OK. I will outline a solution that you can fill in
Given the table A:
u1 v1 (x1 y1) ... repeated for many images
0. Create a verb 'solveeqn' that will solve one system, given
x = 200x2 array of u v
y = 2x200 array of x y
1. Create
uv =. 2 {."1 A
xy =. 2 }. |: A
2. Run
_2 uv&solveeqn\ xy
You will get all your answers
Henry Rich
On 9/8/2012 8:35 PM, pascha wrote:
My fault again. I had to make difference between y and yi
a-h will be derived in least-square sense, which are the final result. There
are 50 x (a-h) unknowns correspond to each equation.
The structure of actual data is:
u1 v1 x1,1 y1,1 ... x1,50 y1,50
u2 v2 x2,1 y2,1 ... x2,50 y2,50
u3 v3 x3,1 y3,1 ... x3,50 y3,50
... ... ...
u200 v200 x200,1 y200,1 ... x200,50 y200,50
e.g. x(200,1) means "x" value of point 200 in image 1 and y(200,1) means "y"
value of point 200 in image number 1.
x(200,50) means "x" value of point 200 in image number 50, etc. So each
column corresponds to "x" or "y" in one image but the image has several
points (200 points). u,v have the same structure as x,y but are referred to
the image 0 (reference image).
In general x(n,m) is "x" value of point 'n' in image 'm' and y(n,m) is "y"
value of point 'n' in image 'm'
In order to make system of equation for image 'm' we have:
u1 x1,m y1,m 1 0 0 0
-u1*x1,m -u1*y1,m
v1 0 0 0 x1,m y1,m 1
-v1*x1,m -v1*y1,m
u2 x2,m y2,m 1 0 0 0
-u2*x2,m -u2*y2,m
v2 0 0 0 x2,m y2,m 1
-v2*x2,m -v2*y2,m
... =
u200 x200,m y200,m 1 0 0 0
-u200*x200,m -u200*y200,m
v200 0 0 0 x200,m y200,m 1
-v200*x200,m -v200*y200,m
Considering Y=AX, left hand-side (above) is Y and right-hand side is A and
obviously X can be derived as: X=: Y%.A
We have 'm' system of equation (m=50) which I have to extract from the data
and place them in the system of equation above.
Henry Rich wrote:
From this I'm pretty sure that the problem can be solved without loops
or boxing, but I still have no idea what any of the values
u v y xi a-h
mean, or what their shapes are. Also, the description uses 'row' and
'column' to describes things that seem to be matrices rather than row
and column vectors.
A small example would help. Or the actual shapes of the entities
involved.
Or, I suppose, someone who understands this description better than I
do...
Henry Rich
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