Image convolution optimization using sparse matrix vector multiplication technique

Image convolution is an integral operator in the field of digital image processing. For any operation to be processed in images say whether it is edge detection, image smoothing, image blurring, etc. process of convolution comes into picture. Generally in image processing the convolution is done by using a mask known as the kernel. As the values of the kernel is changed the operation on image also changes. For each operation, the kernel will be different. In the conventional way of image convolution, the number of multiplications are very high. Thereby the time complexity is also high. In this paper, a new and efficient method is proposed to do convolution on the images with lesser time complexity. We exploit the sub matrix structure of the kernel matrix and systematically assign the values to a new H matrix. Since the produced H matrix is a spare matrix, the output is realized here by using Sparse Matrix Vector Multiplication technique. Compressed Row Storage format (CSR) is the format that is used here for the Sparse Matrix Vector Multiplication (SMVM) technique. Using the CSR format with Sparse Matrix Vector Multiplication technique, convolution processes achieves 3.4 times and 2.4 times faster than conventional methods for image smoothing and edge detection operations respectively.