Search Results for: world plane

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.

Let’s recap the important points from the topics we have covered about homogeneous coordinates, image formation, camera modeling and planar homographies.

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 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 […]

It is common to think about an assembly task being specified in terms of coordinates in the 3D world. An alternative approach is to consider the task in terms of the relative position of objects in one or more views of the task — visual servoing.

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)).

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.

How is an image formed? The real world has three dimensions but an image has only two. We can use linear algebra and homogeneous coordinates to understand what’s going on. This more general approach allows us to model the positions of pixels in the sensor array and to derive relationships between points on the image […]

We learn how to describe the position and orientation of objects on a 2-dimensional plane. We introduce the notion of reference frames as a basis for describing the position of objects in two dimensions.

We use MATLAB and some Toolbox functions to compute an homography and also apply it.