22 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
Ubiquitous Positioning: A Taxonomy for Location Determination on Mobile Navigation System
The location determination in obstructed area can be very challenging
especially if Global Positioning System are blocked. Users will find it
difficult to navigate directly on-site in such condition, especially indoor car
park lot or obstructed environment. Sometimes, it needs to combine with other
sensors and positioning methods in order to determine the location with more
intelligent, reliable and ubiquity. By using ubiquitous positioning in mobile
navigation system, it is a promising ubiquitous location technique in a mobile
phone since as it is a familiar personal electronic device for many people.
However, as research on ubiquitous positioning systems goes beyond basic
methods there is an increasing need for better comparison of proposed
ubiquitous positioning systems. System developers are also lacking of good
frameworks for understanding different options during building ubiquitous
positioning systems. This paper proposes taxonomy to address both of these
problems. The proposed taxonomy has been constructed from a literature study of
papers and articles on positioning estimation that can be used to determine
location everywhere on mobile navigation system. For researchers the taxonomy
can also be used as an aid for scoping out future research in the area of
ubiquitous positioning.Comment: 15 Pages, 3 figure
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
PRS-Net: Planar Reflective Symmetry Detection Net for 3D Models
In geometry processing, symmetry is a universal type of high-level structural
information of 3D models and benefits many geometry processing tasks including
shape segmentation, alignment, matching, and completion. Thus it is an
important problem to analyze various symmetry forms of 3D shapes. Planar
reflective symmetry is the most fundamental one. Traditional methods based on
spatial sampling can be time-consuming and may not be able to identify all the
symmetry planes. In this paper, we present a novel learning framework to
automatically discover global planar reflective symmetry of a 3D shape. Our
framework trains an unsupervised 3D convolutional neural network to extract
global model features and then outputs possible global symmetry parameters,
where input shapes are represented using voxels. We introduce a dedicated
symmetry distance loss along with a regularization loss to avoid generating
duplicated symmetry planes. Our network can also identify generalized cylinders
by predicting their rotation axes. We further provide a method to remove
invalid and duplicated planes and axes. We demonstrate that our method is able
to produce reliable and accurate results. Our neural network based method is
hundreds of times faster than the state-of-the-art methods, which are based on
sampling. Our method is also robust even with noisy or incomplete input
surfaces.Comment: Corrected typo
PRS-Net: planar reflective symmetry detection net for 3D models
In geometry processing, symmetry is a universal type of high-level structural information of 3D models and benefits many geometry processing tasks including shape segmentation, alignment, matching, and completion. Thus it is an important problem to analyze various symmetry forms of 3D shapes. Planar reflective symmetry is the most fundamental one. Traditional methods based on spatial sampling can be time-consuming and may not be able to identify all the symmetry planes. In this paper, we present a novel learning framework to automatically discover global planar reflective symmetry of a 3D shape. Our framework trains an unsupervised 3D convolutional neural network to extract global model features and then outputs possible global symmetry parameters, where input shapes are represented using voxels. We introduce a dedicated symmetry distance loss along with a regularization loss to avoid generating duplicated symmetry planes. Our network can also identify generalized cylinders by predicting their rotation axes. We further provide a method to remove invalid and duplicated planes and axes. We demonstrate that our method is able to produce reliable and accurate results. Our neural network based method is hundreds of times faster than the state-of-the-art methods, which are based on sampling. Our method is also robust even with noisy or incomplete input surfaces