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.
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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 […]
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.
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.
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 […]
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)).
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 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.
We use MATLAB and some Toolbox functions to compute an homography and also apply it.
We can derive a linear relationship between the coordinates of points on an arbitrary plane in the scene and the coordinate of that point in the image. This is the planar homography and it has a number of everyday uses which might surprise you.