We study the complexity of the parallel Givens factorization of a square matrix of size n on a shared memory architecture composed with p identical processors (coarse grained EREW PRAM). We show how to construct an asymptotically optimal algorithm. We deduce that the time complexity is equal to:and that the minimum number of processors in order to compute the Givens factorization in asymptotically optimal time (2n + o(n)) is equal to pOPt = n/(2These results complete previous analysis presented in the case where the number of processors is unlimited.

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International audienceRecent investigations illustrate that view-based methods, with pose normalization pre-processing get better performances in retrieving rigid models than other approaches and still the most popular and practical methods in the field of 3D shape retrieval. In this paper we present an improvement of 3D shape retrieval methods based on bag-of features approach. These methods use this approach to integrate a set of features extracted from 2D views of the 3D objects using the SIFT (Scale Invariant Feature Transform) algorithm into histograms using vector quantization which is based on a global visual codebook. In order to improve the retrieval performances, we propose to associate to each 3D object its local visual codebook instead of a unique global codebook. The experimental results obtained on the Princeton Shape Benchmark database, for the BF-SIFT method proposed by Ohbuchi et al. and CM-BOF proposed by Zhouhui et al., show that the proposed approach performs better than the original approach

Abstract.Despite of the variety of approaches proposed in the literature in order to improve the execution time of the 3D shape retrieval [14,15], the challenge that still remains is to design a 3D shape retrieval method that allows the large scale retrieval and, in the same time, respects the relevance of the obtained results. In this work, we deal with the problem of the large scale of 3D shape retrieval by proposing new implementations on multi-core environment. At our knowledge, a few partial works based on HPC (High Performance Computing), have been proposed in the literature [1,2]. The proposed solutions are designed for the GPU (Graphical Processing Unit) and concern only the step of the extraction of the SIFT salient local features. In order to optimally exploit the potential of the multi-core architectures, we have studied different data distributions. Experimental results, under OpenMP environment, show that the large scale retrieval can be achieved using the multi-core environment.

This paper addresses the problem of 3D shape retrieval in large databases of 3D objects (large scale retrieval). While this problem is emerging and interesting as the size of 3D object databases grows rapidly, the main two issues the community has to focus on are: computational efficiency of 3D object retrieval and the quality of retrieved results. In this work we are interested by the problem of the computational efficiency where we propose to accelerate the BF-SIFT method by exploiting the potential of the GPU to reduce the computation times of the shape indexing of the query and the shape matching using the GPU. Experimental results show that the execution time is significantly reduced, this promises that the large scale retrieval can be achieved using the GPU.