(a) Formulate Step 1 and the gradient magnitude image computation in Step 2 of the Canny algorithm using 1-D instead of 2-D convolutions.
(b) What is the computational advantage of using the 1-D convolution approach as opposed to implementing a 2-D convolution. Assume that the 2-D Gaussian filter in Step 1 is sampled into an array of size n × n and the input image is of size M × N. Express the computational advantage as the ratio of the number of multiplications required by each method.
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