Cris’s Image Analysis Blog

In an earlier post, I described and implemented a method, that was published recently, to stitch together photographs from a panoramic set. In a comment this morning, Panda asked about the parameters that direct the region merging in the watershed that I used. This set me to think about how much region merging the watershed should do. The only limitation that I can think of, is that we need two regions: one touching the left image and one toughing the right. We can easily do this with a seeded watershed: we create two seeds, one at each end of the region where the stitch should be, and run a seeded watershed. This watershed will not create new regions. You should see it as a region growing algorithm, more than a watershed. However, the regions are grown according to the watershed algorithm: low grey values first. That insures that, when the two regions meet, it happens at a line with high grey values (a “ridge” in the grey-value landscape). The graph cut algorithm can now be left out: the region growing algorithm does everything.

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First of all: Happy New Year!

Over the holidays I’ve been learning about dithering, the process of creating the illusion of many grey levels using only black and white dots. This is used when displaying an image on a device with fewer than the 64 or so grey levels that we can distinguish, such as an ink-jet printer (which prints small, solid dots), and also when quantizing an image to use a color map (remember the EGA and VGA computer displays?). It turns out that this is still an active research field. I ran into the paper Structure-aware error diffusion, ACM Transactions on Graphics 28(5), 2009, which improves upon a method presented a year earlier, which in turn improved on the state of the art by placing dots to optimize the appearance of thin lines. This got me interested in the basic algorithms, which I had never studied before. Hopefully this post will give an understanding of dithering and its history.

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Last month I wrote a post showing how to calculate the perimeter of an object using its chain code. In this post I want to review several more measures that can be easily obtained from the chain codes: the minimum bounding box; the object’s orientation, maximum length and minimum width; and the object’s area. The bounding box and area are actually easier computed from the binary image, but if one needs to extract the chain code any way (for example to compute the perimeter) then it’s quite efficient to use the chain code to compute these measures, rather than using the full image. To obtain the chain codes, one can use the algorithm described in the previous post, or the DIPimage function dip_imagechaincode.

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In the previous post I discussed simple techniques to estimate the boundary length of a binarized object. These techniques are based on the chain code. This post will detail how to obtain such a chain code. The algorithm is quite simple, but might not be trivial to understand. Future posts will discuss other measures that can be derived from such a chain code.

In short, the chain code is a way to represent a binary object by encoding only its boundary. The chain code is composed of a sequence of numbers between 0 and 7. Each number represents the transition between two consecutive boundary pixels, 0 being a step to the right, 1 a step diagonally right/up, 2 a step up, etc. In the post Measuring boundary length, I gave a little more detail about the chain code. Worth repeating here from that post is the figure containing the directions associated to each code:

The chain code thus has as many elements as there are boundary pixels. Note that the position of the object is lost, the chain code encodes the shape of the object, not its location. But we only need to remember the coordinates of the first pixel in the chain to solve that. Also note, the chain code encodes a single, solid object. If the object has two disjoint parts, or has a hole, the chain code will not be able to describe the full object.

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Oftentimes we segment an image to find objects of interest, and then measure these objects — their area, their perimeter, their aspect ratio, etc. etc. Measuring the area is accomplished simply by counting the number of pixels. But measuring the perimeter is not as simple. If we simply count the number of boundary pixels we seriously underestimate the boundary length. This is just not a good method. A method only slightly more complex can produce an unbiased estimate of boundary length. I will show how this method works in this post. There exist several much more complex methods, that can further improve this estimate under certain assumptions. However, these are too complex to be any fun. I’ll leave those as an exercise to the reader. :)

Because we will examine only the boundary of the object, the chain code representation is the ideal one. What this does, is encode the boundary of the object as a sequence of steps, from pixel to pixel, all around the object. We thus reduce the binary image to a simple sequence of numbers. In future posts I’ll explain a simple algorithm to obtain such a chain code, and show how to use chain codes to obtain other measures. In this post we’ll focus on how to use them to measure boundary length.

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