Spherical Harmonic Transforms and Convolutions on the GPU

Abstract We present implementations of the spherical harmonic forward and inverse transforms on the GPU using CUDA. We implement two algorithms for the SH transform: the direct method and the semi-naive. Our direct method has low storage requirements due to our on-the-fly computation of the associated Legendre functions, and it can perform large transform sizes and non-power-of-two sizes. Our semi-naive implementation is faster than state-of-the-art CPU implementations by a factor of between five and six, depending on the transform size. We target our implementations at spherical panoramic image processing where a large number of basis functions are required. We apply our tool to decompose panoramic images into an overcomplete spherical wavelet model for spherical convolution. We present timings, errors, and application examples of our implementations.

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