Measuring Dissimilarity Between Curves by Means of Their Granulometric Size Distributions

The choice of a dissimilarity measure between curves is a key point for clustering functional data. Functions are usually pointwise compared and, in many situations, this approach is not appropriate. Mathematical Morphology provides us with a toolbox to overcome this problem. We propose some dissimilarity measures based on morphological granulometries and their performance is evaluated on some functional datasets.

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