Luca Chiarabini

Complexity reduction on two-dimensional convolutions for image processing

Presented here is a method for reducing the computational complexity of two-dimensional linear convolutions used in image processing like binary image scaling. This method is a hybrid of convolving at run-time and convolving by table lookup. The convolution step in image processing usually calculates a weighted average of an area of the input image by calculating the entry-by-entry multiplication of the input pixels with a weight table. This method partitions the calculations in the convolution step and stores pre-calculated partial results in lookup tables. When the convolution step takes place, a binary indexing is used to retrieve the partial results and the final result is obtained by summing up the partial results. A line cache and a double buffering scheme are designed to reduce memory access in table lookup. Space and time complexities are analyzed and compared to the conventional two-dimensional linear convolutions. We demonstrate that an order of magnitude reduction in the computational cost can be achieved. Examples, test images and performance data are provided.