Our long term goal is to design a comprehensive computer vision system “from first principles”. These principles come initially from one of the most fundamental fields of mathematics, topology. The idea is that just as mathematics rests on topology (and algebra), computer vision should be built on a firm topological foundation.

Algebraic topology is a well established discipline within mathematics. Its main computational tools have been implemented as software (CHomP, Computational Homology Project, and others). However, this theory and these tools are only applicable to binary images.

A framework for analysis of gray scale images has been under development. It is called Pixcavator. It includes both an image analysis software and an SDK. Pixcavator was further developed into a product that also includes image management and database capabilities.

Future projects include the development of:

• protocols for applying the framework for specific tasks (e.g., tumor measurement),
• new methods that resolve the ambiguity of the boundaries of objects in gray scale images,
• integration of the existing image analysis methods into the framework,
• a framework for video (first binary, then gray scale, etc),
• a framework for color images (and other multichannel images),
• a framework for 3D images (first binary, then gray scale, etc).