View Full Version : Aliasing Problem ....

Peter Sinclair
05-28-1997, 10:11 AM
Ray, for your interest.


I'm sorry to have missed your original posting, but having read your recent
note, and some of the responses, I'd like to add a few words.

In your original note you make it clear that ...

1) You are in fact making MEASUREMENTS ("... visual inspection of the
vertical coordinate data ..."), and that your concern is not a VISUAL
phenomenon produced by alaising (the "wagon wheel effect").

2) The problem you are encountering appears to be limited to the
"vertical component" of the motion. I'm going to assume that
you are using the term "vertical" in the loose sense as it might
be used in "vertical hold", and that the problem is NOT really
associated with a global (X,Y,Z) coordinate system aligned with
the true (gravitation, global) vertical. More precisely, I'm
going to assume that your problem appears to be associated with
the "V" or "Y" component of your two-dimensional (U,V) IMAGE

If these two statements are correct, I suspect you don't have an
aliasing problem, per se. What I think you are seeing is a 30Hz
artifact introduced by an interlaced signal. John Greaves alluded
to this in his note to you, but let me see if I can explain WHY
you are seeing the artifact.

An interlaced image consists of two fields, each acquired in 1/60th
second. For simplicity, consider a hypothetical CCD array consisting
of 512 pixel ("horizontal") by 480 ("vertical"). In order to create
an interlaced image, the camera would first sample (ONLY) the odd rows
of pixels in 1/60th second, and then (ONLY) the even ones in 1/60th

In order to create an image on your (familar) TV screen, the data from
the first sample would be used to produce the scan lines for the "odd"
(or first) field (again in 1/60th second), and the second sample would
be used to produce the scan lines for the "even" or (second) field.
Under normal circumstances, these two fields would be interwoven (in
1/30th second) to produce the "interlaced" scan you see on the screen.
But you don't want to "look" at the image, you want to extract edge
information. Let's see what happens when the image is digitized ...

Consider a single "target" spanning six TV lines ...

---------------XXX---------- LINE 1 -- part of the "odd" (1st) field
-------------OOOOOOO-------- LINE 2 -- part of the "even" (2nd) field
-----------XXXXXXXXXXX------ LINE 3 -- part of the "odd" (1st) field
-----------OOOOOOOOOOO------ LINE 4 -- part of the "even" (2nd) field
-------------XXXXXXX-------- LINE 5 -- part of the "odd" (1st) field
---------------OOO---------- LINE 6 -- part of the "even" (2nd) field

If your digitizer is sampling at 1/60th second, and your signal is
interlaced, what will happen? In the first 1/60th second, the digitizer
will sample the odd field and identify the target with "XXX". It's not
difficult to see that the centroid of the XXXX cluster is somewhere in
the middle of LINE 3--actually, the sixth "X" in the illustration. But
when the digitizer samples the next "image (in the second 1/60th second)
it samples the even field and thus identifies the target with "OOO".
Again, it's not difficult to see that the centroid of the OOOO cluster
is the sixth "O" in LINE 4. If you continue this process ... odd field,
even field, it's not hard to see that the centroid of a STATIC target
will appear to "hop" up and down. In fact it will do so in a very
regular fashion.

Let's put some numbers on things. If the centroid goes down (in 1/60th
second) and back up (in 1/60th second), it goes through 1 cycle in 1/30th
second. Thus the "vertical" displacement of the IMAGE coordinates
acquire a 30Hz "buzz". Now remember that your digitizer examines every
other line in the original image, so the ("vertical") displacement
between a line in the "odd" field and a line in the "even" field is one-half
of one (digitizer) pixel. So the amplitude of the "buzz" is one-half of
one pixel.

If all this has made sense to you, what I think you have is a very stable
30 Hz artifact, with a one-half pixel amplitude, superimposed on the real
(motion) data you are trying to acquire. You can check this buy doing a
spectral analysis on the "vertical" component of you IMAGE data (before
it has been treated or fed through any photogrammetric algorithm.)

Now, more to the point, how do you remove the artifact? If you must use
a "broadcast" (interlaced) signal, then you might want to use a camera
which can be run non-interlaced. That is, a switch can be set in the
camera to limit the sampling to the "odd" (or "even") fields. Clearly,
if you do this, the "buzz" will go away because your digitizer will see
only odd fields every 1/60th second. I would recommend the NEC TI-124B
camera for this application. I have several of these cameras in my
inventory and I can tell you that they produce excellent results. (No,
I'm not on the NEC payroll!!) If you want to run more than one camera
in a synchronous, non-interlaced mode, then there are a variety of
standard machine vision cameras you can use to "lock" to the TI-124B
in a master-slave fashion. (I'll avoid further commercialism--If you
need further information, drop me a note.)

Finally, if you've already created your images, then you can remove the
30 Hz "buzz" analytically. The best way to do this is at the source ...
by adding half of one pixel to the "V" component of the even fields.

I hope all this has been helpful--and not too long-winded. Let me know
how things work out.

Chairman-Elect, SPIE Working Group on High-Speed Photography,
Videography and Photonics

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