4,144 research outputs found
Geodesic Distance Histogram Feature for Video Segmentation
This paper proposes a geodesic-distance-based feature that encodes global
information for improved video segmentation algorithms. The feature is a joint
histogram of intensity and geodesic distances, where the geodesic distances are
computed as the shortest paths between superpixels via their boundaries. We
also incorporate adaptive voting weights and spatial pyramid configurations to
include spatial information into the geodesic histogram feature and show that
this further improves results. The feature is generic and can be used as part
of various algorithms. In experiments, we test the geodesic histogram feature
by incorporating it into two existing video segmentation frameworks. This leads
to significantly better performance in 3D video segmentation benchmarks on two
datasets
A Low-Dimensional Representation for Robust Partial Isometric Correspondences Computation
Intrinsic isometric shape matching has become the standard approach for pose
invariant correspondence estimation among deformable shapes. Most existing
approaches assume global consistency, i.e., the metric structure of the whole
manifold must not change significantly. While global isometric matching is well
understood, only a few heuristic solutions are known for partial matching.
Partial matching is particularly important for robustness to topological noise
(incomplete data and contacts), which is a common problem in real-world 3D
scanner data. In this paper, we introduce a new approach to partial, intrinsic
isometric matching. Our method is based on the observation that isometries are
fully determined by purely local information: a map of a single point and its
tangent space fixes an isometry for both global and the partial maps. From this
idea, we develop a new representation for partial isometric maps based on
equivalence classes of correspondences between pairs of points and their
tangent spaces. From this, we derive a local propagation algorithm that find
such mappings efficiently. In contrast to previous heuristics based on RANSAC
or expectation maximization, our method is based on a simple and sound
theoretical model and fully deterministic. We apply our approach to register
partial point clouds and compare it to the state-of-the-art methods, where we
obtain significant improvements over global methods for real-world data and
stronger guarantees than previous heuristic partial matching algorithms.Comment: 17 pages, 12 figure
Holographic Entropy Cone with Time Dependence in Two Dimensions
In holographic duality, if a boundary state has a geometric description that
realizes the Ryu-Takayanagi proposal then its entanglement entropies must obey
certain inequalities that together define the so-called holographic entropy
cone. A large family of such inequalities have been proven under the assumption
that the bulk geometry is static, using a method involving contraction maps. By
using kinematic space techniques, we show that in two boundary (three bulk)
dimensions, all entropy inequalities that can be proven in the static case by
contraction maps must also hold in holographic states with time dependence.Comment: 37 pages, 10 figure
Generalized minimal principle for rotor filaments
To a reaction-diffusion medium with an inhomogeneous anisotropic diffusion tensor D, we add a fourth spatial dimension such that the determinant of the diffusion tensor is constant in four dimensions. We propose a generalized minimal principle for rotor filaments, stating that the scroll wave filament strives to minimize its surface area in the higher-dimensional space. As a consequence, stationary scroll wave filaments in the original 3D medium are geodesic curves with respect to the metric tensor G = det(D)D-1. The theory is confirmed by numerical simulations for positive and negative filament tension and a model with a non-stationary spiral core. We conclude that filaments in cardiac tissue with positive tension preferentially reside or anchor in regions where cardiac cells are less interconnected, such as portions of the cardiac wall with a large number of cleavage planes
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