Multi-scale local features based on anisotropic heat diffusion and global eigen-structure

Abstract

Multi-scale local feature detection enables downstream registration and recognition tasks in medical image analysis. This paper articulates a novel robust method for multi-scale local feature extraction on volumetric data. The central idea is the elegant unification of local/global eigen-structures within the powerful framework of anisotropic heat diffusion. First, the local vector field is constructed by way of Hessian matrix and its eigenvectors/eigenvalues. Second, anisotropic heat kernels are computed using the vector field’s global graph Laplacian. Robust local features are manifested as extrema across multiple time scales, serving as volumetric heat kernel signature. To tackle the computational challenge for massive volumetric data, we propose a multiresolution strategy for hierarchical feature extraction based on our feature-preserving down-sampling approach. As a result, heat kernels and local feature identification can be approximated at a coarser level first, and then are pinpointed in a localized region at a finer resolution. Another novelty of this work lies at the initial heat design directly using local eigenvalue for anisotropic heat diffusion across the volumetric domain. We conduct experiments on various medical datasets, and draw comparisons with 3D SIFT method. The diffusion property of our local features, which can be interpreted as random walks in statistics, makes our method robust to noise, and gives rise to intrinsic multi-scale characteristics.