The most accurate methods for automatic classification of chromosomes under a light microscope today extract numerical features from band-pattern profiles along their longitudinal axes. The construction of a reliable axis is a crucial step in this process. We propose a new way based on the dominant points of the contour and cubic splines. The dominant points serve as candidates for the tips of the chromosome or its chromatids. Ambiguities are dissolved by the recently proposed method of variants for object identification. A Voronoi diagram decomposes the chromosome in slices for profile extraction. The method improves the currently best classification results significantly yielding a test-set error rate of 0.6% applied to a data set of the band level 200.