#### Spatial Operators

lesson

We introduce spatial operators by a simple example of taking the average value of all pixels in a box surrounding each input pixel. The result is a blurring or smoothing of the input image.

lesson

We introduce spatial operators by a simple example of taking the average value of all pixels in a box surrounding each input pixel. The result is a blurring or smoothing of the input image.

lesson

We run into problems when we take all of the pixels in a box around an input pixel and that pixel is close to one of the edges of the image. Let’s look at some strategies to deal with edge pixels.

lesson

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.

lesson

In order to determine the size and distance of objects in the scene our brain uses a number of highly evolved tricks. Let’s look at some of these.

lesson

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)).

lesson

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.

lesson

If we look at a binary image we can easily see distinct regions, that is, sets of pixels the same color as their neighbours. We call these blobs and they’re an important way of achieving an object rather than pixel view of the scene. We can describe these blobs by their area, centroid position, bounding […]

lesson

Taking an average of pixels in a box leads to artefacts such as ringing which we can remedy by taking a weighted average of all the pixels in the box surrounding the input pixel. The set of weights is referred to as a kernel. A common kernel used for image smoothing is the Gaussian kernel.

lesson

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.

lesson

An image is a two dimensional projection of a three dimensional world. The big problem with this projection is that big distant objects appear the same size as small close objects. For people, and robots, it’s important to distinguish these different situations. Let’s look at how humans and robots can determine the scale of objects […]