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Binary and Grey Scale Moments

Keywords: Grey Scale Moments, eccentricity

Categories: Pattern Recognition and Image Processing


Author(s): H.W. Hughes

In computer vision, moments are scalar values that encode some property of the shape or distribution of an object. They are often used as a compact representation of simple binary shapes, because: (i) they are easy to compute (i.e., real-time hardware to compute moments exists), and (ii) a few different moments are often sufficient to characterise uniquely a limited set of shapes. It is also possible to calculate functions of the moments that are invariant to translation, rotation and scale changes. The ijth moment (mij ) of a binary image about the centre of mass (x0,y0) is given by:

mij=(x0-x)i(y0-y)j

By varying the parameters i and j the resulting moment can yield a number of useful results such as the area and the eccentricityeccentricity. For a grey scale image whose intensity can be expressed as a function,f(x,y) ofx and y , the moment mij is given by:

mij=f(x,y)(x0-x)i(y0-y)j


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