A comparison of the speeds of three convolution algorithms

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Abstract
The speeds of three computer algorithms suitable for use in three-dimensional radiotherapy planning codes were compared. Two of the algorithms are based on ray-tracing methods, the first algorithm uses a fast ray-tracing procedure directly and the second employs a table lookup procedure, the table was originally calculated by ray tracing. The third algorithm was a convolution procedure using the fast Fourier transform. Benchmark programs were written to compare the fundamental running speeds of the three algorithms operating on three-dimensional arrays of various sizes. The convolution procedure employing the three-dimensional fast Fourier transform had the shortest running times on a VAX/750 (Digital Equipment Corp.) computer. We concluded that this algorithm holds significant potential for practical three-dimensional dose calculations.