1,698 research outputs found
Ordered Statistics Vertex Extraction and Tracing Algorithm (OSVETA)
We propose an algorithm for identifying vertices from three dimensional (3D)
meshes that are most important for a geometric shape creation. Extracting such
a set of vertices from a 3D mesh is important in applications such as digital
watermarking, but also as a component of optimization and triangulation. In the
first step, the Ordered Statistics Vertex Extraction and Tracing Algorithm
(OSVETA) estimates precisely the local curvature, and most important
topological features of mesh geometry. Using the vertex geometric importance
ranking, the algorithm traces and extracts a vector of vertices, ordered by
decreasing index of importance.Comment: Accepted for publishing and Copyright transfered to Advances in
Electrical and Computer Engineering, November 23th 201
Simplification Resilient LDPC-Coded Sparse-QIM Watermarking for 3D-Meshes
We propose a blind watermarking scheme for 3-D meshes which combines sparse
quantization index modulation (QIM) with deletion correction codes. The QIM
operates on the vertices in rough concave regions of the surface thus ensuring
impeccability, while the deletion correction code recovers the data hidden in
the vertices which is removed by mesh optimization and/or simplification. The
proposed scheme offers two orders of magnitude better performance in terms of
recovered watermark bit error rate compared to the existing schemes of similar
payloads and fidelity constraints.Comment: Submitted, revised and Copyright transfered to IEEE Transactions on
Multimedia, October 9th 201
Worst Configurations (Instantons) for Compressed Sensing over Reals: a Channel Coding Approach
We consider the Linear Programming (LP) solution of the Compressed Sensing
(CS) problem over reals, also known as the Basis Pursuit (BasP) algorithm. The
BasP allows interpretation as a channel-coding problem, and it guarantees
error-free reconstruction with a properly chosen measurement matrix and
sufficiently sparse error vectors. In this manuscript, we examine how the BasP
performs on a given measurement matrix and develop an algorithm to discover the
sparsest vectors for which the BasP fails. The resulting algorithm is a
generalization of our previous results on finding the most probable
error-patterns degrading performance of a finite size Low-Density Parity-Check
(LDPC) code in the error-floor regime. The BasP fails when its output is
different from the actual error-pattern. We design a CS-Instanton Search
Algorithm (ISA) generating a sparse vector, called a CS-instanton, such that
the BasP fails on the CS-instanton, while the BasP recovery is successful for
any modification of the CS-instanton replacing a nonzero element by zero. We
also prove that, given a sufficiently dense random input for the error-vector,
the CS-ISA converges to an instanton in a small finite number of steps. The
performance of the CS-ISA is illustrated on a randomly generated matrix. For this example, the CS-ISA outputs the shortest instanton (error
vector) pattern of length 11.Comment: Accepted to be presented at the IEEE International Symposium on
Information Theory (ISIT 2010). 5 pages, 2 Figures. Minor edits from previous
version. Added a new reference
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