4,016 research outputs found
Connectivity-Enforcing Hough Transform for the Robust Extraction of Line Segments
Global voting schemes based on the Hough transform (HT) have been widely used
to robustly detect lines in images. However, since the votes do not take line
connectivity into account, these methods do not deal well with cluttered
images. In opposition, the so-called local methods enforce connectivity but
lack robustness to deal with challenging situations that occur in many
realistic scenarios, e.g., when line segments cross or when long segments are
corrupted. In this paper, we address the critical limitations of the HT as a
line segment extractor by incorporating connectivity in the voting process.
This is done by only accounting for the contributions of edge points lying in
increasingly larger neighborhoods and whose position and directional content
agree with potential line segments. As a result, our method, which we call
STRAIGHT (Segment exTRAction by connectivity-enforcInG HT), extracts the
longest connected segments in each location of the image, thus also integrating
into the HT voting process the usually separate step of individual segment
extraction. The usage of the Hough space mapping and a corresponding
hierarchical implementation make our approach computationally feasible. We
present experiments that illustrate, with synthetic and real images, how
STRAIGHT succeeds in extracting complete segments in several situations where
current methods fail.Comment: Submitted for publicatio
Pruned Continuous Haar Transform of 2D Polygonal Patterns with Application to VLSI Layouts
We introduce an algorithm for the efficient computation of the continuous
Haar transform of 2D patterns that can be described by polygons. These patterns
are ubiquitous in VLSI processes where they are used to describe design and
mask layouts. There, speed is of paramount importance due to the magnitude of
the problems to be solved and hence very fast algorithms are needed. We show
that by techniques borrowed from computational geometry we are not only able to
compute the continuous Haar transform directly, but also to do it quickly. This
is achieved by massively pruning the transform tree and thus dramatically
decreasing the computational load when the number of vertices is small, as is
the case for VLSI layouts. We call this new algorithm the pruned continuous
Haar transform. We implement this algorithm and show that for patterns found in
VLSI layouts the proposed algorithm was in the worst case as fast as its
discrete counterpart and up to 12 times faster.Comment: 4 pages, 5 figures, 1 algorith
Minimizing the stabbing number of matchings, trees, and triangulations
The (axis-parallel) stabbing number of a given set of line segments is the
maximum number of segments that can be intersected by any one (axis-parallel)
line. This paper deals with finding perfect matchings, spanning trees, or
triangulations of minimum stabbing number for a given set of points. The
complexity of these problems has been a long-standing open question; in fact,
it is one of the original 30 outstanding open problems in computational
geometry on the list by Demaine, Mitchell, and O'Rourke. The answer we provide
is negative for a number of minimum stabbing problems by showing them NP-hard
by means of a general proof technique. It implies non-trivial lower bounds on
the approximability. On the positive side we propose a cut-based integer
programming formulation for minimizing the stabbing number of matchings and
spanning trees. We obtain lower bounds (in polynomial time) from the
corresponding linear programming relaxations, and show that an optimal
fractional solution always contains an edge of at least constant weight. This
result constitutes a crucial step towards a constant-factor approximation via
an iterated rounding scheme. In computational experiments we demonstrate that
our approach allows for actually solving problems with up to several hundred
points optimally or near-optimally.Comment: 25 pages, 12 figures, Latex. To appear in "Discrete and Computational
Geometry". Previous version (extended abstract) appears in SODA 2004, pp.
430-43
Fast Hierarchical Clustering and Other Applications of Dynamic Closest Pairs
We develop data structures for dynamic closest pair problems with arbitrary
distance functions, that do not necessarily come from any geometric structure
on the objects. Based on a technique previously used by the author for
Euclidean closest pairs, we show how to insert and delete objects from an
n-object set, maintaining the closest pair, in O(n log^2 n) time per update and
O(n) space. With quadratic space, we can instead use a quadtree-like structure
to achieve an optimal time bound, O(n) per update. We apply these data
structures to hierarchical clustering, greedy matching, and TSP heuristics, and
discuss other potential applications in machine learning, Groebner bases, and
local improvement algorithms for partition and placement problems. Experiments
show our new methods to be faster in practice than previously used heuristics.Comment: 20 pages, 9 figures. A preliminary version of this paper appeared at
the 9th ACM-SIAM Symp. on Discrete Algorithms, San Francisco, 1998, pp.
619-628. For source code and experimental results, see
http://www.ics.uci.edu/~eppstein/projects/pairs
Inhomogeneous extragalactic magnetic fields and the second knee in the cosmic ray spectrum
Various experiments indicate the existence of a second knee around energy
E=3.10^{17} eV in the cosmic ray spectrum. This feature could be the signature
of the end of the galactic component and of the emergence of the extragalactic
one, provided that the latter cuts off at low energies. Recent analytical
calculations have shown that this cut-off could be a consequence of the
existence of extragalactic magnetic fields: low energy protons diffuse on
extragalactic magnetic fields and cannot reach the observer within a given
time. We study the influence of inhomogeneous magnetic fields on the magnetic
horizon, using a new semi-analytical propagation code. Our results indicate
that, at a fixed value of the volume averaged magnetic field , the amplitude
of the low energy cut-off is mainly controled by the strength of magnetic
fields in the voids of the large scale structure distribution.Comment: 15 pages, 10 figures. Version to appear in PRD (minor changes
Convolutional Neural Networks for Counting Fish in Fisheries Surveillance Video
We present a computer vision tool that analyses video from a CCTV system installed on fishing trawlers to monitor discarded fish catch. The system aims to support expert observers who review the footage and verify numbers, species and sizes of discarded fish. The operational environment presents a significant challenge for these tasks. Fish are processed below deck under fluorescent lights, they are randomly oriented and there are multiple occlusions. The scene is unstructured and complicated by the presence of fishermen processing the catch. We describe an approach to segmenting the scene and counting fish that exploits the -Fields algorithm. We performed extensive tests of the algorithm on a data set comprising 443 frames from 6 belts. Results indicate the relative count error (for individual fish) ranges from 2\% to 16\%. We believe this is the first system that is able to handle footage from operational trawlers
- …