Improving the accuracy of isotropic granulometries

Morphological sieves are capable of classifying objects in images according to their size. They yield a granulometry, which describes the imaged structure. The discrete sieve has some disadvantages that its continuous-domain counterpart does not have: sampled disks (used as isotropic structuring elements) are rather anisotropic, especially at small scales, and their area, as a function of the size in the continuous domain, shows jumps at apparently arbitrary locations. These problems cause a severe bias and low precision of the derived size distribution. Therefore we propose a new digitization scheme for implementing continuous sieves. First we increase the sampling density of the structuring element and the image. This does not add new detail to the image, but yields a sampled structuring element that is a much better approximation to its continuous counterpart, and thereby substantially reduces the discretization error. The second innovation is to shift the structuring element with respect to the sampling grid; this makes the size increments smoother, and further reduces the discretization errors. These ideas are validated on synthetic images. We also show that the proposed improvements allow for a finer scale sampling. 2006 Elsevier B.V. All rights reserved.