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)

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)