zernikeMoments            package:EBImage            R Documentation

_E_x_t_r_a_c_t_i_o_n _o_f _Z_e_r_n_i_k_e _m_o_m_e_n_t_s _f_r_o_m _i_m_a_g_e _o_b_j_e_c_t_s.

_D_e_s_c_r_i_p_t_i_o_n:

     Computation of Zernike moment features from image objects.

_U_s_a_g_e:

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

_A_r_g_u_m_e_n_t_s:

       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.

_D_e_t_a_i_l_s:

     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)'.

_V_a_l_u_e:

     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'.

_A_u_t_h_o_r(_s):

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

_R_e_f_e_r_e_n_c_e_s:

     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_: <URL:
     http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/SHUTLER3/node11.html>

_S_e_e _A_l_s_o:

     'getFeatures'

_E_x_a_m_p_l_e_s:

      example(getFeatures)

