Tensor scale: A local morphometric parameter with applications to computer vision and image processing

Abstract

Scale is a widely used notion in image analysis that evolved in the form of scale-space theory whose key idea is to represent and analyze an image at various resolutions. Recently, the notion of localized scale—a space-variant resolution scheme—has drawn significant research interest. Previously, we reported local morphometric scale using a spherical model. A major limitation of the spherical model is that it ignores structure orientation and anisotropy, and therefore fails to be optimal in many imaging applications including biomedical ones where structures are inherently anisotropic and have mixed orientations. Here, we introduce a new concept called “tensor scale”—a local morphometric parameter yielding a unified representation of structure size, orientation, and anisotropy. Also, a few applications of tensor scale in computer vision and image analysis, especially, in image filtering are illustrated. At any image point, its tensor scale is the parametric representation of the largest ellipse (in 2D) or ellipsoid (in 3D) centered at that point and contained in the same homogeneous region. An algorithmic framework to compute tensor scale at any image point is proposed and results of its application on several real images are presented. Also, performance of the tensor scale computation method under image rotation, varying pixel size, and background inhomogeneity is studied. Results of a quantitative analysis evaluating performance of the method on 2D brain phantom images at various levels of noise and blur, and a fixed background inhomogeneity are presented. Agreement between tensor scale images computed on matching image slices from two 3D magnetic resonance data acquired simultaneously using different protocols are demonstrated. Finally, the application of tensor scale in anisotropic diffusive image filtering is presented that encourages smoothing inside a homogeneous region and also along edges and elongated structures while discourages blurring across them. Both qualitative and quantitative results of application of the new filtering method have been presented and compared with the results obtained by spherical scale-based and standard diffusive filtering methods.