237,033 research outputs found
Subsumption Algorithms for Three-Valued Geometric Resolution
In our implementation of geometric resolution, the most costly operation is
subsumption testing (or matching): One has to decide for a three-valued,
geometric formula, if this formula is false in a given interpretation. The
formula contains only atoms with variables, equality, and existential
quantifiers. The interpretation contains only atoms with constants. Because the
atoms have no term structure, matching for geometric resolution is hard. We
translate the matching problem into a generalized constraint satisfaction
problem, and discuss several approaches for solving it efficiently, one direct
algorithm and two translations to propositional SAT. After that, we study
filtering techniques based on local consistency checking. Such filtering
techniques can a priori refute a large percentage of generalized constraint
satisfaction problems. Finally, we adapt the matching algorithms in such a way
that they find solutions that use a minimal subset of the interpretation. The
adaptation can be combined with every matching algorithm. The techniques
presented in this paper may have applications in constraint solving independent
of geometric resolution.Comment: This version was revised on 18.05.201
Growth rates of geometric grid classes of permutations
Geometric grid classes of permutations have proven to be key in investigations of classical permutation pattern classes. By considering the representation of gridded permutations as words in a trace monoid, we prove that every geometric grid class has a growth rate which is given by the square of the largest root of the matching polynomial of a related graph. As a consequence, we characterise the set of growth rates of geometric grid classes in terms of the spectral radii of trees, explore the influence of "cycle parity" on the growth rate, compare the growth rates of geometric grid classes against those of the corresponding monotone grid classes, and present new results concerning the effect of edge subdivision on the largest root of the matching polynomial
Convolutional neural network architecture for geometric matching
We address the problem of determining correspondences between two images in
agreement with a geometric model such as an affine or thin-plate spline
transformation, and estimating its parameters. The contributions of this work
are three-fold. First, we propose a convolutional neural network architecture
for geometric matching. The architecture is based on three main components that
mimic the standard steps of feature extraction, matching and simultaneous
inlier detection and model parameter estimation, while being trainable
end-to-end. Second, we demonstrate that the network parameters can be trained
from synthetically generated imagery without the need for manual annotation and
that our matching layer significantly increases generalization capabilities to
never seen before images. Finally, we show that the same model can perform both
instance-level and category-level matching giving state-of-the-art results on
the challenging Proposal Flow dataset.Comment: In 2017 IEEE Conference on Computer Vision and Pattern Recognition
(CVPR 2017
Robust 3-Dimensional Object Recognition using Stereo Vision and Geometric Hashing
We propose a technique that combines geometric hashing with stereo vision. The idea is to use the robustness of geometric hashing to spurious data to overcome the correspondence problem, while the stereo vision setup enables direct model matching using the 3-D object models. Furthermore, because the matching technique relies on the relative positions of local features, we should be able to perform robust recognition even with partially occluded objects. We tested this approach with simple geometric objects using a corner point detector. We successfully recognized objects even in scenes where the objects were partially occluded by other objects. For complicated scenes, however, the limited set of model features and required amount of computing time, sometimes became a proble
Geometry Helps to Compare Persistence Diagrams
Exploiting geometric structure to improve the asymptotic complexity of
discrete assignment problems is a well-studied subject. In contrast, the
practical advantages of using geometry for such problems have not been
explored. We implement geometric variants of the Hopcroft--Karp algorithm for
bottleneck matching (based on previous work by Efrat el al.) and of the auction
algorithm by Bertsekas for Wasserstein distance computation. Both
implementations use k-d trees to replace a linear scan with a geometric
proximity query. Our interest in this problem stems from the desire to compute
distances between persistence diagrams, a problem that comes up frequently in
topological data analysis. We show that our geometric matching algorithms lead
to a substantial performance gain, both in running time and in memory
consumption, over their purely combinatorial counterparts. Moreover, our
implementation significantly outperforms the only other implementation
available for comparing persistence diagrams.Comment: 20 pages, 10 figures; extended version of paper published in ALENEX
201
Constraint-based stereo matching
The major difficulty in stereo vision is the correspondence problem that requires matching features in two stereo images. Researchers describe a constraint-based stereo matching technique using local geometric constraints among edge segments to limit the search space and to resolve matching ambiguity. Edge segments are used as image features for stereo matching. Epipolar constraint and individual edge properties are used to determine possible initial matches between edge segments in a stereo image pair. Local edge geometric attributes such as continuity, junction structure, and edge neighborhood relations are used as constraints to guide the stereo matching process. The result is a locally consistent set of edge segment correspondences between stereo images. These locally consistent matches are used to generate higher-level hypotheses on extended edge segments and junctions to form more global contexts to achieve global consistency
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