It is possible to orientate chromosomes vertically with a morphological "rose des directions" using successive erosions. The larger the particle is, the longer the operation is. However, the iterations can be reduced by submitting not the particle itself, but a Top-Hat version of the image, or the particle skeleton or the particle contour yielding similar results with a reduced cost.
The first rose-des-directions was obtained with the original particle, I didn't compute the total amount of erosion, but finding the principal orientation around 120° required around 50 successive erosions, whereas only 16 erosions are necessary if the particle skeleton is analysed, 30 erosions with the Top-Hat filtered image or 20 with the contour.
With a more complex image, the "rose des directions" detects the orientation of the larger chromosome.