## A Parallel Pipeline Convolution for Perspective Projection in Real-Time Volume Rendering

(The Journal of the Institute of Image Information and Television Engineers, 2000.)

This paper describes a convolution with a systolic array structure for perspective projection in real-time volume graphics based on the shear-warp method. In the original method, the further the ray proceeds, the more voxels are required to calculate the convolution. The increase in required voxels makes it difficult to implement the method in a VLSI-oriented architecture. We implement a 3D convolution using three serial 1D convolutions along the X, Y, and Z axes, which reduces the number of calculation units from M^3 to 3M, where the convolution is calculated for the M^3 area. The number of pipelines for the rays is V^2 for V^3 voxel datasets. If the hardware of a single pipeline can calculate the V rays, then each of the implemented pipelines is assigned to V theoretical pipelines (for V^2 rays). The number of hardware pipelines should be much smaller than V theoretical pipelines in actual implementation. We folded the theoretical pipelines and reduced them to a certain number of hardware pipelines. We examined the relation between the folding process and its necessary time delay. The architecture can generate an image of a 256^3 voxel dataset (V=256) at 30Hz with four pipelines. In addition, the architecture can be extended easily for 512^3 (V=512) and 1024^3 (V=1024) datasets, with 32 pipelines and 256 pipelines. Our architecture has processing scalability.