New Technique for Binary Morphological Shape-Based Interpolation

Abstract

In this paper we consider shape-based methods to generate additional slices in 3D binary volumes. The focused interpolation approaches, named SIMOL and BORS, are based on morphological and logical operators. Given two adjacent slices [Formula: see text] and [Formula: see text] of the binary image set, the methods iteratively generate a sequence of new slices showing a gradual transition between the corresponding shapes. First, we analyze the SIMOL and BORS techniques and highlight their problems. Then we present the main contribution of this paper: a new interpolation scheme, called SIMOL-NEW, that combines the iterative scheme of BORS and an interpolation kernel generated through SIMOL framework. Next, we compare SIMOL-NEW and BORS approaches using theoretical elements and computational experiments. The latter are executed using: (a) benchmark shapes; (b) simple volumes defined by sphere and paraboloid; (c) combination of ellipsoids; (d) a fork-like volume; (e) Cylinder Minus Sphere. The conclusion is that SIMOL-NEW performs closer to BORS for the cases (a) and (c) but it is more accurate than BORS in the tests (b) and (d). Besides, we offer comparisons of state-of-the-art approaches in shape-based interpolation and SIMOL-NEW using ground truth volumes (d) and (e). The computational experiment report that SIMOL-NEW gets outstanding results regarding the ability to recover the target volume.