SpatialVx (version 0.3)

Mij: Raw Image Moments.

Description

Calculate the raw Hu image moment Mij.

Usage

Mij(x, s, i = 0, j = 0)

Arguments

x

A matrix.

s

A two-column matrix giving the location coordinates. May be missing in which case they are assumed to be integers giving the row and column numbers.

i,j

Integer giving the moment order for each coordinate x and y, resp.

Value

• A single numeric giving the desired moment is returned.

Details

The raw moment M_{ij} (Hu 1962) is calculated by

M_{ij} = sum(x^i * y^j * Im[i, j])

where x and y are the pixel coordinates and Im is the (image) matrix. Various useful properties of an image may be gleaned from certain moments. For example, the image area is given by M_{00}, and the image centroid is (M_{10} / M_{00}, M_{01} / M_{00}). The image orientation angle can also be derived.

References

Hu, M. K. (1962) Visual Pattern Recognition by Moment Invariants. IRE Trans. Info. Theory, IT-8, 179--187.

See Also

imomenter

Examples

data(geom000)

Mij(geom000) # area