AUTHOR: Lowell Johnson
Creates a geometric or radiometric mapping grid using the finite element method (triangulation) for surface fitting.
None
FINITE was created to generate a LAS grid from predefined control points. The control points define the transformation between input and output image coordinates or radiometric amplitudes at those points.
Rather than fitting all of the control points with a single polynomial "best fit" transform, the finite element method is used to allow for a more flexible fit. A triangular mesh is generated from the control points. A first degree polynomial transform is associated with each triangle such that the transforms are continuous across triangle boundaries.
- if RADIOMETRIC then
- Read point locations and brightness shift values
- else (GEOMETRIC)
- Read point pair (input, output) locations.
- end if
- Compute first order polynomial fit of points.
- if RADIOMETRIC then
- Calculate the brightness shift values of the four triangulation corner points projected outside the image border.
- end if
- Calculate the locations of the four triangulation corner locations:
where
- left point = minline - delta, (minsamp + maxsamp)/2
- top point = (minline + maxline)/2, maxsamp + delta
- right point = (minline + maxline)/2, minsamp - delta
- bottom point = maxline + delta, (minsamp + maxsamp)/2
- minline, maxline = the minimum and maximum line locations of the input points
- minsamp, maxsamp = the minimum and maximum sample locations of the input points
- delta = 5 * (maxline - minline + maxsamp - minsamp)
- Triangulate the control points using the Delaunay triangulation method.
- if RADIOMETRIC then
- At each grid intersection,locate the containing triangle and compute the radiometric difference value based on the first order polynomial fit of the three vertices of the triangle.
- else (GEOMETRIC)
- At each grid intersection, locate the containing triangle and compute the input location of the grid based on the first order polynomial fit of the three vertices of the triangle.
- end if
- Write the grid.
ALGORITHM REFERENCES:
Finite Element Surface Interpolation, June Thormosdgard
What is Dirichlet Tessellation?