Optical Pendulum

[Francois LE COAT]

Hi,

Do you know something about the experiment of the "Optical Pendulum"?

<https://www.youtube.com/watch?v=cDJZVWEvhrc>

A camera is suspended upon a cable, and an image is shot at the rest
position. Then you push the pendulum, so that the camera oscillates,
and new images are acquired when the pendulum moves.

The goal is to evaluate the eight parameters that determine the
position of the camera, from the rest position to the actual one.
Because the pendulum oscillates, we obtain a pseudo-sinusoidal.

The eight parameters are the perspective transform that happens
from an image, to the others. That means translations <Tx,Ty,Tz>
rotations <Rx,Ry,Rz> and two perspective parameters <Sx,Sy>.

That's what we can see in the above video. Each images, and the
corresponding perspective transform parameters, compared to rest.

Best regards,

--
Dr. François LE COAT
CNRS - Paris - France
<https://hebergement.universite-paris-saclay.fr/lecoat>

[Francois LE COAT]

Hi,

Francois LE COAT writes:
> Do you know something about the experiment of the "Optical Pendulum"?
>
>     <https://www.youtube.com/watch?v=cDJZVWEvhrc>
>
> A camera is suspended upon a cable, and an image is shot at the rest
> position. Then you push the pendulum, so that the camera oscillates,
> and new images are acquired when the pendulum moves.
>
> The goal is to evaluate the eight parameters that determine the
> position of the camera, from the rest position to the actual one.
> Because the pendulum oscillates, we obtain a pseudo-sinusoidal.
>
> The eight parameters are the perspective transform that happens
> from an image, to the others. That means translations <Tx,Ty,Tz>
> rotations <Rx,Ry,Rz> and two perspective parameters <Sx,Sy>.
>
> That's what we can see in the above video. Each images, and the
> corresponding perspective transform parameters, compared to rest.

The goal is to measure a global movement, when it is observed by the
camera. There are devices that determine the position, such as the GPS
(Global Positioning System). We can measure the inclination with a
gyrometer, the acceleration with an accelerometer, the speed with an
odometer. The goal is to measure all this by the image, with a camera.

Why?

For example when we send robots to the planet Mars (Perseverance and
Ingenuity recently), and we want to pilot them with the means at our
disposal... On planet Earth there is a positioning system by GPS, which
works with a network of satellites. But on Mars it does not exist. To
navigate on Mars, we find our way with a camera. To do this, you have
to measure the movement of the camera. This is the goal of our
experiment. Measuring the movement of the camera... The robots that
move on Mars have navigation cameras. These are their eyes. It's as
efficient as a GPS.

[Francois LE COAT]

I made a new video demonstration, with the optical pendulum experiment:

<https://www.youtube.com/watch?v=PXbWNW7duCY>

We can see the image taken at the pendulum's rest. Then each of the
images, when it oscillates. We see the perspective transformation
between each image, to the rest, in image plane, i.e. in two dimensions.
Then using the parameters obtained in 2D from the transformation, a
virtual camera moves in 3D, using Persistence Of Vision software.
It is an illustration of the use that we can have in 3D of the
parameters: in translation <Tx,Ty,Tz>, in rotation <Rx,Ry,Rz> and
in perspective <Sx,Sy>. It is a question of determining from the images,
the movement in space of the camera. The movement in space between two
images is completely described by eight parameters. POV-Ray is very well
suited to represent the trajectory in 3D, because it is a free image
synthesis software. Of course, all these computations are not yet done
at the rate of video. It will probably be necessary to design a hardware
acceleration, to obtain a smoother video...

[Francois LE COAT]

A new video from the Optical Pendulum was realized which is a little
smoother, dissociating acquisitions from the parameters' computation...

<https://www.youtube.com/watch?v=N2SQStXsz6U>

It may help to understand. A 50 images sequence is first acquired,
and then processed sequentially. You may better perceive the
camera-pendulum's oscillation.

[Francois LE COAT]

Hi,

Here is the "projective transform" I'm finally writing about...

<https://www.youtube.com/watch?v=mnei7j-KRu8>

It includes 8 parameters (Rx,Ry,Rz,Tx,Ty,Tz,Sx,Sy) which are
present in POV-Ray. I use it to represent the motion of cameras.

[Francois LE COAT]

Hi,

A WEB page was made to illustrate the "optical pendulum" experiment:

<https://hebergement.universite-paris-saclay.fr/lecoat/demoweb/optical_pendulum.html>

We determinate translation, rotation and perspective transformations.
On this WEB page you can see the pendulum swinging live... This is
not really fast for the moment, but we're trying to accelerate it :-)

[Francois LE COAT]

Hi,

Francois LE COAT writes:

> A WEB page was made to illustrate the "optical pendulum" experiment:
>
> <https://hebergement.universite-paris-saclay.fr/lecoat/demoweb/optical_pendulum.html>
>
>
> We determinate translation, rotation and perspective transformations.
> On this WEB page you can see the pendulum swinging live... This is
> not really fast for the moment, but we're trying to accelerate it :-)

Here is the experimentation of the optical pendulum at its true rhythm
on a Dell Precision T3400 computer, Intel Core2 Quad Q6600 (2.4 GHz,
FSB 1066 MHz, 8 MB L2 cache, four cores)...

<https://www.youtube.com/watch?v=3HnVTz1BPsU>

It is a machine which hosts GNU/Linux Mageia 8 in its 32-bits version,
and that is used to the maximum performances, thanks to multi-processing
and charge load balancing on the four cores. The calculation rate of the
eight movement parameters is at the time order of a second. Hardware
acceleration of algorithmic processing is envisaged.