Authors:
Eugen Funk
1
;
Laurence S. Dooley
2
and
Anko Boerner
1
Affiliations:
1
German Aerospace Center (DLR), Germany
;
2
The Open University, United Kingdom
Keyword(s):
Shape Reconstruction, Radial Basis Function Interpolation, L1 Total Variation Minimization, Iterative Large Scale Optimization
Related
Ontology
Subjects/Areas/Topics:
Applications
;
Computer Vision, Visualization and Computer Graphics
;
Geometry and Modeling
;
Image and Video Analysis
;
Image-Based Modeling
;
Pattern Recognition
;
Robotics
;
Shape Representation and Matching
;
Software Engineering
Abstract:
With the emergence in 3D sensors such as laser scanners and 3D cameras, large 3D point clouds can now be sampled from physical objects within a scene. The raw 3D samples delivered by these sensors however, do not contain any information about the environment the objects exist in, which means that further geometrical high-level modelling is essential. In addition, issues like sparse data measurements, noise, missing samples due to occlusion, and the inherently huge datasets involved in such representations makes this task extremely challenging. This paper addresses these issues by presenting a new 3D shape modelling framework for samples acquired from 3D sensor. Motivated by the success of nonlinear kernel-based approximation techniques in the statistics domain, existing methods using radial basis functions are applied to 3D object shape approximation. The task is framed as an optimization problem and is extended using non-smooth L1 total variation regularization. Appropriate convex e
nergy functionals are constructed and solved by applying the Alternating Direction Method of Multipliers approach, which is then extended using Gauss-Seidel iterations. This significantly lowers the computational complexity involved in generating 3D shape from 3D samples, while both numerical and qualitative analysis confirms the superior shape modelling performance of this new framework compared with existing 3D shape reconstruction techniques.
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