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View Full Version : Re: camera angles in 3-D

Jesus Dapena
12-07-1995, 06:22 AM
To the Biomch-L readership:

From a purely photogrammetric standpoint, an angle of about 90
degrees between the optical axes of the cameras is the best. If the optical
axes of the cameras are too parallel to each other, then small errors in
digitizing will lead to large errors in the 3D coordinates of the digitized
points. This is simply due to geometry. (Sorry, it's very hard to make the
appropriate drawing in an email message, but I'll try using words; you will
have to take into account that one word is worth 0.001 pictures.)

First let's represent the case of the cameras set up at a 90-degree
angle. Imagine a horizontal line ("line 1") going from point A on the left
of a piece of paper (the position of camera 1) to point B on the right of
the piece of paper, and a vertical line ("line 2") going from point C at the
bottom of your piece of paper (the position of camera 2) to point D near the
top of your piece of paper. The two lines intersect at a point E that
represents the true location of a point that you digitized in both cameras.
Now, imagine a third line ("line 3"), passing through point C but slanting a
litle bit toward the right (say, 5 degrees) with respect to line 2. Line 3
will intersect line 1 at point F, a little bit to the right of point E. The
distance between points E and F represents the error in the calculated 3D
coordinates of the point.

Now, let's represent the case of two cameras set up at a very narrow
angle (20 degrees). Imagine the same horizontal line ("line 1") described
above, going from point A to point B. Then, imagine a line ("line 4") that
passes through point E, but which is tilted at a 20-degree angle with
respect to the horizontal, sloping upward slightly from left to right. Mark
a point "G" on line 4 somewhere below point A. Finally, consider a line
("line 5") which passes through point G, but is 5 degrees closer to the
horizontal than line 4. Line 5 will intersect line 1 at point H. The
distance between point E and point H will be larger than the distance
between point E and point F. This is why the camera set-up with the
90-degree angle is the best.

The problem with the 90-degree set-up is that if you are digitizing
***surface*** markers on your subject, there will be a lot of points that
will be visible to camera 1 but not to camera 2, or to camera 2 but not to
camera 1. All of those points will then be unavailable for your analysis,
because you can only get 3D coordinates for points that are visible to BOTH
cameras. If your cameras point more parallel to each other, there will be
more points visible simultaneously to both cameras. But then the accuracy
gets worse because you are farther from the ideal 90 degree angle.

In view of this problem, the people that work with surface markers
need to make a compromise between the 90-degree angle (which makes it
impossible to reconstruct the 3D coordinates of many points, because one or
the other camera can't see a given point) and an excessively narrow angle
(which allows many more surface markers to be visible to both cameras
simultaneously, but is inherently less accurate). Different rules of thumb
have been given for the best compromise between the two conflicting goals.

NOTE: The compromise is only needed if you work with surface
markers. If you ***don't*** work with surface markers (for instance, if you
estimate directly from your images the locations of internal landmarks such
as joint centers), then you don't get to see directly most of your landmarks
anyway, and in that case you might as well use a camera angle that is
reasonably close to 90 degrees. (For instance, anything between 70 and 110
degrees should be pretty good.)

---
Jesus Dapena
Department of Kinesiology
Indiana University
Bloomington, IN 47405, USA
1-812-855-8407 (office phone)
dapena@valeri.hper.indiana.edu (email)