Part 1.1

The gradient magnitude image is calculated with the following steps:

1. Convolve the image with finite difference operators (D_x and D_y) to obtain the gradient of each pixel along x and y axis.
2. Calculate the norm of the gradient at each pixel. Suppose the gradient along the x and y axis are G_x and G_y respectively. Then the norm of the gradient is (G_x^2 + G_y^2)^(0.5)

The resulting image is:

Part 1.2

The results are as follows.

• Gradient along x axis:

• Gradient along y axis:

• Gradient magnitude:

The resulting image has clearer edges and less noise. It identifies the edges better without introducing as much noise as before.

Part 1.3

• Example image:

• Case 1:

• Case 2:

• Case 3 (failure):

Part 2.1

Part 2.2

• Example image

Steps:



Result:


• Water and Paint (no color)

Steps:



Result:


• Failed attemp

Steps:



Result:

Extra credit:

Color on high frequency provides more details and works better.

• Water and Paint (with color)

Steps:



Result:


• Example (with color)

Steps:



Result:

Part 2.3

Example 1:

Example 2:

Part 2.4

• Apple + Orange

Effect:



Process:


• Moon + Jupiter

Effect:



Process:


• Man + Taj Mahal (irregular mask)

Effect:



Mask:



Process: