### Find the gradient magnitude and gradient direction

Assignment Help Basic Computer Science
##### Reference no: EM1357187

1- Convolve the sub-image shown below with a 3x3 mean filter. What is the  output of the convolution at the center entry of the sub-image? What if you use a 3x3 median filter?

4 1 6 1 3
3 2 7 7 2
2 5 7 3 7
1 4 7 1 3
0 1 6 4 4

2- 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.

3- 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.

4- 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)

5- Generate the mask for 255x ∇2 G(x, y), for σ = 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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