Most of the recent content has come from two main sources. First, I have been adding, as before, examples of image analysis from the users of Pixcavator. The second is the course I’ve been teaching since last fall: Introductory algebraic topology. I plan to add more content from the courses that I teach: Vector calculus (this summer), Introductory differential geometry (next fall), and maybe also something of lower level like Calc1 (next winter).

What is the goal? I would like the site to cover a big chunk of the math curriculum, interlinked within and with the computer vision / image analysis topics (see The Mathematics of Computer Vision). Even though the format is identical to Wikipedia the presentation is very different. This is a textbook: more details, more examples, exercises, etc. It can still be used for reference.

The content comes directly from my lectures. I use Tablet PC with Windows Journal. I started doing this last fall and I really love the results: bright, colorful slides, but with the spontaneity and flexibility of a chalkboard. Later I transcribe the lectures into text, put it on the site, and simply copy the illustrations. (Plus, I don’t have to deal with chalk on my shoes, pants, and lungs!) I think this approach has huge advantages over the common practice of simply posting video lectures online: searchability, cross-linking, speed of download, the person can read and work at his own pace, etc.

Q: We need to “measure all the seedlings area (by dividing by the number of them I can get indication to their area and structure, and other parameters I can get)… The area covered is 80*80cm.”

The screenshot shows the results of my experiment. Here the red contours surround the darker areas (vegetation) and green surround the lighter areas inside. So, the total coverage is 60 – 9 = 51%. Unfortunately, I was unable to separate the seedlings from the rest of the vegetation.

There is also work with ecological researchers to measure vegetation coverage but mostly with horizontal shots.

Other examples of image analysis

I added a list of recent customers of ours here.

I also created a page for the course I am teaching: Introductory algebraic topology. The outline is there already and some of the articles have been written. The second one is Homology as a equivalence relation. Consider the question, What is a tunnel? It’s not as simple as it seems. It takes some work to find a good answer, the main part of which is: A tunnel is an equivalence class of closed surves.

Over the following months (it’s a two semester course) I’ll keep adding material as the course progresses.

I am also teaching Advanced calculus and some of this stuff will also find its way into the wiki.

The site is being restructured right now. The goal is to integrate the Computer Vision wiki (mostly content) with the rest of the site (mostly product information). Virtually all of this content has already moved to the wiki. The only exception will be this blog. The menu at the top of this page will be removed and the pages it links to will be disabled, eventually.

This is the new welcome page of the site.

Please update your bookmarks, links, etc.

I updated several articles in the wiki in order to incorporate the new writing and images from my last talk. 

I updated both Binary images and Gray scale images, as well as their follow-ups: algorithms, pseudocode, and implementation. Also: Topology graph, Graph representation of gray scale images, Tree representation of images, Filtering output data, and some others.

The total is now 193 pages with 584 uploaded files, i.e., illustrations.

When I discovered that Google puts my tiny article at #3 for search of “Betti numbers”  (after Wikipedia and Wolfram MathWorld), I thought “OK, they don’t know anything, this is just an algorithm”. But now my own American Mathematical society links to that article! I must say I am so flattered… I also humbly promise to improve the article.

The page the AMS’s site is on Mathematics Events at the 2009 AAAS Meeting  which, incidentally, has some interesting discussion about applications of topology. That reminds me also that there will be a short course on Applied Algebraic Topology  at IMA in June that some readers of this blog might find interesting.

BTW there wes a huge spike of traffic to the site over the weekend. It was fueled by reddit, Delicious and StumleUpon. Nice too.

FAQ, Frequently Asked Questions

Can you help me analyze these images?

We may be able to provide you with a sample of what Pixcavator can find in your images. For more meaningful results, however, the image should be analyzed by a person who knows that he needs to find in the image. One way to accomplish that is by experimenting with Pixcavator. We can help with that. However, we are unfamiliar with the terminology of your field and can’t tell what you are looking for based solely on your verbal explanations. Ideally, you would provide us with a few images that have been analyzed manually. Then we would try to reproduce your results with our software. Then, if this works, we could try to apply the analysis to other images. For more read the wiki article on technical support.

I am interested in purchasing your software. Since I work for a school I was wondering if you offered an educator’s discount?

There is only one price at this time, except for a free student version here. It has some limitations though…

I am a researcher at .. University. How do you normally handle orders/payment from a large institution?

There is just one way of purchasing at this time – by credit card (or PayPal) – that does not involve contracts, invoices, etc.

Is there any way to utilize Pixcavator from within a Visual Basic application, so I could streamline the process of obtaining the information that we need?

The whole Pixcavator is written in C++ using MS Visual Studio. There is also a way to call a C++ library from a Visual Basic program.

Can I apply a conversion factor to convert area in pixels to area in sq-in, or would I need to do that in Excel afterward?

At this time there is no feature that would convert automatically, so, yes, you’d have to use Excel.

