2,363 research outputs found
Piecewise rigid curve deformation via a Finsler steepest descent
This paper introduces a novel steepest descent flow in Banach spaces. This
extends previous works on generalized gradient descent, notably the work of
Charpiat et al., to the setting of Finsler metrics. Such a generalized gradient
allows one to take into account a prior on deformations (e.g., piecewise rigid)
in order to favor some specific evolutions. We define a Finsler gradient
descent method to minimize a functional defined on a Banach space and we prove
a convergence theorem for such a method. In particular, we show that the use of
non-Hilbertian norms on Banach spaces is useful to study non-convex
optimization problems where the geometry of the space might play a crucial role
to avoid poor local minima. We show some applications to the curve matching
problem. In particular, we characterize piecewise rigid deformations on the
space of curves and we study several models to perform piecewise rigid
evolution of curves
Furniture models learned from the WWW: using web catalogs to locate and categorize unknown furniture pieces in 3D laser scans
In this article, we investigate how autonomous robots can exploit the high quality information already available from the WWW concerning 3-D models of office furniture. Apart from the hobbyist effort in Google 3-D Warehouse, many companies providing office furnishings already have the models for considerable portions of the objects found in our workplaces and homes. In particular, we present an approach that allows a robot to learn generic models of typical office furniture using examples found in the Web. These generic models are then used by the robot to locate and categorize unknown furniture in real indoor environments
Four-dimensional tomographic reconstruction by time domain decomposition
Since the beginnings of tomography, the requirement that the sample does not
change during the acquisition of one tomographic rotation is unchanged. We
derived and successfully implemented a tomographic reconstruction method which
relaxes this decades-old requirement of static samples. In the presented
method, dynamic tomographic data sets are decomposed in the temporal domain
using basis functions and deploying an L1 regularization technique where the
penalty factor is taken for spatial and temporal derivatives. We implemented
the iterative algorithm for solving the regularization problem on modern GPU
systems to demonstrate its practical use
A Total Fractional-Order Variation Model for Image Restoration with Non-homogeneous Boundary Conditions and its Numerical Solution
To overcome the weakness of a total variation based model for image
restoration, various high order (typically second order) regularization models
have been proposed and studied recently. In this paper we analyze and test a
fractional-order derivative based total -order variation model, which
can outperform the currently popular high order regularization models. There
exist several previous works using total -order variations for image
restoration; however first no analysis is done yet and second all tested
formulations, differing from each other, utilize the zero Dirichlet boundary
conditions which are not realistic (while non-zero boundary conditions violate
definitions of fractional-order derivatives). This paper first reviews some
results of fractional-order derivatives and then analyzes the theoretical
properties of the proposed total -order variational model rigorously.
It then develops four algorithms for solving the variational problem, one based
on the variational Split-Bregman idea and three based on direct solution of the
discretise-optimization problem. Numerical experiments show that, in terms of
restoration quality and solution efficiency, the proposed model can produce
highly competitive results, for smooth images, to two established high order
models: the mean curvature and the total generalized variation.Comment: 26 page
Motion Cooperation: Smooth Piece-Wise Rigid Scene Flow from RGB-D Images
We propose a novel joint registration and segmentation approach to estimate scene flow from RGB-D images. Instead of assuming the scene to be composed of a number of independent rigidly-moving parts, we use non-binary labels to capture non-rigid deformations at transitions between
the rigid parts of the scene. Thus, the velocity of any point can be computed as a linear combination (interpolation) of the estimated rigid motions, which provides better results
than traditional sharp piecewise segmentations. Within a variational framework, the smooth segments of the scene and their corresponding rigid velocities are alternately refined
until convergence. A K-means-based segmentation is employed as an initialization, and the number of regions is subsequently adapted during the optimization process to capture any arbitrary number of independently moving objects.
We evaluate our approach with both synthetic and
real RGB-D images that contain varied and large motions. The experiments show that our method estimates the scene flow more accurately than the most recent works in the field, and at the same time provides a meaningful segmentation of the scene based on 3D motion.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Spanish Government under the grant programs FPI-MICINN 2012 and DPI2014- 55826-R (co-founded by the European Regional Development Fund), as well as by the EU ERC grant Convex Vision (grant agreement no. 240168)
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