HEAT KERNEL BASED 3D RECONSTRUCTION OF OBJECTS FROM 2D PARALLEL CONTOURS

Imaging modalities such as Magnetic Resonance Imaging (MRI) and Computed Tomography (CT) produce sequences of planar parallel cross-sectional images taken at regular or irregular intervals of 3D objects (brain, coronary arteries, etc). In order to reconstruct a 3D object which has been imaged using MRI or CT there is a need for a fast, accurate and robust algorithm. Reconstruction usually starts with an appropriate segmentation algorithm that detects the trace of the 3D object boundary on each 2D image. Segmentation can be either manual, semi-automatic or ideally automatic. After segmentation, one needs to "glue" together the contours in order to reconstruct the 3D object. Both the segmentation technique and the method used to glue individual contours affect the quality of the reconstructed object. In this paper we introduce a novel initialization that speeds up a semi-automatic segmentation technique recently developed by Chan and Vese (IEE Trans. Im. Proc., vol. 10, No. 2, February 2001, pp 266-277). We implement Vese and Chan (Int. J. Comp. Vis. vol 50, N0. 2, 2002, pp 271-293) multi-phase segmentation using relaxed Gauss-Seidel method. As a result we obtain an algorithm faster than the one proposed by Vese and Chan. We employ the heat kernel to piece together 2D parallel contours in order to obtain 3D reconstruction. This approach is preferred because of the slowness of 3D segmentation using level sets. In case of large volumes we indicate how to use fast Gauss transform to achieve fast reconstruction. Numerical experiments are provided to support our methodology.