During a retina inspection one of the most common pathology is Drusen deposits. Some computer assisted methods have been created to solve this problem and especially avoid the subjectivity of the doctors (”MD3RI a Tool for Computer-Aided Drusens Contour Drawing”) [1].

An image from this paper is below:

Pixcavator easily produces similar results:  

Another example is ice cracking (thanks to Nikolay Makarenko for the idea). The image is analyzed with Pixcavator with settings 596-63.

An iceberg is born!

These kind of examples will appear in the wiki under Case studies.

The paper (PDF, 10 pages, 360K) describes the algorithm behind Pixcavator. The algorithm is presented in detail in the wiki but this is a new and improved exposition. I reconsidered some of the terminology, re-wrote the pseudocode, and improved illustrations. There is also a gap in the wiki - when an edge is added to the image, case 4 is missing. I’ll have to re-write a few articles. The presentation in the paper is less detailed (in terms of examples, images etc) but it is a bit more thorough.

Abstract: The paper provides a method of image segmentation of binary and gray scale images. For binary images, the method captures not only connected components but also the holes. For gray scale images, there are two kinds of “connected components” – dark regions surrounded by lighter areas or light regions surrounded by darker areas.

The long term goal is to design a computer vision system “from first principles”. The last sentence in the abstract is one such principle. Keep in mind (of course) that if every dark region surrounded by a lighter area is an object, it does not mean that every object is a dark region surrounded by a lighter area (or vice versa). In a way, these are “potential” objects and you still have to filter and/or group them to find the “real” ones. So there must be more first principles.

The paper does not go far beyond this stage. The main step is – all potential objects are recorded in the “topology graph” (“frame graph” in the wiki). Then only one method of filtering is presented (the one based on size).

All feedback is welcome.

This came as a question from one of our users. The picture explains the problem: there is a bee frame with several hundred sealed brood. They are visible as tan hexagons (the dark circles are empty cells). Now, count them! Just like that – an outdoors photo taken with a regular digital camera, no registration, no calibration, etc.

The problem is interesting but also quite challenging. The sealed cells aren’t separated enough from each other to count them one by one with 100% accuracy. For that the image would need a higher resolution. If, however, the goal is just an estimate, Pixcavator can help. Then the task is less about counting and more about measuring… and some elementary school math.

First I cropped the image. Then I analyzed it with 100-130 settings, no shrinking. The result is 311 dark objects (clusters of empty cells) with the average size 1,255. So the total area of the empty cells is

311*1,255 = 390,305.

Since the image is 1,394×709, the area covered by sealed cells is

1,394*709 - 390,305 = 598,041.

Just in case I decided to validate this number from another source. I analyzed the negative with 100-110 settings. Then I just picked the largest object in the table - the cluster of all sealed cells. Its area is 613,814. Since the empty cells inside of this area aren’t taken into account, the result is higher than the first estimate. The difference is however less than 3%.

At this point you need to estimate the size of a cell. Looking at a few individual cells in the table may give you an estimate, but it would take some work with Excel. Instead I did actual measuring - on the screen. I counted 10 cells in a row and measured the length with a ruler - 34 mm. So each cell is about 3.4×3.4 mm. Next I measured the image - 270×136 mm. So the number of cells is

270*136/(3.4*3.4) = 36,720.

(The user won’t need this computation because the actual number is known). Then the size of the cell is

(the size of the image in pixels) / (the number of cells) = 1,394*709/36,720 = 269.

Finally, the number of sealed cells is

(the total area) / (the size of each) = 598,041/269 = 2,223.

The hand counted number is 2,198. The error is about 1%!

You can reproduce these results with Pixcavator version 3.0 or earlier and this full size image: http://inperc.com/wiki/images/7/7d/Bee_brood-cropped.jpg.

On several occasions I was asked: Why wouldn’t we add a second slider to the size ruler? The logic is very convincing: “the first slider removes objects from analysis that are too small - with the second slider you can exclude objects that are too large”. There are real life problems that need this kind of analysis.

