HOMEWORK PROBLEM SET#2, DUE TUESDAY OCT.6

1. Consider the convolution of an image by an nxn template, A, followed by the convolution by an nxn template B. In general is the order of convolution by A and then by B commutative ? If so, prove it. If not show a counterexample.

2.

• Generate the 5x5 template for a 2-D Gaussian with standard deviation equal to 1 pixel length.

• Apply it to a step edge (make up your favorite object gray value and background gray value).

• Now apply a 3x3 Laplacian template and identify the zero-crossings that constitute edge pixels.

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