New Page 1

This page summarizes some of the most interesting results that I saw while grading the project. Thank you to all for permitting me to post these results on the web.

Best Polynomial Interpolation

This honor belongs to Mr. Xiangwei Zhang who experimented with many different forward and inverse mappings with different orders. He also had a very nice scheme for doing a piecewise mapping.

	Paper
	Matlabfiles: global_forward, global_inverse, piece_forward, piece_inverse

Neural Networks for Transformations

This paper used neural networks to learn the transformations. It also contains a nice section on spherize transformations.

paper and spherize.m

Nice Overall Project

This project had unique aspects in both sections. Mr. Pan Du and Mr. Zhenyu Zhang experimented with local and global approximation methods in Part I and used different noise reduction filters such as median, smoothing and Weiner filters in Part II.

Preprocessing:proj1_preprocess.m

Note: Before running the following program, please download these two files: The point position info before distortion: project1_o.mat. The point position info after distortion: project1_d.mat

Method 1: Based on regional information (Divide the whole image into small piece of rectangles)proj1_method1.m

Improved Method 1: Using symmetric information to get more points proj1_method1_improved.m

Method 2: Based on global information (Using function fitting method) proj1_method2.m

	Report
	Matlab files for Part 1:
	Matlab files for Part 2:

1. clean.m is for the clean image
2. noisy.m is for the noisy image without improvement
2. noisy_sigma.m is for the noisy image improved by change sigma
3. noisy_median.m is for the noisy image improved by median-smoothing
4. noisy_wiener.m is for the noisy image improved by wiener filter

Most "interesting" results:

These were images that I really enjoyed. I'm sure that everybody got some results like this somewhere along the way to finding an algorithm. If you got some really bizarre results, please submit them to me.

This looks like Coover underwater with sinusoidal waves.

This is Coover in your dreams (nightmares) with an endless hallway.

	Unmatched pixels before interpolation. This is a neat high-dimensional manifold.

	Picture taken of the time when giant spiders invaded Coover. Note how straight the doors and lines are.