A WEB page was made to illustrate the "optical pendulum" experiment:
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 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 camer
>>> 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 GP
>>> (Global Positioning System). We can evaluate rotations with a gyromet
>>> 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, whi
>>> works with a network of satellites. But on Mars it does not exists. T
>>> 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 dimensio
>>> 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 imag
>>> the movement in space of the camera. The movement in space between tw
>>> images is completely described by eight parameters. POV-Ray is very w
>>> suited to represent the trajectory in 3D, because it is a free image
>>> synthesis software. Of course, all these computations are not yet don
>>> at the rate of video. It will probably be necessary to design a hardw
>>> 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
>> Thanks to Bald Eagle with the help on POV-Ray perspective transform!
> Here is the perspective transform that we are speaking about...
> There are three rotations, three translations, and two perspective
> parameters that are observed when the image is projected (Skew).
> Here you can see the transformation rendered with POV-Ray...
> The motion in space of the camera is determined from the images
> of the optical pendulum, thanks to the perspective cinematic model.
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