How can I known the total number of pixels for each color in the attached image?

Unfortunately, Pixcavator does not have this feature at this time. The way the current version of Pixcavator analyzes image is channel by channel. A feature similar to what you need is planned for 2009. If you would like to be informed about the latest developments, please sign up for our newsletter here.

What is the runtime fee for the library? Is it $150?

Pixcavator itself costs $150. The price of the library highly depends on how you use it and other circumstances. You can try the free version described here.

I’m trying to transfer my copy of Pixcavator to my new machine. However, during activation I get an error that the maximum number of activations is reached. Is there anything that you can do about this?

We encounter installation issues once in a while. They are usually quickly settled. Activation, however, is taken care entirely by Protexis. Please visit their support site.

Can I get a refund for Pixcavator?

Yes, within 30 days. You will have to contact us first then the refund will be processed by Protexis as the seller of record.

I can’t copy Pixcavator to another computer. Is Pixcavator a single-try demo version?

No, but it is licensed to one computer at a time. You should just reactivate it.

I decided to rename the wiki, from “Computer Vision Wiki” to “Computer Vision Primer”. “Wiki” is just such a general (and generic) term that it is easy to confuse our wiki with other wikis related to computer vision. The word “primer” helps to make a point about what makes ours different – we focus on the fundamentals and try to keep it very accessible. CVprimer.com is also easy to remember. Finally, when I get to turn this into a book, Computer Vision Primer will be a good title.

There have been some additions to the wiki. I did quite a lot of editing throughout, for example, Overview. I started to add articles on measurements of objects: saliency, mass, average contrast, diameter, minor and major axes, Euler number, Robustness of geometry and topology. Those are still quite thin. In article Machine learning in computer vision I summarized the recent blog posts on the subject. There are also many red links – those are articles I plan to write.

Pixcavator PE (photo editing) is to be released in just a few weeks. It is a simplified version of the image analysis version but it will also have a couple of new features. These features and many more will appear in Pixcavator 2.5.

cellAnalyst has now an online counterpart. You can upload your images, analyze them, save the data, and search images – all in your browser. Create your free account here. Feedback will be appreciated… Meanwhile, AssaySoft has been incorporated.

From the three previous posts on the topic (Lengths of digital curves, parts 1, 2, 3) and a little presentation I gave recently I created an article for the wiki. In comparison, analysis is more extensive and there are more illustrations. At the end there are two examples of computation of roundness with Pixcavator 2.4. Circles have roundness close to 90, squares close to 80. It works quite well for large objects. You can now distinguish between circles and squares and between squares and elongated objects. For example, you have now a new way to automatically count (round) cells in the image and ignore (rough edged) noise.

• We hit 20,000 downloads! About 5,000 are downloads of Pixcavator 2.3. So far no complaints about any serious bugs. In reality there are some problems with the measurements of light objects. They are being fixed.
• Article on measuring objects was added. It makes more precise what is being computed, especially for gray scale images. More examples will be added.

• Article on Objects in gray scale images was added, also for binary images. I continue with the plan of giving more details to the description of main algorithm (Binary Images and Grayscale Images), but in separate articles. This approach gives more flexibility to the reader (and the writer).
• Article on Image Search was extended and isn’t “under construction” anymore.
• I started on the Pixcavator Tutorial focused on scientific image analysis.
• Under “computer vision for beginners”, the wiki is #2 on Google. Cool…

Last week:

• The article on Cell Decomposition of Images was added. The approach is explained in detail and its advantages over the graph representation of binary images are also discussed. The latter topic is interesting on its own. It should be addressed as a part of a broader issue – continuous v. discrete. Maybe one day…
• The article on Related Approaches was expanded significantly. I added some examples and even some (limited) discussion of literature.
• The slide show on the binary algorithm was added to the main page of the wiki. Thanks Ash!
• The demo program for the analysis of binary images was made available too. It is the program explained in this article.

Last week
·        A short page was added under “For researchers” – How it works. It gives an initial idea of how and why Pixcavator works with a link to the wiki. Hopefully, there will be a link to a paper here in the near future.
·        The article on Binary Images is mostly finished, pending feedback. I’ve made good progress with Grayscale Images too.
·        I started to add answers to exercises. The wiki is starting to take a shape of an online textbook. Interesting…
·        A PowerPoint slide show was added that explains the basics of our approach. It will be updated regularly until it takes the form of a paper.
·        We’ve had technical difficulties with the blog…

Last week:

• An instructional video was added. A bit crude but should help the user to learn how to use Pixcavator for image analysis.
• The article on analysis of binary images was significantly expanded and improved. There is still a need for more examples and illustrations. Grayscale Images needs even more work.
• The article Topological Features of Images was rewritten and now is more or less complete. It’s an introduction to topological analysis in 3D.
• The articles on homology are in progress.