An Analytic Approach to Tensor Scale with an Efficient Algorithm and Applications to Image Filtering

Scale is a widely used notion in image analysis 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 have introduced a local morphometric scale using an ellipsoidal model that yields a unified representation of structure size, orientation, and anisotropy. In our previous works, tensor scale was described using an algorithmic approach and a precise analytic definition was missing. Here, we formulate an analytic definition for tensor scale in n-dimensional (n-D) images and present an efficient computational solution in 2- and 3-D. Finally, we present an application of tensor scale in medical image filtering. Results of new tensor scale computation algorithm are presented. Also, the performance of tensor scale based image filtering is compared with various approaches of diffusive filtering and the results found are very promising.