Precision of Geometric Moments in Picture analysis

Measuring how much an object has a ring-like shape

“…Indeed, the quantity ´´S G(x, y)d xdy appearing in formula (14), for the computation of M k (S) can be expressed as a linear combination of the moments m 0,0 (S), m 2,0 (S), m 0,2 (S), m 2,2 (S), m 4,0 (S), and m 0,4 (S), (see the expression for G(x, y) in ( 7)). In accordance with [18], the precision of computation of the normalized geometric moments m a,b (S) = (Area_of_S) (a+b+2)/2 • ´´G x a y b d xdy from the corresponding binary image is bounded above with O(1/r), where r is the number of pixels per length unit. So, if picture resolution increases, the error in the computation of the moments used decreases, by the rate of r. The error term can be improved under certain smoothness conditions on the boundary of S (e.g.…”

“…So, if picture resolution increases, the error in the computation of the moments used decreases, by the rate of r. The error term can be improved under certain smoothness conditions on the boundary of S (e.g. there are no straight sections on the boundary of S)more details are in [18].…”

An affine moment invariant for multi-component shapes

“…Being an area based measure, i.e. a measure that uses all of the shape points for its computation, it is efficient to compute [9,11]. This is not a…”

“…Note 1. With pixelised images, an efficient approximation (see [7]) of A(S) can be computed in O(N) time, where N is the number of pixels, in the digitized image of S. The moments µ p,q (S), in (7), are approximated by…”