Help for MORPH

MORPH is used to produce intermediate images between two input images.
It will use the geometric distortion between the input images
and will introduce a percentage of this distortion into the outputs.
It will also weight the input images proportionately with their 
distance from the inputs in intensity. 
  The geometric distortion is determined by programs TRACKER or 
TRACKER2 which create a tiepoint grid using hundreds or thousands of
points not necessarily in a regular pattern. Each output is
the sum of both inputs weighted in intensity and interpolated in position.

Method:
If there are N output images and we are interested in output image
number n where n <= N. And if we have two input images called left
and right, Then the weighting would be:
right_weight = n/(N+1)
left_weight=1-right_weight
Each tiepoint is interpolated to give it's equivalent position for image n.
tiepoint_line_image_n=tiepoint_line_left_input*left_weight                        tiepoint_line_right_input*right_weight
tiepoint_samp_image_n=tiepoint_samp_left_input*left_weight                        tiepoint_samp_right_input*right_weight
We then create a regular grid on image n and for each intersection locate
the nearest tiepoint on n in each of the four quadrants. If more points
are desired the rest are found from the nearest remaining points 
(see NPTS keyword). 
We then fit
x and y polynomials going from n to the left and right images of the form:
Y=Axy+By+Cx+D  and X=Exy+Fy+Gx+H for each grid intersection ( INC keyword).
The box INC by INC centered on the grid intersection is then mapped via the
polynomials onto the left and right images. This determines where a pixel 
on n comes from in both input images. Each point is averaged by linearly
weighting each polynomial based upon how far the point is from the center
of that polynomial. Weighting is done horizontally only between adjacent
polynomials.
   The DN value in each input image is interpolated bilinearly and then
combined to give the DN value for that pixel in n, thus:
DN_n(X,Y)=DN_left*left_weight+DN_right*right_weight.

Restrictions:
Morph must place all the inputs into memory as 16 bit images. Restrictions
can easily be aleviated by changing the parameter statement in the main
program and recompiling it. 
At the moment:
  the two input images cannot exceed 1000 lines by 1000 pixels.
  the number of tiepoints cannot exceed 10000.
  the ratio of NS/INC cannot exceed 150.
In the NPTS=4 mode if a grid point has less than 4 points (one in each 
quadrant) the grid point area is abandoned. This leads to blank space
around the output images. Higher values of NPTS permits extrapolation.

Example:

tracker2 inp=(left.img,right.img) out=mark.img    grid=100 nlw=11 nsw=11 edge=10 'print window=(2,1) look=(5,5)    limit=(8,8) see=1
morph inp=(left.img,right.img,mark.img) frames=2 name=morph

(tracker2 generates a grid of tiepoints in the mark file. Morph uses
the tiepoints field to determine the amount of distortion  between the
images. In this case it generates two outputs 1/3 and 2/3 of the way
between left and right images. Each output is weighted in intensity
linearly between the inputs. Thus morph1.img has 2/3 the weight of
left.img and 1/3 the weight of right.img . 
The output images are named: morph1.img and morph2.img)

HISTORY

Written By: J Lorre			Nov 15 1992
Cognizant Programmer: J Lorre

PARAMETERS: