A mathematical comment on the formulae for the aggregation index and the shape index

Ina recent paper [Landscape Ecol. 15: 591–601 (2000)] He et al. describedanaggregation index AI _i to measure pixelaggregation within a single class i. We show that thecommonly used shape index SI _i is related to theproposed aggregation metric as SI _i =(A _i) +AI _i(1 –(A _i)), with(A _i) dependent on class areaA _i only. Moreover, it is shown that thenormalized shape index, SI _i ^*,equals (1 – AI _i). We conclude thatAI _i does not provide any information notprovided by SI _i, orSI _i ^*.This revised version was published online in May 2005 with corrections to the Cover Date.