Posts Tagged ‘perimeter’

## More chain code measures

Wednesday, October 13th, 2010

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`.

## How to obtain the chain code

Monday, September 27th, 2010

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.

## Measuring boundary length

Tuesday, September 14th, 2010

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. ðŸ™‚

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.