On Improving the Efficiency of Tensor Voting

• Published in: IEEE transactions on pattern analysis and machine intelligence 2011-11, Vol.33 (11), p.2215-2228
• Main Authors: Moreno, R., Garcia, M. A., Puig, D., Pizarro, L., Burgeth, B., Weickert, J.
• Format: Article
• Language: English
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Approximation; Approximation methods; Biological and medical sciences; Complexity; Complexity theory; Computational efficiency; Computer science; control theory; systems; Computing time; curveness and junctionness propagation; Eigenvalues and eigenfunctions; Exact sciences and technology; Fundamental and applied biological sciences. Psychology; Information technology; Informationsteknik; Mathematical analysis; Mathematical models; nonlinear approximation; Perception; perceptual grouping; Perceptual methods; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Shape; Signal processing; Signalbehandling; Studies; Surface treatment; TECHNOLOGY; TEKNIKVETENSKAP; Tensile stress; tensor voting; Tensors; Theoretical computing; Three dimensional displays; Vision; Voting
• ISSN: 0162-8828; 1939-3539; 1939-3539; 2160-9292
• DOI: 10.1109/TPAMI.2011.23

This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor voting and the stick component of the plate tensor voting must reinforce surfaceness, the plate components of both the plate and ball tensor voting must boost curveness, whereas junctionness must be strengthened by the ball component of the ball tensor voting. Two new parameters have been proposed for the second formulation in order to control the potentially conflictive influence of the stick component of the plate vote and the ball component of the ball vote. Results show that the proposed formulations can be used in applications where efficiency is an issue since they have a complexity of order O(1). Moreover, the second proposed formulation has been shown to be more appropriate than the original tensor voting for estimating saliencies by appropriately setting the two new parameters.