9,480 research outputs found
SHREC'16: partial matching of deformable shapes
Matching deformable 3D shapes under partiality transformations is a challenging problem that has received limited focus in the computer vision and graphics communities. With this benchmark, we explore and thoroughly investigate the robustness of existing matching methods in this challenging task. Participants are asked to provide a point-to-point correspondence (either sparse or dense) between deformable shapes undergoing different kinds of partiality transformations, resulting in a total of 400 matching problems to be solved for each method - making this benchmark the biggest and most challenging of its kind. Five matching algorithms were evaluated in the contest; this paper presents the details of the dataset, the adopted evaluation measures, and shows thorough comparisons among all competing methods
Time Discrete Geodesic Paths in the Space of Images
In this paper the space of images is considered as a Riemannian manifold
using the metamorphosis approach, where the underlying Riemannian metric
simultaneously measures the cost of image transport and intensity variation. A
robust and effective variational time discretization of geodesics paths is
proposed. This requires to minimize a discrete path energy consisting of a sum
of consecutive image matching functionals over a set of image intensity maps
and pairwise matching deformations. For square-integrable input images the
existence of discrete, connecting geodesic paths defined as minimizers of this
variational problem is shown. Furthermore, -convergence of the
underlying discrete path energy to the continuous path energy is proved. This
includes a diffeomorphism property for the induced transport and the existence
of a square-integrable weak material derivative in space and time. A spatial
discretization via finite elements combined with an alternating descent scheme
in the set of image intensity maps and the set of matching deformations is
presented to approximate discrete geodesic paths numerically. Computational
results underline the efficiency of the proposed approach and demonstrate
important qualitative properties.Comment: 27 pages, 7 figure
Multiple Shape Registration using Constrained Optimal Control
Lagrangian particle formulations of the large deformation diffeomorphic
metric mapping algorithm (LDDMM) only allow for the study of a single shape. In
this paper, we introduce and discuss both a theoretical and practical setting
for the simultaneous study of multiple shapes that are either stitched to one
another or slide along a submanifold. The method is described within the
optimal control formalism, and optimality conditions are given, together with
the equations that are needed to implement augmented Lagrangian methods.
Experimental results are provided for stitched and sliding surfaces
Deformable Prototypes for Encoding Shape Categories in Image Databases
We describe a method for shape-based image database search that uses deformable prototypes to represent categories. Rather than directly comparing a candidate shape with all shape entries in the database, shapes are compared in terms of the types of nonrigid deformations (differences) that relate them to a small subset of representative prototypes. To solve the shape correspondence and alignment problem, we employ the technique of modal matching, an information-preserving shape decomposition for matching, describing, and comparing shapes despite sensor variations and nonrigid deformations. In modal matching, shape is decomposed into an ordered basis of orthogonal principal components. We demonstrate the utility of this approach for shape comparison in 2-D image databases.Office of Naval Research (Young Investigator Award N00014-06-1-0661
Soliton Dynamics in Computational Anatomy
Computational anatomy (CA) has introduced the idea of anatomical structures
being transformed by geodesic deformations on groups of diffeomorphisms. Among
these geometric structures, landmarks and image outlines in CA are shown to be
singular solutions of a partial differential equation that is called the
geodesic EPDiff equation. A recently discovered momentum map for singular
solutions of EPDiff yields their canonical Hamiltonian formulation, which in
turn provides a complete parameterization of the landmarks by their canonical
positions and momenta. The momentum map provides an isomorphism between
landmarks (and outlines) for images and singular soliton solutions of the
EPDiff equation. This isomorphism suggests a new dynamical paradigm for CA, as
well as new data representation.Comment: published in NeuroImag
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