Part 1: Fun with Filters¶

Part 1.1: Part 1.1: Finite Difference Operator¶

In order to compute dradient magnitudes, we subtract two numbers along a direction of the image, typically along the x or y axis.

This is the best possible approximation of the image surface's slope as adjacency is the closest two pixel samples can get.

In order to compute this we treat it as a convolution with [-1, 1] or it's transpose. For added robustness to noise we combine this with a guassian filter to produce a Derivative of Gaussian Filter (DoG)

Part 1.2: Derivative of Gaussian (DoG) Filter¶

In the above image we can see highlighted either vertical horizontal edges, depending on which filter is used. (Dx = vertical)

Below we compare the result of applying the derivative and gaussian operators as separate kernels or combined kernels. (convolved together)

Part 2: Fun with Frequencies!¶

Part 2.1: Image "Sharpening"¶

Part 2.2: Hybrid Images¶

Despite being aligned, the picture does not have the desired effect because the shape of cat and dog heads is too different.

Part 2.3: Gaussian and Laplacian Stacks¶

Part 2.4: Multiresolution Blending (a.k.a. the oraple!)¶