4,780 research outputs found
Geodesic-Preserving Polygon Simplification
Polygons are a paramount data structure in computational geometry. While the
complexity of many algorithms on simple polygons or polygons with holes depends
on the size of the input polygon, the intrinsic complexity of the problems
these algorithms solve is often related to the reflex vertices of the polygon.
In this paper, we give an easy-to-describe linear-time method to replace an
input polygon by a polygon such that (1)
contains , (2) has its reflex
vertices at the same positions as , and (3) the number of vertices
of is linear in the number of reflex vertices. Since the
solutions of numerous problems on polygons (including shortest paths, geodesic
hulls, separating point sets, and Voronoi diagrams) are equivalent for both
and , our algorithm can be used as a preprocessing
step for several algorithms and makes their running time dependent on the
number of reflex vertices rather than on the size of
Subclass Discriminant Analysis of Morphological and Textural Features for HEp-2 Staining Pattern Classification
Classifying HEp-2 fluorescence patterns in Indirect Immunofluorescence (IIF) HEp-2 cell imaging is important for the differential diagnosis of autoimmune diseases. The current technique, based on human visual inspection, is time-consuming, subjective and dependent on the operator's experience. Automating this process may be a solution to these limitations, making IIF faster and more reliable. This work proposes a classification approach based on Subclass Discriminant Analysis (SDA), a dimensionality reduction technique that provides an effective representation of the cells in the feature space, suitably coping with the high within-class variance typical of HEp-2 cell patterns. In order to generate an adequate characterization of the fluorescence patterns, we investigate the individual and combined contributions of several image attributes, showing that the integration of morphological, global and local textural features is the most suited for this purpose. The proposed approach provides an accuracy of the staining pattern classification of about 90%
Automatic normal orientation in point clouds of building interiors
Orienting surface normals correctly and consistently is a fundamental problem
in geometry processing. Applications such as visualization, feature detection,
and geometry reconstruction often rely on the availability of correctly
oriented normals. Many existing approaches for automatic orientation of normals
on meshes or point clouds make severe assumptions on the input data or the
topology of the underlying object which are not applicable to real-world
measurements of urban scenes. In contrast, our approach is specifically
tailored to the challenging case of unstructured indoor point cloud scans of
multi-story, multi-room buildings. We evaluate the correctness and speed of our
approach on multiple real-world point cloud datasets
Multi-Agent Deployment for Visibility Coverage in Polygonal Environments with Holes
This article presents a distributed algorithm for a group of robotic agents
with omnidirectional vision to deploy into nonconvex polygonal environments
with holes. Agents begin deployment from a common point, possess no prior
knowledge of the environment, and operate only under line-of-sight sensing and
communication. The objective of the deployment is for the agents to achieve
full visibility coverage of the environment while maintaining line-of-sight
connectivity with each other. This is achieved by incrementally partitioning
the environment into distinct regions, each completely visible from some agent.
Proofs are given of (i) convergence, (ii) upper bounds on the time and number
of agents required, and (iii) bounds on the memory and communication
complexity. Simulation results and description of robust extensions are also
included
On the Power of Manifold Samples in Exploring Configuration Spaces and the Dimensionality of Narrow Passages
We extend our study of Motion Planning via Manifold Samples (MMS), a general
algorithmic framework that combines geometric methods for the exact and
complete analysis of low-dimensional configuration spaces with sampling-based
approaches that are appropriate for higher dimensions. The framework explores
the configuration space by taking samples that are entire low-dimensional
manifolds of the configuration space capturing its connectivity much better
than isolated point samples. The contributions of this paper are as follows:
(i) We present a recursive application of MMS in a six-dimensional
configuration space, enabling the coordination of two polygonal robots
translating and rotating amidst polygonal obstacles. In the adduced experiments
for the more demanding test cases MMS clearly outperforms PRM, with over
20-fold speedup in a coordination-tight setting. (ii) A probabilistic
completeness proof for the most prevalent case, namely MMS with samples that
are affine subspaces. (iii) A closer examination of the test cases reveals that
MMS has, in comparison to standard sampling-based algorithms, a significant
advantage in scenarios containing high-dimensional narrow passages. This
provokes a novel characterization of narrow passages which attempts to capture
their dimensionality, an attribute that had been (to a large extent) unattended
in previous definitions.Comment: 20 page
Supporting Focus and Context Awareness in 3D Modelling Tasks Using Multi-Layered Displays
Most 3D modelling software have been developed for conventional 2D displays, and as such, lack support for true depth perception. This contributes to making polygonal 3D modelling tasks challenging, particularly when models are complex and consist of a large number of overlapping components (e.g. vertices, edges) and objects (i.e. parts). Research has shown that users of 3D modelling software often encounter a range of difficulties, which collectively can be defined as focus and context awareness problems. These include maintaining position and orientation awarenesses, as well as recognizing distance between individual components and objects in 3D spaces. In this paper, we present five visualization and interaction techniques we have developed for multi-layered displays, to better support focus and context awareness in 3D modelling tasks. The results of a user study we conducted shows that three of these five techniques improve users' 3D modelling task performance
Convex Hulls in Polygonal Domains
We study generalizations of convex hulls to polygonal domains with holes. Convexity in Euclidean space is based on the notion of shortest paths, which are straight-line segments. In a polygonal domain, shortest paths are polygonal paths called geodesics. One possible generalization of convex hulls is based on the "rubber band" conception of the convex hull boundary as a shortest curve that encloses a given set of sites. However, it is NP-hard to compute such a curve in a general polygonal domain. Hence, we focus on a different, more direct generalization of convexity, where a set X is geodesically convex if it contains all geodesics between every pair of points x,y in X. The corresponding geodesic convex hull presents a few surprises, and turns out to behave quite differently compared to the classic Euclidean setting or to the geodesic hull inside a simple polygon. We describe a class of geometric objects that suffice to represent geodesic convex hulls of sets of sites, and characterize which such domains are geodesically convex. Using such a representation we present an algorithm to construct the geodesic convex hull of a set of O(n) sites in a polygonal domain with a total of n vertices and h holes in O(n^3h^{3+epsilon}) time, for any constant epsilon > 0
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