3D reconstruction model of vessel based on object-oriented quantization

This paper discusses such a binary three-dimensional (3D) vessel model whose voxel will be '1' if it belongs to vessel volume otherwise it will be '0'. The model can be considered as a stack piled up by a series of slices, and each slice is a 2D binary image. A digital subtraction angiogram (DSA) image is a projection of the 3D vessel model in certain angle, while the projection of a slice is a line in the DSA image. The paper is thus to discuss the representation of the slice projection and the reconstruction model. Based on an assumption of parallel ray geometry, a binary projection model of the slice is introcded, which can be describe by Boolean Radon Transform (BRT). Then a nonlinear quantitative model of DSA image is presented. Simultaneous a slice reconstruction algorithm is developed, which is called optimal square wave decomposition (OSWD). In the end, some simulation results are given, which prove validity of the models.