9,630 research outputs found
Inner and outer approximation of convex sets using alignment
We show that there exists, for each closed bounded convex set C in the Euclidean plane with nonempty interior, a quadrangle Q having the following two properties. Its sides support C at the vertices of a rectangle r and at least three of the vertices of Q lie on the boundary of a rectangle R that is a dilation of r with ratio 2. We will prove that this implies that quadrangle Q is contained in rectangle R and that, consequently, the inner approximation r of C has an area of at least half the area of the outer approximation Q of C. The proof makes use of alignment or Schüttelung, an operation on convex sets
Distribution of Aligned Letter Pairs in Optimal Alignments of Random Sequences
Considering the optimal alignment of two i.i.d. random sequences of length
, we show that when the scoring function is chosen randomly, almost surely
the empirical distribution of aligned letter pairs in all optimal alignments
converges to a unique limiting distribution as tends to infinity. This
result is interesting because it helps understanding the microscopic path
structure of a special type of last passage percolation problem with correlated
weights, an area of long-standing open problems. Characterizing the microscopic
path structure yields furthermore a robust alternative to optimal alignment
scores for testing the relatedness of genetic sequences
Face analysis using curve edge maps
This paper proposes an automatic and real-time system for face analysis, usable in visual communication applications. In this approach, faces are represented with Curve Edge Maps, which are collections of polynomial segments with a convex region. The segments are extracted from edge pixels using an adaptive incremental linear-time fitting algorithm, which is based on constructive polynomial fitting. The face analysis system considers face tracking, face recognition and facial feature detection, using Curve Edge Maps driven by histograms of intensities and histograms of relative positions. When applied to different face databases and video sequences, the average face recognition rate is 95.51%, the average facial feature detection rate is 91.92% and the accuracy in location of the facial features is 2.18% in terms of the size of the face, which is comparable with or better than the results in literature. However, our method has the advantages of simplicity, real-time performance and extensibility to the different aspects of face analysis, such as recognition of facial expressions and talking
Partial Sum Minimization of Singular Values in Robust PCA: Algorithm and Applications
Robust Principal Component Analysis (RPCA) via rank minimization is a
powerful tool for recovering underlying low-rank structure of clean data
corrupted with sparse noise/outliers. In many low-level vision problems, not
only it is known that the underlying structure of clean data is low-rank, but
the exact rank of clean data is also known. Yet, when applying conventional
rank minimization for those problems, the objective function is formulated in a
way that does not fully utilize a priori target rank information about the
problems. This observation motivates us to investigate whether there is a
better alternative solution when using rank minimization. In this paper,
instead of minimizing the nuclear norm, we propose to minimize the partial sum
of singular values, which implicitly encourages the target rank constraint. Our
experimental analyses show that, when the number of samples is deficient, our
approach leads to a higher success rate than conventional rank minimization,
while the solutions obtained by the two approaches are almost identical when
the number of samples is more than sufficient. We apply our approach to various
low-level vision problems, e.g. high dynamic range imaging, motion edge
detection, photometric stereo, image alignment and recovery, and show that our
results outperform those obtained by the conventional nuclear norm rank
minimization method.Comment: Accepted in Transactions on Pattern Analysis and Machine Intelligence
(TPAMI). To appea
Optimal Joint Power and Subcarrier Allocation for MC-NOMA Systems
In this paper, we investigate the resource allocation algorithm design for
multicarrier non-orthogonal multiple access (MC-NOMA) systems. The proposed
algorithm is obtained from the solution of a non-convex optimization problem
for the maximization of the weighted system throughput. We employ monotonic
optimization to develop the optimal joint power and subcarrier allocation
policy. The optimal resource allocation policy serves as a performance
benchmark due to its high complexity. Furthermore, to strike a balance between
computational complexity and optimality, a suboptimal scheme with low
computational complexity is proposed. Our simulation results reveal that the
suboptimal algorithm achieves a close-to-optimal performance and MC-NOMA
employing the proposed resource allocation algorithm provides a substantial
system throughput improvement compared to conventional multicarrier orthogonal
multiple access (MC-OMA).Comment: Submitted to Globecom 201
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