102,183 research outputs found
Reliable RANSAC Using a Novel Preprocessing Model
Geometric assumption and verification with RANSAC has become a crucial step for corresponding to local features due to its wide applications in biomedical feature analysis and vision computing. However, conventional RANSAC is very time-consuming due to redundant sampling times, especially dealing with the case of numerous matching pairs. This paper presents a novel preprocessing model to explore a reduced set with reliable correspondences from initial matching dataset. Both geometric model generation and verification are carried out on this reduced set, which leads to considerable speedups. Afterwards, this paper proposes a reliable RANSAC framework using preprocessing model, which was implemented and verified using Harris and SIFT features, respectively. Compared with traditional RANSAC, experimental results show that our method is more efficient
Computing a Compact Spline Representation of the Medial Axis Transform of a 2D Shape
We present a full pipeline for computing the medial axis transform of an
arbitrary 2D shape. The instability of the medial axis transform is overcome by
a pruning algorithm guided by a user-defined Hausdorff distance threshold. The
stable medial axis transform is then approximated by spline curves in 3D to
produce a smooth and compact representation. These spline curves are computed
by minimizing the approximation error between the input shape and the shape
represented by the medial axis transform. Our results on various 2D shapes
suggest that our method is practical and effective, and yields faithful and
compact representations of medial axis transforms of 2D shapes.Comment: GMP14 (Geometric Modeling and Processing
On the matrix square root via geometric optimization
This paper is triggered by the preprint "\emph{Computing Matrix Squareroot
via Non Convex Local Search}" by Jain et al.
(\textit{\textcolor{blue}{arXiv:1507.05854}}), which analyzes gradient-descent
for computing the square root of a positive definite matrix. Contrary to claims
of~\citet{jain2015}, our experiments reveal that Newton-like methods compute
matrix square roots rapidly and reliably, even for highly ill-conditioned
matrices and without requiring commutativity. We observe that gradient-descent
converges very slowly primarily due to tiny step-sizes and ill-conditioning. We
derive an alternative first-order method based on geodesic convexity: our
method admits a transparent convergence analysis ( page), attains linear
rate, and displays reliable convergence even for rank deficient problems.
Though superior to gradient-descent, ultimately our method is also outperformed
by a well-known scaled Newton method. Nevertheless, the primary value of our
work is its conceptual value: it shows that for deriving gradient based methods
for the matrix square root, \emph{the manifold geometric view of positive
definite matrices can be much more advantageous than the Euclidean view}.Comment: 8 pages, 12 plots, this version contains several more references and
more words about the rank-deficient cas
Optimal relay location and power allocation for low SNR broadcast relay channels
We consider the broadcast relay channel (BRC), where a single source
transmits to multiple destinations with the help of a relay, in the limit of a
large bandwidth. We address the problem of optimal relay positioning and power
allocations at source and relay, to maximize the multicast rate from source to
all destinations. To solve such a network planning problem, we develop a
three-faceted approach based on an underlying information theoretic model,
computational geometric aspects, and network optimization tools. Firstly,
assuming superposition coding and frequency division between the source and the
relay, the information theoretic framework yields a hypergraph model of the
wideband BRC, which captures the dependency of achievable rate-tuples on the
network topology. As the relay position varies, so does the set of hyperarcs
constituting the hypergraph, rendering the combinatorial nature of optimization
problem. We show that the convex hull C of all nodes in the 2-D plane can be
divided into disjoint regions corresponding to distinct hyperarcs sets. These
sets are obtained by superimposing all k-th order Voronoi tessellation of C. We
propose an easy and efficient algorithm to compute all hyperarc sets, and prove
they are polynomially bounded. Using the switched hypergraph approach, we model
the original problem as a continuous yet non-convex network optimization
program. Ultimately, availing on the techniques of geometric programming and
-norm surrogate approximation, we derive a good convex approximation. We
provide a detailed characterization of the problem for collinearly located
destinations, and then give a generalization for arbitrarily located
destinations. Finally, we show strong gains for the optimal relay positioning
compared to seemingly interesting positions.Comment: In Proceedings of INFOCOM 201
DCTM: Discrete-Continuous Transformation Matching for Semantic Flow
Techniques for dense semantic correspondence have provided limited ability to
deal with the geometric variations that commonly exist between semantically
similar images. While variations due to scale and rotation have been examined,
there lack practical solutions for more complex deformations such as affine
transformations because of the tremendous size of the associated solution
space. To address this problem, we present a discrete-continuous transformation
matching (DCTM) framework where dense affine transformation fields are inferred
through a discrete label optimization in which the labels are iteratively
updated via continuous regularization. In this way, our approach draws
solutions from the continuous space of affine transformations in a manner that
can be computed efficiently through constant-time edge-aware filtering and a
proposed affine-varying CNN-based descriptor. Experimental results show that
this model outperforms the state-of-the-art methods for dense semantic
correspondence on various benchmarks
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