Volume Data Matching

Given two functions f(x,y,z) and g(x,y,z). One would like to determine a rigid body rotation to best match the zero level set of the functions.

Reference:
https://www.ebi.ac.uk/training/online/course/structural-volume-data/what-volume-matching
https://www.ebi.ac.uk/training/online/course/structural-volume-data/volume-matching-methodologies

Depth Map from 2D Image(s)

Goal: Create the so-called depth map from either
(i) a pair of left-right images obtained by two cameras with fixed location, or
(ii) one single image using the derivatives of the image intensity.

Some possible approaches:
http://3dstereophoto.blogspot.hk/p/software.html
An example from the Apple App Store: Focos

Mathematical theory of an image editing software/app

Goal: Develop math theories for functions in an image processing app such as Google Picasa, Instagram, Fotor Photo Editor, 美图秀秀, and etc.

Black & White HDR

http://thehdrimage.com/tag/black-white-hdr/
http://www.denzomag.com/2010/09/black-and-white-hdr-photography-amazing-examples/

Goal: Develop a math theory of B&W HDR image formation.

Image Mosaic

Goal: Simplify a given image by a different sampling.

Image Super-resolution

Goal: Super resolution is one of the most important tasks in computer vision and computer graphics. Students will design an image super-resolution technique and study it’s theoretical property and/or a fast implementation of it.

Reference:

http://cgm.technion.ac.il/Computer-Graphics-Multimedia/Undergraduate-Projects/2009/SuperResolution/SuperResolution.html

Image Inpainting using PDE

Goal: http://www.math.ucla.edu/~bertozzi/papers/CH.pdf