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August 3, 2008

Our R&D Plans

Filed under: updates, computer vision/machine vision/AI, mathematics — Peter @ 5:29 pm

Image analysis and computer vision is the extraction of meaningful information from digital images. One of the most prominent application of computer vision is in medical image processing - extraction of information for the purpose of making a medical diagnosis. It can be detection and measurement of tumors, arteriosclerosis or other malign changes or it can be identifying and counting cells, etc. Other main areas are industrial machine vision (automatic quality inspection, robotics, etc) and the military (missile guidance, battlefield awareness, etc).

The science of computer vision consists of an abundance of image analysis methods. These methods have been developed over the years for solving various but often narrow image analysis tasks. The result is that these methods are very task specific and seldom can be applied to a broad range of applications.

Our conclusion is then that as a discipline computer vision lacks a solid mathematical foundation.

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 into a product that also includes image management and database capabilities.

Some further issues remain. 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).

One Response to “Our R&D Plans”

  1. Lim Ee Hai Says:

    Being a maths teacher, sometimes I find it hard to find examples to related math to real applications. Examples can be found easily but an in-depth one with interesting applications are hard to come by. In this post of yours, I found exciting examples to quote and potential sharing quality. I have worked with images before and really appreciate the application of maths (especially matrices) to image processing.
    Well written post!

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