Measuring shape rectangularity

A new method for measuring shape rectangularity is introduced. The new shape measure is invariant with respect to similarity transformations, ranges over the interval (0,1] and picks the value 1 if and only if the measured shape is a rectangle. The measure is theoretically well founded and has a clear geometric meaning, i.e. it indicates how the shape considered differs from a rectangle. So, the measure behaviour can be predicted to some extent, which is always an advantage.