surface minimisation

Hi all,
 
I know what I want to do, but don't know how to go about it!
 
My problem: I have two arrays containing height data.
 
The first array contains relative heights measured in the x-direction.
Essentially, I'm measuring the heights along strips of a surface, but have n
o idea of zero height for any of the strips.
The heights in any one row are correct relative to each other. However, ther
e is no established relationship between the heights in row 1 and the height
s in row 2.
 
eg
 
row 1:   2, 3, 5, 7
row 2:   6, 7, 9, 11
 
row 1 and 2 have the same height variation along the rows but I have no idea
 whether row 2 is actaully 4 units above row 1 or not.
 
The 2nd array contains strips of height data measured in the y-direction. Ag
ain, elements along a row are correct relative to each other, but between ro
ws there is no established relationship.
 
I should be able to use the y-height values to establish the x-height off se
ts or vice versa. However, due to small errors, this is not the case and dep
ending on the path taken (ie use y heights to correct x-heights or vice vers
a) I get differing surfaces

Hi GrahamG,
Thanks for your reply and interest. I haven't got a code written for this bu
t I have a pseudo algorithm written (if you can call it that!). I 
was thinking a "random walk" method would work best.
If I have the actual 6 x 4 height field as shown below:
0 0 2 4 5 6
1 1 4 6 6 7
2 3 4 5 6 7
2 2 5 5 7 8
 
In my measurements I get the X-heights: heights along a row are correct rela
tive to elements in that row
1 1 3 5 6 7
2 2 5 7 7 8
6 7 8 9 10 11
-1-1 2 2 4 5
and Y-heights: heights in a column are correct relative to elements in that 
column.
3 1 2 0 4 -1
4 2 4 2 5 0
5 4 4 1 5 0
5 3 5 1 6 1
Start with an empty array,
choose start point and enter into array.
So if I start with element row 2, col 2 in th X data: height = 8. (rows and 
columns numbered 0->5 and 0->3)
start point (2,2) height= 8
move to next adjacent point in vertical or horizontal direction to star
t point (not diagonal) choice of (1,2), (3,2), (2,1), (2,3).
choose (1,2)
as move in vertical direction check the relation in the Y-data between (2,2)
 and (1,2):
Y (1,2) h=4, Y (2,2) h= 4 =>dh =0
 therefore height (1,2) =8+dh =8+0=8
  move to next adjacent point in vertical or horizontal direc
tion to  point (1,2)
choose (1,3)
as move in horizontal direction check relation in X-data between (1,2) and (
1,2)
X(1,2) h=5, X(1,3) h=7 =>dh = +2
therefore height (1,3) = 8+dh=8+2=10
repeat until all points have been adjusted (keep track with another arr
ay?)
 
This gives the correct relative heights for all points along columns an
d rows.
 
following the above pseudo algorithm would get
4 4 6 8 9 10
5 5 8 10 10 11
6 7 8 9 10 11
6 6 9 9 11 12 
 
each point is 4 greater than actual but relatively correct.
 
Now that I have written it out  like this it becomes a bit clearer for 
me! and will try to implement this solution. In the meantime any help gladly
 accepted.

That was a really good explanation and it seems as though you have a gr
eat idea of how to work on it from here. So as to save us both working on th
e same problem in parallel, if you are a little more confident now I would r
ecommend that you have a fi
rst attempt and if you get to a stage where you are not sure where to procee
de then post it up here and I shall take a look. At the stage of your applic
ation that you are now, you are the expert with your algorithm but once
 you have something, whethe
r it works or not, post it up and then two minds debugging it are better tha
n one. I should be happy to help.
 
best regards