Fuzzy shape-based interpolation

Abstract

Image interpolation is an essential task in medical imaging because of limited and varying spatial and temporal resolution in imaging devices; also, it is a necessary step while rotating an image for different purposes. In the literature, interpolation techniques have been divided into two major groups: image-based and object-based. Shape-based interpolation is a commonly used object-based method and it works on binary images. In this paper, we propose fuzzy shape-based interpolation by using fuzzy distance transform theory that is applicable to fuzzy object representations. The method essentially works in three steps as follows. Step 1: Separately compute the fuzzy distance transform (FDT) of two successive slices. Step 2: Compute the FDT of the target slice by interpolating the FDT values of original slices. Step 3: Compute the fuzzy object representation on the target slice by applying an inverse FDT (iFDT). Fuzzy shapebased interpolation solves a fundamental problem of shape-based interpolation. Specifically, the new method requires no binarization and it accurately handles the fuzziness of objects using fuzzy distance transform. A new theory and algorithm for iFDT are proposed here to compute the original fuzzy membership map form its fuzzy distance transform map. The idea of iFDT is essential for directly applying the idea of shape-based interpolation to a fuzzy object representation. The method is being tested on clinical data and compared with binary shape-based interpolation.