Let’s recall the key techniques we’ve covered including monadic and dyadic image processing operations and efficient ways to write these in MATLAB using vectorization.
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Imagine a scene with bright objects against a dark background. Thresholding is a very common monadic operation which transforms the image into one where the pixels have two possible values: true or false which correspond to foreground or background. It can be performed with a single vectorized MATLAB operation.
Images contain many pixels and the normal way to process them is with nested for loops that index each pixel in turn. This is slow and somewhat cumbersome to write. MATLAB has a facility called vectorization that allows us to perform complex matrix operations without any loops.
Diadic operations involve two images of the same size and result in another image. For example adding, subtracting or masking images. As a realistic application we look at green screening to superimpose an object into an arbitrary image.
The orientation of a body in 3D can also be described by two vectors, often called the approach and orientation vectors.
If it’s been a while since you last dealt with eigenvalues and eigenvectors here’s a quick recap of the basics.
For a simple 2-link planar robot we introduce and derive its Jacobian matrix, and also introduce the concept of spatial velocity.
If your knowledge of dynamics is a bit rusty then let’s quickly revise the basics of second-order systems and the Laplace operator. Not rusty? Then go straight to the next section.
We consider multiple objects each with its own coordinate frame. Now we can describe the relationships between the frames and find a vector describing a point with respect to any of these frames. We extend our algebraic notation to ease the manipulation of relative poses. Try your hand at some online MATLAB problems. You’ll need […]
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.