Project 3: Frequencies and Gradients

Xin Chen afh

Part 1 Frequency Domain

Part 1.1 Warmup Image Sharpening

In this section, I've implemented unsharp masking technique as indicated by the following formula:

On the left is the original image and on the right is the sharpend image with alpha = 0.5.

Part 1.2 Hybrid Images

The goal of this part of the assignment is to create hybrid images using the approach described in the SIGGRAPH 2006 paper by Oliva, Torralba, and Schyns. Hybrid images are static images that change in interpretation as a function of the viewing distance. The basic idea is that high frequency tends to dominate perception when it is available, but, at a distance, only the low frequency (smooth) part of the signal can be seen. By blending the high frequency portion of one image with the low-frequency portion of another, you get a hybrid image that leads to different interpretations at different distances.

Results

Friend and Elon Musk

Coca Cola and Pepsi

Putin and Trump(Failure Example). After tuning the parameters for a while, I still find it very hard to achieve a good result.

Frequency Analysis

Below I will provide the frequency analysis for the friend and Musk images.

Part 1.3: Gaussian and Laplacian Stacks

In this part, I will implement Gaussian and Laplacian stacks. This will allow us to visualize the result at each leve.

Salvador Dali painting of Lincoln and Gala

Friend and Musk

Part 1.4: Multiresolution Blending

In this part we will blend two images seamlessly using a multi resolution blending as described in the 1983 paper by Burt and Adelson. An image spline is a smooth seam joining two image together by gently distorting them. Multiresolution blending computes a gentle seam between the two images seperately at each band of image frequencies, resulting in a much smoother seam.

Part 2 Gradient Domain Fushion

Introduction

In this part we will explore gradient domain processing using poisson blending. We will formulate our objective as a least squares problem. Given the pixel intensities of the source image s and of the target image t, we want to solve for new intensity values v within the source region S. The poisson blending formula is as follows:

where each i is a pixel in the source region S, and each j is a 4-neighbor of i.

Part 2.1 Toy Problem

We will approach this part by solving a simple problem. We will recover the original image(on the left) by computing the x and y gradients from an image s, then use all the gradients, plus one pixel intensity, to reconstruct an image v.

Our original vs Reconstructed result is as follows:

Part 2.2 Poisson Blending

Results

Camal in the Dessert

Ginevra de Benci, Mona Lisa

Crow flying onto a temple. This isn't very good as the color of the crow turns red. This is probably due to the fact that the background of the crow image is blue whereas the background for the temple image is closer to white.

Original Input Images

Results Comparison with Naive Copying