title: Tensor scale: An analytic approach with efficient computation and applications.
abstract: 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 forn-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 andn-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 basedn-linear interpolation is evaluated in comparison with standardn-linear and windowed-sinc interpolation methods.
authors.affiliation: Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA 52242, United States.
authors.forename: Ziyue
authors.initials: Z
authors.lastname: Xu
authors.affiliation: Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA 52242, United States ; Department of Radiology, University of Iowa, Iowa City, IA 52242, United States.
authors.forename: Punam K
authors.initials: PK
authors.lastname: Saha
authors.affiliation: Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA 52242, United States.
authors.forename: Soura
authors.initials: S
authors.lastname: Dasgupta
keywords: Image filtering; Image interpolation; Local scale; Morphometry; Scale-space; Tensor scale