Search Results for: linear algebra

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 recap 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)).

For a simple 2-link planar robot we introduce and derive its Jacobian matrix, and also introduce the concept of spatial velocity.

We learn how to describe the 2D pose of an object by a 3×3 homogeneous transformation matrix which has a special structure. Try your hand at some online MATLAB problems. You’ll need to watch all the 2D “Spatial Maths” lessons to complete the problem set.

We repeat the process of the last section but this time consider it as an algebraic problem.

Let’s recap the important points about spatial operators. Linear operators can be used to smooth images and determine gradients. Template matching can be used to find a face in a crowd. Non-linear operators such as rank filters can be used for noise removal, and mathematical morphology treats shapes according to their compatibility with a structuring […]

So far we have taken a linear combination of pixels in the box around the input pixel, but non-linear operations like sorting and ranking the pixel values also prove to be very useful. We look at the median filter which is much better at removing salt and pepper noise from image than simple smoothing.

All mechanical systems exhibit friction and we learn about two broad classes of friction: linear and non-linear.