Symmetry Considerations Applied to Hardware Convolvers for Image Filtering

Systolic arrays are arrays of simple closely coupled processors organised so that streams of input data, results, and partial results circulate. For operations of a regular nature on large data sets systolic arrays offer a practical means of computation es pecially suited to VLSI implementation. This paper focuses on the design of systolic arrays to perform one and two dimensional convolutions. One dimensional systolic convolvers are first discussed and it is shown how to take advantage of non-productive cycles to effectively double the output of Kung WI convolvers. For sym metric 1-D filters, it is shown how to modify the systolic elements to take account of such symmetry, thereby almost doubling the efficiency, An important class of two dimensional systolic arrays is dis- cussed in which a single image data stream enters and the required line delays are supplied by video line buffers. The natural size of the systolic array for performing an D * D convolution is just D/sup 2/. A method is demonstrated for the incorporation of both axial and diagonal symmetry into the design of systolic convolvers. Many important image processing operations possess these symmetries, For 2-D convolutions involving both axial and diagonal symmetry, the utilisation of symmetry leads to just three types of array elements with close to an eightfold savings in compleadty.