11,741 research outputs found
Capacity Scaling for Graph Cuts in Vision
Capacity scaling is a hierarchical approach to graph representation that can improve theoretical complexity and practical efficiency of max-flow/min-cut algorithms. Introduced by Edmonds, Karp, and Dinic [7, 6] in 1972, capacity scaling is well known in the combinatorial optimization community. Surprisingly, this major performance improving technique is overlooked in computer vision where graph cut methods typically solve energy minimization problems on huge N-D grids and algorithms β efficiency is a widely studied issue [3, 12, 16, 10]. Unlike some earlier hierarchical methods addressing efficiency of graph cuts in imaging, e.g. [16], capacity scaling preserves global optimality of the solution. This is the main motivation for our work studying capacity scaling in the context of vision. We show that capacity scaling significantly reduces non-polynomial theoretical time complexity of the max-flow algorithm in [3] to weakly polynomial O(m 2 n 2 log(U)) where U is the largest edge weight. While [3] is the fastest method for many applications in vision, capacity scaling gives several folds speed-ups for problems with large number of local minima. The effect is particularly strong in 3D applications with denser neighborhoods
Minimizing a sum of submodular functions
We consider the problem of minimizing a function represented as a sum of
submodular terms. We assume each term allows an efficient computation of {\em
exchange capacities}. This holds, for example, for terms depending on a small
number of variables, or for certain cardinality-dependent terms.
A naive application of submodular minimization algorithms would not exploit
the existence of specialized exchange capacity subroutines for individual
terms. To overcome this, we cast the problem as a {\em submodular flow} (SF)
problem in an auxiliary graph, and show that applying most existing SF
algorithms would rely only on these subroutines.
We then explore in more detail Iwata's capacity scaling approach for
submodular flows (Math. Programming, 76(2):299--308, 1997). In particular, we
show how to improve its complexity in the case when the function contains
cardinality-dependent terms.Comment: accepted to "Discrete Applied Mathematics
Spread spectrum-based video watermarking algorithms for copyright protection
Merged with duplicate record 10026.1/2263 on 14.03.2017 by CS (TIS)Digital technologies know an unprecedented expansion in the last years. The consumer can
now benefit from hardware and software which was considered state-of-the-art several years
ago. The advantages offered by the digital technologies are major but the same digital
technology opens the door for unlimited piracy. Copying an analogue VCR tape was certainly
possible and relatively easy, in spite of various forms of protection, but due to the analogue
environment, the subsequent copies had an inherent loss in quality. This was a natural way of
limiting the multiple copying of a video material. With digital technology, this barrier
disappears, being possible to make as many copies as desired, without any loss in quality
whatsoever. Digital watermarking is one of the best available tools for fighting this threat.
The aim of the present work was to develop a digital watermarking system compliant with the
recommendations drawn by the EBU, for video broadcast monitoring. Since the watermark
can be inserted in either spatial domain or transform domain, this aspect was investigated and
led to the conclusion that wavelet transform is one of the best solutions available. Since
watermarking is not an easy task, especially considering the robustness under various attacks
several techniques were employed in order to increase the capacity/robustness of the system:
spread-spectrum and modulation techniques to cast the watermark, powerful error correction
to protect the mark, human visual models to insert a robust mark and to ensure its invisibility.
The combination of these methods led to a major improvement, but yet the system wasn't
robust to several important geometrical attacks. In order to achieve this last milestone, the
system uses two distinct watermarks: a spatial domain reference watermark and the main
watermark embedded in the wavelet domain. By using this reference watermark and techniques
specific to image registration, the system is able to determine the parameters of the attack and
revert it. Once the attack was reverted, the main watermark is recovered. The final result is a
high capacity, blind DWr-based video watermarking system, robust to a wide range of attacks.BBC Research & Developmen
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