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Figure 5 : Détection of cells from a population of cells and artefacts, cells being marked by their nuclei. Let x be a point of a cell that contains a nucleus. There exists a path in the cell linking x and a point y of the nucleus. In other words, the géodésie distance between x and the nuclei is finite. Mathematically speaking, the population of cells with a nucleus is : {x CX | d^(x,Y) < + °°} 4 - MORPHOLOGICAL TRANSFORMATIONS AND GEODESIC DISTANCE FUNCTION In the space X with the géodésie metric dv, it is possible A to generalize the transformations commonly used in mathematical morpho- logy (3) i) if Y C X, points at a géodésie distance less than X from Y constitute a set called "X-dilated set from Y in X" and denoted D (Y;X) . - ... A (see fig. 6). DX(Y;X) = {x C X | dx(x,Y) < X}