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Two-Dimensional Convolution on a Pyramid Computer
July 1988 (vol. 10 no. 4)
pp. 590-593

An algorithm for convolving a k*k window of weighting coefficients with an n*n image matrix on a pyramid computer of O(n/sup 2/) processors in time O(logn+k/sup 2/), excluding the time to load the image matrix, is presented. If k= Omega ( square root log n), which is typical in practice, the algorithm has a processor-time product O(n/sup 2/ k/sup 2/) which is optimal with respect to the usual sequential algorithm. A feature of the algorithm is that the mechanism for controlling the transmission and distribution of data in each processor is finite state, independent of the values of n and k. Thus, for convolving two (0, 1)-valued matrices using Boolean operations rather than the typical sum and product operations, the processors of the pyramid computer are finite-state.

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Index Terms:
2D convolution; computerised picture processing; computational complexity; pyramid computer; window; image matrix; finite state; Boolean operations; Boolean functions; computational complexity; computerised picture processing; matrix algebra; parallel architectures
J.H. Chang, O.H. Ibarra, T.C. Pong, S.M. Sohn, "Two-Dimensional Convolution on a Pyramid Computer," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 4, pp. 590-593, July 1988, doi:10.1109/34.3920
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