Fun with Filters and Frequencies!

Overview

We took this project as an opportunity to use filters and frequencies towards creating hybrid images, finding edges, and sharpening and blending images.

Part 1: Fun with Filters

1.1: Finite Difference Operator

1. To find the partial derivatives, I convolved the image with Dx = [-1, 1] and Dy = [1, -1]^T using scipy.signal.convolve2d.

Gradient x

Gradient y

2. Computed the gradient magnitude image: (np.sqrt(grad_x**2 + grad_y**2))

Gradient Magnitude

3. Threshold: np.max(grad_magnitude) * 0.36
4. Created Binary Edge Image using the threshold.

Edges

1.2: Derivative of Gaussian (DoG) Filter

Approach 1:

1. Created a Gaussian filter with ( sigma = 2 ). Blurred the image by convolving it with the Gaussian filter using convolve2d.

Blurred cameraman (sigma = 2 )

2. Convolved the blurred image with Dx and Dy to get the partial derivatives.

Gradient x (DoG)

Gradient y (DoG)

3. Computed gradient magnitude and created binary edge image:

Gradient Magnitude (DoG)

Edges (DoG)

Approach 2: The difference in this approach was first convolving the Gaussian filter with Dx and Dy and then applying it to the blurred image. The results were almost identical, with slightly wider edges.