zernikeMoments {EBImage} | R Documentation |
Computation of Zernike moment features from image objects.
zernikeMoments(x, ref, N = 12, R = 30, apply.Gaussian, pseudo)
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. |
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)
.
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
.
Oleg Sklyar, osklyar@ebi.ac.uk; Mike Smith, msmith@ebi.ac.uk, 2007
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
example(getFeatures)