Low-level Feature Detection Using the Boundary Tensor

Abstract

Tensors are a useful tool for the detection of low-level features such as edges, lines, corners, and junctions because they can represent feature strength and orientation in a way that is easy to work with. However, traditional approaches to define feature tensors have a number of disadvantages. By means of the first and second order Riesz transforms, we propose a new approach called the boundary tensor. Using quadratic convolution equations, we show that the boundary tensor overcomes some problems of the older tensor definitions. When the Riesz transform is combined with the Laplacian of Gaussian, the boundary tensor can be efficiently computed in the spatial domain. The usefulness of the new method is demonstrated for a number of application examples.¹

This work was performed during a visit at the Computer Vision Lab of the University of Linköping, Sweden. I’d like to thank G. Granlund, M. Felsberg and K. Nordberg for many valuable discussions, and the Informatics Department of the University of Hamburg for their generous support of this visit.