setcov               package:spatstat               R Documentation

_S_e_t _C_o_v_a_r_i_a_n_c_e _o_f _a _W_i_n_d_o_w

_D_e_s_c_r_i_p_t_i_o_n:

     Computes the set covariance function of a window.

_U_s_a_g_e:

      setcov(W)

_A_r_g_u_m_e_n_t_s:

       W: A window (object of class '"owin"'.

_D_e_t_a_i_l_s:

     The set covariance function of a region W in the plane is the
     function C(v) defined for each vector v as the area of the
     intersection between W and W+v, where W+v is the set obtained by
     shifting (translating) W by v.

     We may interpret C(v) as the area of the set of all points x in W
     such that x+v also lies in W.

     This command computes a discretised approximation to the set
     covariance function of any plane region W represented as a window
     object (of class '"owin"', see 'owin.object'). The return value is
     a pixel image (object of class '"im"') whose greyscale values are
     values of the set covariance function.

     The set covariance is computed using the Fast Fourier Transform,
     unless 'W' is a rectangle, when an exact formula is used.

_V_a_l_u_e:

     A pixel image (an object of class '"im"') representing the set
     covariance function of 'W'.

_A_u_t_h_o_r(_s):

     Adrian Baddeley adrian@maths.uwa.edu.au <URL:
     http://www.maths.uwa.edu.au/~adrian/> and Rolf Turner
     rolf@math.unb.ca <URL: http://www.math.unb.ca/~rolf>

_S_e_e _A_l_s_o:

     'owin', 'as.owin', 'erode.owin'

_E_x_a_m_p_l_e_s:

       w <- owin(c(0,1),c(0,1))
       v <- setcov(w)
       plot(v)

