Alternative Methods for Counting Overlapping Grains in Digital Images

Standard granulometry methods are used to count the number of disjoint grains in digital images. For the case of overlapping grains, the standard method is not effective. Two alternative methods for counting overlapping grains in digital images are proposed. The methods are based on mathematical morphology and are suitable for grains of circular shape. The standard and overlapping methods were tested with a Monte-Carlo simulation using 32500 synthetic images with various grain sizes and quantities, as well as different levels of noise. The overall average counting error for all images tested with intermediate amount of noise (zero mean Gaussian noise with σ = 0.05) was 6.03% for the standard method, and 4.40% and 3.56% for the overlapping methods. The performance of the proposed methods was found to be much better than the standard method for images with significant overlap between grains.