Find the gradient magnitude and gradient direction


1-Consider the sub-image shown above. Find the gradient magnitude and gradient direction at the center entry using the following operators. (Hint: Calculate for just the center pixel not the entire sub-image)
(a) The Prewitt operator, and
(b) The Sobel operator.

2-  Compare the time complexity of convolution with a n x n kernel when using:
(a) direct convolution with the 2-D mask, and
(b) a separable kernel.

3-  Prove the following properties of the Gaussian function,
(a) Symmetry: G(x) =G(-x)
(b) Product of two Gaussians is a Gaussian: G1(x) xG2(x)= G(x)

4-  Generate the mask for 255x ?2G(x, y), for _ = 1. Truncate all the mask values to the nearest integer (Hint: 1- Write a program. 2-?2 is the Laplacian Operator 

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Basic Computer Science: Find the gradient magnitude and gradient direction
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