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Re: Optical Pendulum

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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 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.
>>
>> 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...
> 
> 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.

Best regards,

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

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Optical Pendulum Francois LE COAT <lecoat@atari.org> - 2021-10-24 19:15 +0200
  Re: Optical Pendulum Francois LE COAT <lecoat@atari.org> - 2021-11-15 19:30 +0100
    Re: Optical Pendulum Francois LE COAT <lecoat@atari.org> - 2022-04-12 16:06 +0200
      Re: Optical Pendulum Francois LE COAT <lecoat@atari.org> - 2022-05-03 13:45 +0200
        Re: Optical Pendulum Francois LE COAT <lecoat@atari.org> - 2022-05-06 12:45 +0200
          Re: Optical Pendulum Francois LE COAT <lecoat@atari.org> - 2023-03-21 15:30 +0100
            Re: Optical Pendulum Francois LE COAT <lecoat@atari.org> - 2023-11-21 11:00 +0100

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