Counting white blood cells using morphological granulometries

We describe a modification of the mixture proportion estimation algorithm b ased on the granulometric mixing theorem. The modified algorithm is applied to the problem of counting different types of white blood cells in bone ma rrow images. In principle, the algorithm can be used to count the proportio n of cells in each class without explicitly segmenting and classifying them . The direct application of the original algorithm does rot converge well f or more than two classes. The modified algorithm uses prior statistics to i nitially segment the mixed pattern spectrum and then applies the one-primit ive estimation algorithm to each initial component Applying the algorithm t o one class at a time results in better convergence. The counts produced by the modified algorithm on six classes of cells-myeloblast, promyelocyte, m yelocyte, metamyelocyte, band, and PolyMorphoNuclear (PMN)-are very close t o the human expert's numbers; the deviation of the algorithm counts is simi lar to the deviation of counts produced by human experts. The important tec hnical contributions are that the modified algorithm uses prior statistics for each shape class in place elf prior knowledge of the total number of ob jects in an image, and it allows for more than one primitive from each clas s. (C) 2000 SPIE and IS&T. [S1017-9909(00)00602-4].