6,212 research outputs found
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
BPS Spectra, Barcodes and Walls
BPS spectra give important insights into the non-perturbative regimes of
supersymmetric theories. Often from the study of BPS states one can infer
properties of the geometrical or algebraic structures underlying such theories.
In this paper we approach this problem from the perspective of persistent
homology. Persistent homology is at the base of topological data analysis,
which aims at extracting topological features out of a set of points. We use
these techniques to investigate the topological properties which characterize
the spectra of several supersymmetric models in field and string theory. We
discuss how such features change upon crossing walls of marginal stability in a
few examples. Then we look at the topological properties of the distributions
of BPS invariants in string compactifications on compact threefolds, used to
engineer black hole microstates. Finally we discuss the interplay between
persistent homology and modularity by considering certain number theoretical
functions used to count dyons in string compactifications and by studying
equivariant elliptic genera in the context of the Mathieu moonshine
Real Time Animation of Virtual Humans: A Trade-off Between Naturalness and Control
Virtual humans are employed in many interactive applications using 3D virtual environments, including (serious) games. The motion of such virtual humans should look realistic (or ânaturalâ) and allow interaction with the surroundings and other (virtual) humans. Current animation techniques differ in the trade-off they offer between motion naturalness and the control that can be exerted over the motion. We show mechanisms to parametrize, combine (on different body parts) and concatenate motions generated by different animation techniques. We discuss several aspects of motion naturalness and show how it can be evaluated. We conclude by showing the promise of combinations of different animation paradigms to enhance both naturalness and control
Einstein-Gauss-Bonnet black holes in de Sitter spacetime and the quasilocal formalism
We propose to compute the action and global charges of the asymptotically de
Sitter solutions in Einstein-Gauss-Bonnet theory by using the counterterms
method in conjunction with the quasilocal formalism. The general expression of
the counterterms and the boundary stress tensor is presented for spacetimes of
dimension . We apply this tehnique for several different solutions in
Einstein-Gauss-Bonnet theory with a positive cosmological constant. Apart from
known solutions, we consider also vacuum rotating black holes with equal
magnitude angular momenta.Comment: 13 pages, 3 figures, typos corrected, text and one figure improve
Geometric, Variational Integrators for Computer Animation
We present a general-purpose numerical scheme for time integration of Lagrangian dynamical systemsâan important
computational tool at the core of most physics-based animation techniques. Several features make this
particular time integrator highly desirable for computer animation: it numerically preserves important invariants,
such as linear and angular momenta; the symplectic nature of the integrator also guarantees a correct energy
behavior, even when dissipation and external forces are added; holonomic constraints can also be enforced quite
simply; finally, our simple methodology allows for the design of high-order accurate schemes if needed. Two key
properties set the method apart from earlier approaches. First, the nonlinear equations that must be solved during
an update step are replaced by a minimization of a novel functional, speeding up time stepping by more than a
factor of two in practice. Second, the formulation introduces additional variables that provide key flexibility in the
implementation of the method. These properties are achieved using a discrete form of a general variational principle
called the Pontryagin-Hamilton principle, expressing time integration in a geometric manner. We demonstrate
the applicability of our integrators to the simulation of non-linear elasticity with implementation details
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