Convolution and Cross-Correlation

1) = 3 6 8 3 5 1 = -1 0 1 = -1 0 1 Using the above values for I, f, and g, show that convolution is associative while cross-correlation is not. Recall associativity means ( ) = ( ) . Show all work.

2)

If we convolve an anisotropic (not symmetric) N X N Gaussian filter with an image of size R X C, how many add and multiply operations will be required in total to filter the entire image?

What if we use a symmetric N X N Gaussian filter instead? How many add and multiply operations will be required in total to filter the entire image? Write your answers in terms of N, R, and C. You can handle the boundary in any way of your choice. Make it clear in your answer your choice for dealing with the boundary. Show all work.