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This paper considers the problem of constructing shape measures; we start by giving a short overview of areas of practical application of such measures. Shapes can be characterised in terms of a set of properties, some of which are Boolean in nature. E.g. is this shape convex? We show how it is possible in many cases to turn such Boolean properties into continuous measures of that property e.g. convexity, in the range [0-1]. We give two general principles for constructing measures in this way,doi:10.1142/s0218654304000614 fatcat:tats7vlypbhblippicfepliwoq