1. Suppose a is a filter and b is a patch of an image:
a = np.array([1, 2, 1],
             [2, 4, 2],
                          [1, 2, 1]]) / 16
                          b = np.zeros((3,3))
                          b[:3,0] = 1
                          b[1,1] = 2

1a. Compute the output pixel in a convolution when the filter a overlaps the image neighborhood b. Use array operations and the sum function.

1b. Compute the same product as above, but using the dot function. Hint: you'll need to reshape the inputs to dot first!


2. Load the van.png image and save out a grayscale version computed by averaging the three color channels; be sure to do the averaging in floating-point

3a.Load the van image do a naive 2x subsampling: drop every other row and column and save out the half-size version.

3b. Load the van image and do a naive 2x upsampling: repeat every other row and column twice.