A hardware implementation of the discrete Pascal transform for image processing

Thomas J. Goodman; Maurice F. Aburdene

doi:10.1117/12.650739

16 February 2006 A hardware implementation of the discrete Pascal transform for image processing

Thomas J. Goodman, Maurice F. Aburdene

Proceedings Volume 6064, Image Processing: Algorithms and Systems, Neural Networks, and Machine Learning; 60640H (2006) https://doi.org/10.1117/12.650739
Event: Electronic Imaging 2006, 2006, San Jose, California, United States

Abstract

The discrete Pascal transform is a polynomial transform with applications in pattern recognition, digital filtering, and digital image processing. It already has been shown that the Pascal transform matrix can be decomposed into a product of binary matrices. Such a factorization leads to a fast and efficient hardware implementation without the use of multipliers, which consume large amounts of hardware. We recently developed a field-programmable gate array (FPGA) implementation to compute the Pascal transform. Our goal was to demonstrate the computational efficiency of the transform while keeping hardware requirements at a minimum. Images are uploaded into memory from a remote computer prior to processing, and the transform coefficients can be offloaded from the FPGA board for analysis. Design techniques like as-soon-as-possible scheduling and adder sharing allowed us to develop a fast and efficient system. An eight-point, one-dimensional transform completes in 13 clock cycles and requires only four adders. An 8x8 two-dimensional transform completes in 240 cycles and requires only a top-level controller in addition to the one-dimensional transform hardware. Finally, through minor modifications to the controller, the transform operations can be pipelined to achieve 100% utilization of the four adders, allowing one eight-point transform to complete every seven clock cycles.

Citation Download Citation

Thomas J. Goodman and Maurice F. Aburdene "A hardware implementation of the discrete Pascal transform for image processing", Proc. SPIE 6064, Image Processing: Algorithms and Systems, Neural Networks, and Machine Learning, 60640H (16 February 2006); https://doi.org/10.1117/12.650739

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