Pattern spectra are image histograms that feature the distribution of image details with respect to some attribute measure. They are typically computed from granulometries which provide the necessary set of conditions to ensure a notion of order. In this paper we investigate means of describing order in the absence of operators and thus granulometries. We provide a case study on the multi-scale segmentation transform of the image domain to sets of single linkage connected components based on some dissimilarity measure. The nesting of consequent partitions, computed along the dissimilarity measure range, leads to the notion of partition pyramids. These are multi-scale partition representation structures characterised by large redundancies due to component replicas at various scales. We constrain this to the compact representation of partition hierarchies based on which we can compute efficiently pattern spectra and other filtering/segmentation transforms.

OUZOUNIS Georgios;  SOILLE Pierre; 

2011-08-31

Springer Verlag

JRC62785

https://publications.jrc.ec.europa.eu/repository/handle/JRC62785,   

10.1007/978-3-642-21569-8_10,