Spatial operators are closely related to concepts from signal processing called correlation and convolution. They are similar but different and we discuss the important properties of convolution for Gaussian kernels.
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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.
Using the properties of convolution we can combine a simple derivative kernel with Gaussian smoothing to create a derivative of Gaussian (DoG) kernel which is very useful for edge detection, or a Laplacian of Gaussian (LoG) kernel which is useful for detecting regions.
We will consider a very powerful group of functions, spatial operators, where each output pixel is a function of the corresponding input pixel and its neighbours.
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.
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.
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.
For an image stored as a variable in the MATLAB workspace let’s look at how we access the values of individual pixels in an image using their row and column coordinates. Using the MATLAB colon operator we can extract an intensity profile, extract a submatrix which is a region of the image, flip the image […]
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 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.