||Segmentation is naturally formulated as an inverse problem - what were the imaged objects which lead to the observed image?
For image processing tasks, the dimensionality of the problems are often very large (each pixel is one variable) and a priori information has generally to be incorporated to make problems well posed (s.t. solution exist, is unique and is stable). Such information may be included in the form of a regularization term in the objective function. An example is the popular TV regularization, which leads to solutions that are piecewise smooth (have a sparse gradient magnitude). A good side of TV regularization is that it is a convex function; together with a convex data term this leads to a convex optimization problem that can be efficiently solved. This approach has lead to very successful methods for image denoising, deblurring, super resolution reconstruction, etc.
Unfortunately, the segmentation problem is much more difficult than the image reconstruction type of problems; the crisp assignment of discrete labels to the image pixels leads to non-convex energy functions that are tricky to optimize.
In this Monday's seminar I will talk a bit on our ongoing work on high precision (super resolution, if so desired) segmentation by minimization of a suitably defined objective function. I will outline the design of the objective function and briefly discuss approaches taken for efficiently finding a good solution. I also hope to show some examples how this approach may handle a range of difficulties, such as image noise and image blur.