The site, Computer Vision Primer, has been growing and has reached 379 pages with 1,018 illustrations. In particular, the transcription of the Vector Calculus course that I taught 2009/10 has recently started. Two lecture sets are finished (about 20% of the total) and the third is on the way.

The NSF summer REU program has started. These are the two projects that I will supervise:

• The topology of data by Joseph Snyder; and
• 3D image analysis by James Molchanoff.

• Loading image of sizes >2000×2000 causes the software to stall (fixed, but still impractical for processing).
• Changing the color channels after processing causes messed up data in the Output tab.
• Summary in the Output tab isn’t updated when manually select/deselect objects.
• Some image processing tools in the Tools tab don’t work properly.

I will be supervising 2 students in 1-2 of these areas:

• image analysis, and/or
• image-to-image search, and/or
• topological data analysis.

Temporary page for the projects: Computational science training: 2010 projects.

Wayne [Rasband] had an idea for a command called “Analyze Image” that combines filtering, background correction, segmentation, particle analysis, etc. It would work something like the closed-source, Windows-only  Pixcavator program. As Wayne said, “It would not be an easy thing to create but it would be very popular with ImageJ users”. 

I agree.

The power of the software comes from much newer algorithms. Some of them are described in the papers:

• M. Mrozek, P. Pilarczyk, N. Zelazna, Homology algorithm based on acyclic subspace, Computers and Mathematics with Applications, 55 (2008), 2395 –2412.
• M. Mrozek, B. Batko, Coreduction homology algorithm, Discrete and Computational Geometry, 41 (2009), 96-118.
• M. Mrozek, Cech Type Approach to Computing Homology of Maps
  Discrete and Computational Geometry, accepted
• and a few more which are just in preparation.

We just finish[ed] writing a new, much stronger version of the software which will accept not only cubical complexes but also simplicial complexes and general CW complexes and will produce broader output, in particular homology generators, homology maps and persistence intervals for filtered complexes.

The new version of our software at first will be available from the webpage
of our CAPD group at Jagiellonian University, Krakow, Poland:
http://capd.ii.uj.edu.pl/.

Take a look also at our Homology Software page.

• Your choice of settings in the Output tab (the position of the sliders) is preserved when you load a new image to analyze.
• Your choice of color channels in the Analysis tab is preserved when you load a new image to analyze. With these two the user can apply the same settings to a sequence of images if they are similar in nature. So, we get as close as possible to bulk processing without actually creating this complex feature.
• Luminosity is a new color channel that you can choose. It is computed as a combination of the red, green, and blue values: 0.299*R + 0.587*G + 0.114*B. There are four channels now.
• “Display channel” is a new option in the Analysis tab (just like the one in the Output tab). If you have chosen to shrink the image, the shrunken version is shown. This way you can preview all channels and decide which is the best – before committing to time consuming analysis.
• The “Help” menu provides now the links to the help pages of this wiki. The user’s guide and the license are still provided with the program; they are to be found in the “Pixcavator” folder on your hard disk.
• The actual processing time is shown when it’s done, and a beep is produced – but only if processing has taken more than 5 seconds.
• Up to 2000 contours are now shown on the image and their statistics is also displayed. When there are more than 2000 contours, neither is shown.
• A few bugs have been fixed, some remain.

Download here.

A new research paper that uses Pixcavator:

Adsorption Dynamics of CO on Silica Supported Gold Clusters: Cluster Size Effects in Molecular Beam Scattering Experiments by E. Kadossov, U. Burghaus (Department of Chemistry, Biochemistry, and Molecular Biology, North Dakota State University), link, published in Catalysis Letters.

From the paper:

“We report on particle size effects in the adsorption dynamics (gas-surface energy transfer) of CO, studied by molecular beam scattering… the effect of supported nano-size gold metal clusters on gas-surface energy transfer processes (adsorption dynamics)… For the statistical analysis, commercial imaging analysis software (Pixcavator IA 4.2) was used.”

There are nine, to the best of my knowledge, research papers that used Pixcavator and gave credit.

Outline
This is an introductory, two semester course on algebraic topology and its applications. It is intended for advanced undergraduate and beginning graduate students.

Part 1. Introduction to algebraic topology
Starts with topological issues in digital image analysis, informal introduction of homology

Part 2. Homology theory
Cubical complexes, their homology, and maps

Part 3. Overview of point-set topology
Minimized to the extreme (still could have cut even more)

Part 4. Homology groups
A more formal, group theory based, exposition

Part 5. Homology and uncertainty
Applications in computer vision, image analysis and data analysis

Part 6. Beyond homology
The fundamental group and cohomology

Also, I ran across this white paper from Hewlett-Packard: Algebraic topology for computer vision. Good review and an honest attempt to convince the practitioners to that this is something that they might need to know (good luck with that!).

From simplicity comes complexity. And beauty!