Fit curve to contour

This option locates a contour passing through a user-specified point. The coordinates of this contour are then expressed in terms of the distance along the contour, s, and a least squares fit is generated for this data.

RETURN VALUES The following return values are available through the !!Rn mechanism (note that you will normally require a E, F or G modifier to return the floating point representation of these return variables):

           !!R0,...        Return the coefficients of the fit for the i
                           verses s fits
           !!Ra,...        Return the coefficients of the fit for the j
                           verses s fits
           !!Rn            Returns the number of points on the contour
           !!Rm            Returns 2*pi/!!Rn

Fit contour in which buffer ?

Cursor Positioning: Specify point on contour

Threshold for contour ?

Locate contour in Window or whole Screen ?

{If contour restricted to window}

Window Selection: Region to find contour in

    The DigImage window selection submenu is produced to enable interactive
    specification of the window within which the contour is restricted. For
    information about use of the window submenu, refer to [H Help] after the
    submenu has been started.

Contour found contains !!Rn points. The contour is !R0 Display the contour on which buffer ?

Erase buffer first ?

Plot with what intensity (-1 to suppress) ?

Plot i verses s and j verses s ?

{If plotting i(s) and j(s) curves}

Plot the i vs s and j vs s curves where (-1 for computer monitor) ?

The curve described by the contour is fitted using i=G(s) and j=H(s) where s is the distance along the contour.

Enter the basis functions to be used for G(s). These functions should be separated by colons (:). To suppress the fitting, enter a blank line.

       A(i) = c0 g0(s) + c1 g1(s) + ...

and

       B(j) = d0 h0(s) + d1 h1(s) + ...

where A(i), g0(s), g1(s), ... and B(j), h0(s), h1(s), ... are user-specified functions. The coefficients c0,c1,... and d0,d1,... are determined by a least squares procedure. These coefficients are available to the user through !!R0, !!R1, ... (for c0, c1, ...) and !!Ra, !!Rb, ... (for d0, d1, ...).

This entry specifies the set of functions g0(s), g1(s), ... These functions should be expressed in terms of the distance along the contour, s, and should be separated from eachother by a colon (:). For example, to fit a straight line to A(i), ie. A(i) = a0 + a1*s, you should specify

       1 : s

The following return variables contain values which may assist in specifying appropriate basis functions:

       !!Rn        n, the number of points in the contour
       !!Rp        =2*pi. To fit a circle to a closed contour, use
                   1 : COS(!!GRp*S) : SIN(!!GRp*S)

If you do not wish to fit any curve to the data, enter a blank line.

Enter the function A(i) transforming the i data

    This function should be expressed in terms of i. See the previous prompt
    for further details.

Enter the inverse transform I(a) for the i data

    This function is used to invert the A(i) transform. It should be
    specified in terms of a.

Enter the basis functions to be used for H(s). These functions should be separated by colons (:). To suppress the fitting, enter a blank line.

Enter the function B(j) transforming the j data

    This function should be expressed in terms of j. See the prompt for A(i)
    for further details.

Enter the inverse transform J(b) for the j data

    This function is used to invert the B(j) transform. It should be
    specified in terms of b.

Plot fitted curve using what intensity (-1 to suppress) ?

    The curve fitted to the x,y data will be plotted on the output buffer
    using the intensity specified here. If you do not wish to plot this
    curve, specify the intensity as -1.

Errors, Warnings and Messages

Message:
Fitting curves to data...

Error Message: The chosen pixel can not lie on a contour

    The pixel chosen must have a neighbouring pixel of a lower intensity.
    This is necessary as the contour is is taken to be the pixel with the
    intensity greater than or equal to the threshold defining the contour.
    Thus if there is no neighbouring pixel with an intensity lower than the
    one selected, there can not be a contour passing through the selected
    point.

Error Message: Too many points on contour

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