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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Let’s look at how light rays reflected from an object can form an image. We use the simple geometry of a pinhole camera to describe how points in a three-dimensional scene are projected on to a two-dimensional image plane.
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.
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)).
Let’s recap the important points from the topics we have covered in our discussion of optical flow and visual servoing.
We recap the basics of perspective projection.
We can describe the relationship between a 3D world point and a 2D image plane point, both expressed in homogeneous coordinates, using a linear transformation – a 3×4 matrix. Then we can extend this to account for an image plane which is a regular grid of discrete pixels.
The pinhole camera simplifies the geometry but in practice it results in very dark images. Cameras, as well as our eyes, use a lens to form a brighter image but there are consequences.
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.
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 […]