The image Jacobian depends not only on the image plane coordinates but also the distance from the camera to the points of interest. If this distance is not known, what can we do? Let’s look at how we can determine this distance, and how the optical flow equation can be rearranged to convert from observed […]
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The relationship between world coordinates, image coordinates and camera spatial velocity has some interesting ramifications. Some very different camera motions cause identical motion of points in the image, and some camera motions leads to no change in the image at all in some parts of the image. Let’s explore at these phenomena and how we […]
When a camera moves in the world, points in the image move in a very specific way. The image plane or pixel velocity is a function of the camera‘s motion and the position of the points in the world. This is known as optical flow. Let’s explore the link between camera and image motion.
We previously learnt how to derive a Jacobian which relates the velocity of a point, defined relative to one coordinate frame, to the velocity relative to a different coordinate frame. Now we extend that to the 3D case.
The relationship between world coordinates, image coordinates and camera spatial velocity is elegantly summed up by a single matrix equation that involves what we call the image Jacobian.
Let’s recap the important points from the topics we have covered in our discussion of optical flow and visual servoing.
We use MATLAB and some Toolbox functions to create a robot controller that moves a camera so the image matches what we want it to look like. We call this an image-based visual servoing system.
An image contains a huge amount of pixel data, and a video stream is a massive flow of pixel data. Typically a robot has only a few inputs, the position or velocity of its joints. How do we go from all that camera data to the small amount of data the robot really needs?
We summarise the important points from this lecture.
The linear algebra approach we’ve discussed is very well suited to MATLAB implementation. Let’s look at some toolbox functions that can simulate what cameras do. If you are using a more recent version of MVTB, ie. MVTB 4.x then please change>> cam.project(PW ‘Tcam’, transl(0.1, 0, 0)) to >> cam.project(PW ‘pose’, transl(0.1, 0, 0)).