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Spatial Convolution, Algorithm, Simulation

This paper proposes an algorithm based on sub image-segmentation strategy. The proposed scheme divides a grayscale image into overlapped 6×6 blocks each of which is segmented into four small 3x3 non-overlapped sub-images. A new spatial approach for efficiently computing 2-dimensional linear convolution or cross-correlation between suitable flipped and fixed filter coefficients (sub image for cross-correlation) and corresponding input sub image is presented. Computation of convolution is iterated vertically and horizontally for each of the four input sub-images. The convolution outputs of these four sub-images are processed to be converted from 6×6 arrays to 4×4 arrays so that the core of the original image is reproduced. The present algorithm proposes a simplified processing technique based on a particular arrangement of the input samples, spatial filtering and small sub-images. This results in reducing the computational complexity as compared with other well known FFT-based techniques. This algorithm lends itself for partitioned small sub-images, local image spatial filtering and noise reduction. The effectiveness of the algorithm is demonstrated through some simulation examples.