From: boebert@sctc.com (Earl Boebert)
Subject: Removing Distortion From Bitmapped Drawings?
Organization: SCTC
Lines: 47

Let's say you have a scanned image of a line drawing; in this case a
boat, but it could be anything.  On the drawing you have a set of
reference points whose true x,y positions are known.  

Now you digitize the drawing manually (in this case, using Yaron
Danon's excellent Digitize program).  That is, you use a program which
converts cursor positions to x,y and saves those values when you click
the mouse.

Upon digitizing you notice that the reference point values that come
out of the digitizing process differ in small but significant ways
from the known true values.  This is understandable because the
scanned drawing is a reproduction of the original and there are
successive sources of distortion such as differential expansion and
contraction of paper, errors introduced in the printing process,
scanner errors and what have you.

The errors are not uniform over the entire drawing, so "global"
adjustments such as stretching/contracting uniformly over x or y, or
rotating the whole drawing, are not satisfactory.

So the question is: does any kind soul know of an algorithm for
removing such distortion?  In particular, if I have three sets of
points 

Reference(x,y) (the known true values)

DistortedReference(x,y) (the same points, with known errors)

DistortedData(x,y) (other points, with unknown errors)

what function of Reference and Distorted could I apply to
DistortedData to remove the errors.

I suspect the problem could be solved by treating the distorted
reference points as resulting from the projection of a "bumpy" 3d
surface, solving for the surface and then "flattening" it to remove
the errors in the other data points.

Any kind and informed soul out there have any ideas, or better yet,
pointers to treatments of the same or similar problems?

Thanks,

Earl


