zernikeMoments {EBImage}R Documentation

Extraction of Zernike moments from image objects.

Description

Computation of Zernike moment features from image objects.

Usage

  zernikeMoments(x, ref, N = 12, R = 30, apply.Gaussian, pseudo)

Arguments

x An Image object or an array containing object masks. Object masks are sets of pixels with the same unique integer value.
ref An Image object or an array, containing the intensity values of the objects.
N A numeric. Indicates the maximal order of Zernike polynomials to be computed. Default value is 12.
R A numeric. Defines the radius of the circle in pixels around object centers from which the features are calculated.
apply.Gaussian, pseudo Deprecated.

Details

Zernike features are computed by projecting image objects on the Zernike complex polynomials, using:

z.{nl} = (n+1) / pi * abs( sum_x,y(V*nl(x,y) * i(x,y)) ),

where 0 <= l <= n, n - l is even and i(x,y) is the intensity of the reference image at the coordinates (x,y) that fall withing a circle of radius R from the object's centre. Coordinates are taken relative to the object's centre.

V*nl is a complex conjugate of a Zernike polynomial of degree n and angular dependence l:

Vnl(x,y) = Qnl(x,y) * exp(j*l*theta), where j = sqrt(-1), theta=atan2(y,x), and

Qnl(x,y) = sum[_m=0^((n-l)/2)] ((-1)^m * (n-m)! * r^(n-2*m)) / (m! * ((n-2*m+l)/2)! * ((n-2*m-l)/2)!) , where r = sqrt(x^2+y^2).

Value

Returns a matrix (or a list of matrices if x contains multiple frames) of features computed of the objects present in x and using the intensity values of ref.

Author(s)

Oleg Sklyar, osklyar@ebi.ac.uk; Mike Smith, msmith@ebi.ac.uk, 2007

References

F. Zernike. Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode (Diffraction theory of the cut procedure and its improved form, the phase contrast method). Physica, 1:pp. 689-704, 1934.

Jamie Shutler, Complex Zernike Moments: http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/SHUTLER3/node11.html

See Also

getFeatures

Examples

 example(getFeatures)

[Package EBImage version 3.0.5 Index]