Abstract |
In this lecture I will explain how one can obtain a size distribution, such as a pore size distribution or a fibre length distribution, from an image. Starting with very simple image analysis tools, namely the operations called dilation and erosion, I will build a complex tool capable of obtaining an accurate size distribution. Dilation and erosion are the two basic operations in a discipline called mathematical morphology. These operations transform an image using a probe. The interaction of the probe with the image gives information about the morphology (spatial arrangement) of the sample. A very specific combination of these basic operations, with carefully chosen probes, yields a granulometry, a curve that is directly proportional to a size distribution. I will show how such a granulometry can be precise enough to detect very small changes in the pore sizes of a milk gel, changes too small to see by eye. Next I will construct a probe such that the granulometry yields a length distribution, and I will show how this can be used to distinguish whole from broken rice kernels. I will also introduce a fairly new algorithm, the path closing, which can be used to make the computation of the length distribution much more efficient. I will then show the result of applying this efficient algorithm to a three-dimensional micro-tomographic image of a wood fibre composite material, and discuss a strategy to correct for the bias introduced by the limited field of view of the image.
(This is a repeat of the docent lecture I gave in Umeå on Sept 29.) |