5,978 research outputs found
Spectral Generalized Multi-Dimensional Scaling
Multidimensional scaling (MDS) is a family of methods that embed a given set
of points into a simple, usually flat, domain. The points are assumed to be
sampled from some metric space, and the mapping attempts to preserve the
distances between each pair of points in the set. Distances in the target space
can be computed analytically in this setting. Generalized MDS is an extension
that allows mapping one metric space into another, that is, multidimensional
scaling into target spaces in which distances are evaluated numerically rather
than analytically. Here, we propose an efficient approach for computing such
mappings between surfaces based on their natural spectral decomposition, where
the surfaces are treated as sampled metric-spaces. The resulting spectral-GMDS
procedure enables efficient embedding by implicitly incorporating smoothness of
the mapping into the problem, thereby substantially reducing the complexity
involved in its solution while practically overcoming its non-convex nature.
The method is compared to existing techniques that compute dense correspondence
between shapes. Numerical experiments of the proposed method demonstrate its
efficiency and accuracy compared to state-of-the-art approaches
Disambiguating Multi–Modal Scene Representations Using Perceptual Grouping Constraints
In its early stages, the visual system suffers from a lot of ambiguity and noise that severely limits the performance of early vision algorithms. This article presents feedback mechanisms between early visual processes, such as perceptual grouping, stereopsis and depth reconstruction, that allow the system to reduce this ambiguity and improve early representation of visual information. In the first part, the article proposes a local perceptual grouping algorithm that — in addition to commonly used geometric information — makes use of a novel multi–modal measure between local edge/line features. The grouping information is then used to: 1) disambiguate stereopsis by enforcing that stereo matches preserve groups; and 2) correct the reconstruction error due to the image pixel sampling using a linear interpolation over the groups. The integration of mutual feedback between early vision processes is shown to reduce considerably ambiguity and noise without the need for global constraints
Leveraging Deep Visual Descriptors for Hierarchical Efficient Localization
Many robotics applications require precise pose estimates despite operating
in large and changing environments. This can be addressed by visual
localization, using a pre-computed 3D model of the surroundings. The pose
estimation then amounts to finding correspondences between 2D keypoints in a
query image and 3D points in the model using local descriptors. However,
computational power is often limited on robotic platforms, making this task
challenging in large-scale environments. Binary feature descriptors
significantly speed up this 2D-3D matching, and have become popular in the
robotics community, but also strongly impair the robustness to perceptual
aliasing and changes in viewpoint, illumination and scene structure. In this
work, we propose to leverage recent advances in deep learning to perform an
efficient hierarchical localization. We first localize at the map level using
learned image-wide global descriptors, and subsequently estimate a precise pose
from 2D-3D matches computed in the candidate places only. This restricts the
local search and thus allows to efficiently exploit powerful non-binary
descriptors usually dismissed on resource-constrained devices. Our approach
results in state-of-the-art localization performance while running in real-time
on a popular mobile platform, enabling new prospects for robotics research.Comment: CoRL 2018 Camera-ready (fix typos and update citations
Gauged (2,2) Sigma Models and Generalized Kahler Geometry
We gauge the (2,2) supersymmetric non-linear sigma model whose target space
has bihermitian structure (g, B, J_{\pm}) with noncommuting complex structures.
The bihermitian geometry is realized by a sigma model which is written in terms
of (2,2) semi-chiral superfields. We discuss the moment map, from the
perspective of the gauged sigma model action and from the integrability
condition for a Hamiltonian vector field. We show that for a concrete example,
the SU(2) x U(1) WZNW model, as well as for the sigma models with almost
product structure, the moment map can be used together with the corresponding
Killing vector to form an element of T+T* which lies in the eigenbundle of the
generalized almost complex structure. Lastly, we discuss T-duality at the level
of a (2,2) sigma model involving semi-chiral superfields and present an
explicit example.Comment: 33 page
An Analysis of Errors in Graph-Based Keypoint Matching and Proposed Solutions
International audienceAn error occurs in graph-based keypoint matching when key-points in two different images are matched by an algorithm but do not correspond to the same physical point. Most previous methods acquire keypoints in a black-box manner, and focus on developing better algorithms to match the provided points. However to study the complete performance of a matching system one has to study errors through the whole matching pipeline, from keypoint detection, candidate selection to graph optimisation. We show that in the full pipeline there are six different types of errors that cause mismatches. We then present a matching framework designed to reduce these errors. We achieve this by adapting keypoint detectors to better suit the needs of graph-based matching, and achieve better graph constraints by exploiting more information from their keypoints. Our framework is applicable in general images and can handle clutter and motion discontinuities. We also propose a method to identify many mismatches a posteriori based on Left-Right Consistency inspired by stereo matching due to the asymmetric way we detect keypoints and define the graph
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