National Science Foundation, the CSAIL Systems   
   that Learn Program, the MIT-IBM Watson AI Lab, the Toyota-CSAIL Joint   
   Research Center, Adobe Systems, the Swiss National Science Foundation,   
   the Natural Sciences and Engineering Research Council of Canada, and a   
   Mathworks Fellowship.   
      
       * RELATED_TOPICS   
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   ==========================================================================   
   Story Source: Materials provided by   
   Massachusetts_Institute_of_Technology. Original written by Adam   
   Zewe. Note: Content may be edited for style and length.   
      
      
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   Journal Reference:   
      1. S. Mazdak Abulnaga, Oded Stein, Polina Golland, Justin   
      Solomon. Symmetric   
         Volume Maps: Order-invariant Volumetric Mesh Correspondence with   
         Free Boundary. ACM Transactions on Graphics, 2023; 42 (3): 1 DOI:   
         10.1145/ 3572897   
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   Link to news story:   
   https://www.sciencedaily.com/releases/2023/05/230524181836.htm   
      
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