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Curvature Regularization for Curves and Surfaces in a Global Optimization Framework

Strandmark, Petter (author)
Lund University,Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
Kahl, Fredrik (author)
Lund University,Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
 (creator_code:org_t)
2011
2011
English.
In: Lecture Notes in Computer Science.
  • Conference paper (peer-reviewed)
Abstract Subject headings
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  • Length and area regularization are commonplace for inverse problems today. It has however turned out to be much more difficult to incorporate a curvature prior. In this paper we propose several improvements to a recently proposed framework based on global optimization. We identify and solve an issue with extraneous arcs in the original formulation by introducing region consistency constraints. The mesh geometry is analyzed both from a theoretical and experimental viewpoint and hexagonal meshes are shown to be superior. We demonstrate that adaptively generated meshes significantly improve the performance. Our final contribution is that we generalize the framework to handle mean curvature regularization for 3D surface completion and segmentation.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)
NATURAL SCIENCES  -- Mathematics (hsv//eng)
NATURVETENSKAP  -- Data- och informationsvetenskap -- Datorseende och robotik (hsv//swe)
NATURAL SCIENCES  -- Computer and Information Sciences -- Computer Vision and Robotics (hsv//eng)

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