Progressive attenuation fields: Fast 2D‐3D image registration without precomputation

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Abstract
Computation of digitally reconstructed radiograph (DRR) images is the rate‐limiting step in most current intensity‐based algorithms for the registration of three‐dimensional (3D) images to two‐dimensional (2D) projection images. This paper introduces and evaluates the progressive attenuation field (PAF), which is a new method to speed up DRR computation. A PAF is closely related to an attenuation field (AF). A major difference is that a PAF is constructed on the fly as the registration proceeds; it does not require any precomputation time, nor does it make any prior assumptions of the patient pose or limit the permissible range of patient motion. A PAF effectively acts as a cache memory for projection values once they are computed, rather than as a lookup table for precomputed projections like standard AFs. We use a cylindrical attenuation field parametrization, which is better suited for many medical applications of 2D‐3D registration than the usual two‐plane parametrization. The computed attenuation values are stored in a hash table for time‐efficient storage and access. Using clinical gold‐standard spine image data sets from five patients, we demonstrate consistent speedups of intensity‐based 2D‐3D image registration using PAF DRRs by a factor of 10 over conventional ray casting DRRs with no decrease of registration accuracy or robustness.