Accurate perspective projection calculation using a pixel-pyramid model for iterative cone beam reconstruction

Abstract

The calculation of perspective projection is the essential part in either cone-beam projection or realistic volume rendering. In this paper, we propose a pixel-pyramid model to accurately calculate pixel values in flat-panel-based cone-beam reconstruction. This model faithfully portrays the divergent beam projection on a grilled planar detector. It consists of a pyramidal base (detector pixel facet) and an apex (X-ray source). Through spatial clipping by a flat-panel detector (FPD), a cone is tailored into a pyramid with the base at the FPD, called FPD pyramid, which is then spatially decomposed into pyramidal elements (PYREL). During cone-beam projection, a PYREL intersects the 3D object and produces a frustum, wherein the voxels are accumulated to produce a pixel value. In backprojection, the pixel value is imparted to the same contributive voxels. A voxel’s weight (contribution to a PYREL) is determined by spatial overlapping, which is a piecewise linear function. Through iterative algorithm, accurate cone beam reconstruction is achieved. Since the pyrel model portrays the perspective projection geometry and the voxel weight in a more natural fashion, it can be used for accurate calculation of perspective projection, especially in dealing with severe incomplete data. Simulations and comparisons are provided.