Multiscale Flat Norm Project
Flat norm and Shape Signatures
In this project, the multiscale flat norm signatures that I briefly described in class are to be used to study the multiscale nature of shape spaces and the effectiveness of these rather low level tools in various discrimination tasks with images. Contact for this project is Kevin.
Data Processing pieces:
0) Use several segmentation methods to generate shapes from images. a) simple thresholding b) chan-vese piecewise constant Mumford Shah c) other methods that Tom showed in his demo of kmeans like clustering.
1) Compute the multiscale flatnorm signatures and the 2 components of the flatnorm. This yields a set of points, which we will name S, in the signature representation spaces that we are mapped into by this computation.
2a) Use S to generate distance matrices on test data sets.
2b) Map S using a kernel based method like Kernel PCA or a Support Vector Machine to a higher dimensional space. Use this to solve a recognition/identification problem. Other Machine learning techniques might also be explored. Application of 0-2 to data problems:
1) a) Find a pattern recognition challenge set and b) use 0-2 above to recognize patterns or objects. Other) Evaluate the effectiveness of the metric at fixed scales or using all scales (the signature).
2) do an exploratory multiscale study of a set of multiscale images. By multiscale, I mean natural images that have objects and features at multiple scales. Provided and Not Provided:
Code to compute the flatnorm on 2D images and shapes is available for anyone using Matlab.
You can get code from the web that implement Support Vector Machines. Again, I know code that is available for Matlab.
You should write your own code to do the K-means and other clustering tasks.
You should also write your own code to visualize results.
Report:
I expect a report that is written in Latex and accompanied with working code that I can use to reproduce the results you report. The report should be on the order of 10 pages -- it can be much longer, but I will expect it to be well written and will iterate with you on the writing of the report. I would love those taking this project to consider writing a paper and doing the work necessary for a paper. Notes:
Applied task number one is quite fixed in goal: you want to identify r find objects with as high a reliability as possible. Task two is much more open ended. It is more like observational biology or the observations that others like naturalists make. You need to choose one of these 2 as your focus. (Task one does have an exploratory component -- you are asked to begin to look at how effective the various parts of the multiscale signature are for the task of recognition and identification.)