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Computational Methods for Feature Detection in Optical Images

is to its neighbor. Energy returns a sum of the squared elements in the co-occurrence matrix, returning a value of one for a constant intensity. Homogeneity returns a value of the closeness of the member distribution in the co-occurrence matrix.

A popular method for addressing rotational invariance is to take an average of over the feature values for all the principal orientations, so that co-occurrences that move to a different matrix due to rotational changes will still be measurable.

2.4.1.3. Invariant moments

Invariant moments combine the overall shape of the region and intensity distribution to create a set of values that are considered invariant to rotation, scaling, and translation changes. We will refer to these moment invariants as Hu moments,25 which we attain by first using the discrete version of the moment:

Mij = xiy j I(x, y) (2.47)

xy

to find centroids x¯ = M10/M00, y¯ = M01/M00. We then define the central moments as:

µpq = (x x)¯ p(y y)¯ qI(x, y), (2.48)

xy

where p and q give the moment order. The central moments used in the Hu moments are written as:

µ00 = M00,

µ01 = 0, µ10 = 0,

µ11 = M11 xM¯ 01 = M11 yM¯ 10,

µ20 = M20 xM¯ 10,

µ02 = M02 yM¯ 01,

µ21 = M21 2xM¯ 11 yM¯ 20 + 2x¯ 2M01,

µ12 = M12 2yM¯ 11 xM¯ 02 + 2y¯ 2M10,

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