79,926 research outputs found
Corners-based composite descriptor for shapes
In this paper, a composite descriptor for shape retrieval is proposed. The composite descriptor is obtained based upon corner-points and shape region. In an earlier paper, we proposed a composite descriptor based on shape region and shape contour, however, the descriptor was not effective for all perspective and geometric transformations. Hence, we modify the composite descriptor by replacing contour features with corner-points features. The proposed descriptor is obtained from Generic FourierDescriptors (GFD) of the shape region and the GFD ofthe corner-points. We study the performance of the proposed composite descriptor. The proposed method is evaluated using Item S8 within the MPEG-7 Still Images Content Set. Experimental results show that the proposed descriptor is effective.<br /
3D Shape Estimation from 2D Landmarks: A Convex Relaxation Approach
We investigate the problem of estimating the 3D shape of an object, given a
set of 2D landmarks in a single image. To alleviate the reconstruction
ambiguity, a widely-used approach is to confine the unknown 3D shape within a
shape space built upon existing shapes. While this approach has proven to be
successful in various applications, a challenging issue remains, i.e., the
joint estimation of shape parameters and camera-pose parameters requires to
solve a nonconvex optimization problem. The existing methods often adopt an
alternating minimization scheme to locally update the parameters, and
consequently the solution is sensitive to initialization. In this paper, we
propose a convex formulation to address this problem and develop an efficient
algorithm to solve the proposed convex program. We demonstrate the exact
recovery property of the proposed method, its merits compared to alternative
methods, and the applicability in human pose and car shape estimation.Comment: In Proceedings of CVPR 201
Femtosecond Covariance Spectroscopy
The success of non-linear optics relies largely on pulse-to-pulse
consistency. In contrast, covariance based techniques used in photoionization
electron spectroscopy and mass spectrometry have shown that wealth of
information can be extracted from noise that is lost when averaging multiple
measurements. Here, we apply covariance based detection to nonlinear optical
spectroscopy, and show that noise in a femtosecond laser is not necessarily a
liability to be mitigated, but can act as a unique and powerful asset. As a
proof of principle we apply this approach to the process of stimulated Raman
scattering in alpha-quartz. Our results demonstrate how nonlinear processes in
the sample can encode correlations between the spectral components of
ultrashort pulses with uncorrelated stochastic fluctuations. This in turn
provides richer information compared to the standard non-linear optics
techniques that are based on averages over many repetitions with well-behaved
laser pulses. These proof-of-principle results suggest that covariance based
nonlinear spectroscopy will improve the applicability of fs non-linear
spectroscopy in wavelength ranges where stable, transform limited pulses are
not available such as, for example, x-ray free electron lasers which naturally
have spectrally noisy pulses ideally suited for this approach
Structure from Recurrent Motion: From Rigidity to Recurrency
This paper proposes a new method for Non-Rigid Structure-from-Motion (NRSfM)
from a long monocular video sequence observing a non-rigid object performing
recurrent and possibly repetitive dynamic action. Departing from the
traditional idea of using linear low-order or lowrank shape model for the task
of NRSfM, our method exploits the property of shape recurrency (i.e., many
deforming shapes tend to repeat themselves in time). We show that recurrency is
in fact a generalized rigidity. Based on this, we reduce NRSfM problems to
rigid ones provided that certain recurrency condition is satisfied. Given such
a reduction, standard rigid-SfM techniques are directly applicable (without any
change) to the reconstruction of non-rigid dynamic shapes. To implement this
idea as a practical approach, this paper develops efficient algorithms for
automatic recurrency detection, as well as camera view clustering via a
rigidity-check. Experiments on both simulated sequences and real data
demonstrate the effectiveness of the method. Since this paper offers a novel
perspective on rethinking structure-from-motion, we hope it will inspire other
new problems in the field.Comment: To appear in CVPR 201
Functional Maps Representation on Product Manifolds
We consider the tasks of representing, analyzing and manipulating maps
between shapes. We model maps as densities over the product manifold of the
input shapes; these densities can be treated as scalar functions and therefore
are manipulable using the language of signal processing on manifolds. Being a
manifold itself, the product space endows the set of maps with a geometry of
its own, which we exploit to define map operations in the spectral domain; we
also derive relationships with other existing representations (soft maps and
functional maps). To apply these ideas in practice, we discretize product
manifolds and their Laplace--Beltrami operators, and we introduce localized
spectral analysis of the product manifold as a novel tool for map processing.
Our framework applies to maps defined between and across 2D and 3D shapes
without requiring special adjustment, and it can be implemented efficiently
with simple operations on sparse matrices.Comment: Accepted to Computer Graphics Foru
Functional maps representation on product manifolds
We consider the tasks of representing, analysing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace–Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices
Steklov Spectral Geometry for Extrinsic Shape Analysis
We propose using the Dirichlet-to-Neumann operator as an extrinsic
alternative to the Laplacian for spectral geometry processing and shape
analysis. Intrinsic approaches, usually based on the Laplace-Beltrami operator,
cannot capture the spatial embedding of a shape up to rigid motion, and many
previous extrinsic methods lack theoretical justification. Instead, we consider
the Steklov eigenvalue problem, computing the spectrum of the
Dirichlet-to-Neumann operator of a surface bounding a volume. A remarkable
property of this operator is that it completely encodes volumetric geometry. We
use the boundary element method (BEM) to discretize the operator, accelerated
by hierarchical numerical schemes and preconditioning; this pipeline allows us
to solve eigenvalue and linear problems on large-scale meshes despite the
density of the Dirichlet-to-Neumann discretization. We further demonstrate that
our operators naturally fit into existing frameworks for geometry processing,
making a shift from intrinsic to extrinsic geometry as simple as substituting
the Laplace-Beltrami operator with the Dirichlet-to-Neumann operator.Comment: Additional experiments adde
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