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Tensor scale: An analytic approach with efficient computation and applications
Journal article   Peer reviewed

Tensor scale: An analytic approach with efficient computation and applications

Ziyue Xu, Punam K Saha and Soura Dasgupta
Computer vision and image understanding, Vol.116(10), pp.1060-1075
10/2012
DOI: 10.1016/j.cviu.2012.05.006
PMCID: PMC4519998
PMID: 26236148

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Abstract

► Theoretical formulation of tensor scale – an anisotropic local scale model. ► Efficient algorithm for tensor scale computation in three-dimensions. ► Development and evaluation of tensor scale based anisotropic diffusive filtering. ► Development and evaluation of tensor scale based n-linear interpolation. Scale is a widely used notion in computer vision and image understanding that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, we introduced a notion of local morphometric scale referred to as “tensor scale” using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. In the previous work, tensor scale was described using a 2-D algorithmic approach and a precise analytic definition was missing. Also, the application of tensor scale in 3-D using the previous framework is not practical due to high computational complexity. In this paper, an analytic definition of tensor scale is formulated for n-dimensional (n-D) images that captures local structure size, orientation and anisotropy. Also, an efficient computational solution in 2- and 3-D using several novel differential geometric approaches is presented and the accuracy of results is experimentally examined. Also, a matrix representation of tensor scale is derived facilitating several operations including tensor field smoothing to capture larger contextual knowledge. Finally, the applications of tensor scale in image filtering and n-linear interpolation are presented and the performance of their results is examined in comparison with respective state-of-art methods. Specifically, the performance of tensor scale based image filtering is compared with gradient and Weickert’s structure tensor based diffusive filtering algorithms. Also, the performance of tensor scale based n-linear interpolation is evaluated in comparison with standard n-linear and windowed-sinc interpolation methods.
 Local scale Scale-space Image filtering Tensor scale Morphometry Image interpolation

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