CS 194-26

# Project 2:Fun with Frequencies and Gradients!

Rosa Choe

### Overview

In this project, we use various methods of combining images in the frequency domain and the gradient domain to create interesting pictures.

#### Part 1: Shoot and Digitize Pictures

I took pictures of my room as well as my friends.

#### Part 2: Recover Homographies

In order to warp our images, we need to find the correct transformation to apply to the points. The transformation is a `homography`, meaning the relationship between the original points `p` and the target points `p'` is represented by `p' = Hp`, where `H` is a `3x3` matrix of the form:

We solve for the `H` matrix by finding the least-squares solution to the following overdetermined linear system:

#### Part 3: Rectify Images

Now that we know how to find the correct transformation to warp our images, we can use this method to rectify our images – or warp the image so some flat surface in the image can be made frontal-parallel. We do this by defining a set of 4 points in the source image; defining the corners of some rectangular shape whose perspective makes it non-rectangular in the image. Then we can define a rectangular shape to warp that section of the image to, in order to find `H`. Once we have the correct matrix, we can use inverse warping and bilinear interpolation to map the pixels from the source image to the correct, straightened output image.

Original Rectified