Hi,

Francois LE COAT writes:
> Do you know something about the experiment of the "Optical Pendulum"?
> 
> 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 describe the position of the camera,

> from the rest position to the actual one. Because the pendulum
> oscillates, we obtain pseudo-sinusoidal curves.
> 
> The eight parameters are the perspective transform that happen
> 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 bellow video. Each images, and the corresponding
> perspective transform parameters, compared to the 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 evaluate rotations with a gyrometer
,
> the accelerations 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 exists. 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.
> 
> Here is the video demonstration, with the optical pendulum experiment:
> 

> 
> 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 wel
l
> 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 hardwar
e
> acceleration, to obtain a smoother video...

I realized a new video which is a little smoother, dissociating
acquisitions from the parameters' computation. It may help to
understand:

	<https://www.youtube.com/watch?v=Cjkaw-hw7nw>

Thanks to Bald Eagle with the help on POV-Ray perspective transform!

Best regards,

-- 

<http://eureka.atari.org/>

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