What is wrong with this idea? The problem is that the idea is “binary”. If the image is binary, excluding larger objects is a simple operation. We however deal with gray scale images. Sometimes objects in gray scale images look just like ones in binary images but often they have no well defined boundary. No well defined boundary – no well defined size!

For example, this is a binary image of a circle and that is the same image blurred. There is clearly just one object here and it looks like circle. But what’s its size? It could be a small spot in the middle, or  large circle, or it could be the whole image (why not?). If there are several objects like that, we can’t filter them based on larger/smaller comparison. As a result, we can’t even count them properly because without measuring we can’t tell noise from what’s important.

But wait a minute, of course, our software counts objects! So, how?

The user sets a lower bound on sizes of objects he considers important. Anything smaller is noise. What the user doesn’t know (but should) is what is an object. The definition of an object is in fact very simple:

An object is either a dark region surrounded by lighter area or a light region surrounded by a darker area.

For example, in the above image we have many-many circular objects. Too many, in fact, because we know that there is only one! So, the objects that we’ve found aren’t actual objects but “potential” objects. At this point we need to select just one. How?

We use the bound chosen by the user! We exclude all potential objects that are smaller than this bound. Good, but even now we still have multiple objects. What do we do? We just take the smallest!

Roughly, once the bound is set, the object is allowed to grow until its size is over the bound.

Suppose the bound is 100. Then what we present as the output is objects larger than 100 BUT as close as possible to 100. If the gray level changes very gradually, the objects’ sizes end up almost exactly equal 100. If this is the case, having an upper bound (say 200) in addition to the lower bound would not change the outcome…

That’s why only a single slider for the size is present. If object A is larger than object B, A is at least as important as B. A priori, all things being equal.

The second slider is for contrast and it operates in the exact same way: the object is allowed to grow until its contrast is over the bound. The logic is the same as before: a priori, if object A has a higher contrast than object B, A is at least as important as B.

OK, but what about those real life situations when you need to exclude larger objects? That’s when you turn from image analysis to data analysis. Of course, you’d have to make sure that you have captured all objects that you care about. That’s the hard part.

The data analysis stage is the easy part. If you have captured some noise or objects that you want to exclude, that’s OK. Now you simply filter the objects on the list based on any characteristic you want. Excel has plenty of tools for that. For example, the size is too large or too small. Or the perimeter, the contrast, the roundness, the intensity. Maybe you want only the objects from 100 to 200 pixels in size. Or maybe you are only interested in the objects within 300 pixels from the center of the image. All is easy at this stage.

Pixcavator is a light-weight (336K here) image explorer. Below I list new features and other modifications.

RGB channel-by-channel analysis. It’s an experimental feature, so that you can only use the red or the green for now. This is important for some applications such as microscopy. Different features are sometimes better revealed in different channels. Below: original, analysis in red channel, analysis in green channel.

Analysis summary to include some statistics. The output table contains only the raw data about each object. Of course, if you save the data to Excel, you can get anything from it: average of all columns, histograms, etc. We thought that it would be nice to be able to preview some data: average values of size and contrast. There will be more.

Data displayed based on the location of the mouse. That’s another very convenient feature. You used to have to mark/unmark object in the image and then find the row in the table to see the objects’s measurements. That’s not fun if the table is a hundred rows long. Now you let the mouse hover over the object of your interest and the data from the table is displayed right beneath the image.

Coloring objects. This feature was previewed a couple of weeks ago.

Hiding contours. To see the original image you used to have to go to the Analysis tab. Now you can flick it on and off to see what is hiding under the contours. The marking/unmarking of objects is unaffected.

Some sliders removed. The sliders for roundness and saliency haven’t been used a lot as far as I know. The complexity they add did not seem worthwhile. It does not mean that there will be always just the two sliders. The development of new characteristics for the sliders is under way. They will only be added if they make a significant improvement over what we have now. At least one new slider is coming in the next release.

Shrink slider modified. The shrink slider used to give you the shrink factor in terms of the area of the image. Now if you set itat 2, both of the dimensions will be cut in half while the area (and the processing time) will be cut by 4. This seems simpler. It is also preset to cut the processing time to 10 seconds or less. It seems like 99% of the time the resolution is excessive relative to the features being sought.