12,954 research outputs found
Gauge Invariant Framework for Shape Analysis of Surfaces
This paper describes a novel framework for computing geodesic paths in shape
spaces of spherical surfaces under an elastic Riemannian metric. The novelty
lies in defining this Riemannian metric directly on the quotient (shape) space,
rather than inheriting it from pre-shape space, and using it to formulate a
path energy that measures only the normal components of velocities along the
path. In other words, this paper defines and solves for geodesics directly on
the shape space and avoids complications resulting from the quotient operation.
This comprehensive framework is invariant to arbitrary parameterizations of
surfaces along paths, a phenomenon termed as gauge invariance. Additionally,
this paper makes a link between different elastic metrics used in the computer
science literature on one hand, and the mathematical literature on the other
hand, and provides a geometrical interpretation of the terms involved. Examples
using real and simulated 3D objects are provided to help illustrate the main
ideas.Comment: 15 pages, 11 Figures, to appear in IEEE Transactions on Pattern
Analysis and Machine Intelligence in a better resolutio
Robust Non-Rigid Registration with Reweighted Position and Transformation Sparsity
Non-rigid registration is challenging because it is ill-posed with high
degrees of freedom and is thus sensitive to noise and outliers. We propose a
robust non-rigid registration method using reweighted sparsities on position
and transformation to estimate the deformations between 3-D shapes. We
formulate the energy function with position and transformation sparsity on both
the data term and the smoothness term, and define the smoothness constraint
using local rigidity. The double sparsity based non-rigid registration model is
enhanced with a reweighting scheme, and solved by transferring the model into
four alternately-optimized subproblems which have exact solutions and
guaranteed convergence. Experimental results on both public datasets and real
scanned datasets show that our method outperforms the state-of-the-art methods
and is more robust to noise and outliers than conventional non-rigid
registration methods.Comment: IEEE Transactions on Visualization and Computer Graphic
From Multiview Image Curves to 3D Drawings
Reconstructing 3D scenes from multiple views has made impressive strides in
recent years, chiefly by correlating isolated feature points, intensity
patterns, or curvilinear structures. In the general setting - without
controlled acquisition, abundant texture, curves and surfaces following
specific models or limiting scene complexity - most methods produce unorganized
point clouds, meshes, or voxel representations, with some exceptions producing
unorganized clouds of 3D curve fragments. Ideally, many applications require
structured representations of curves, surfaces and their spatial relationships.
This paper presents a step in this direction by formulating an approach that
combines 2D image curves into a collection of 3D curves, with topological
connectivity between them represented as a 3D graph. This results in a 3D
drawing, which is complementary to surface representations in the same sense as
a 3D scaffold complements a tent taut over it. We evaluate our results against
truth on synthetic and real datasets.Comment: Expanded ECCV 2016 version with tweaked figures and including an
overview of the supplementary material available at
multiview-3d-drawing.sourceforge.ne
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