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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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 learn how to describe the orientation of an object by a 2×2 rotation matrix which has some special properties. 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 learn how to describe the orientation of an object by a 3×3 rotation matrix which has some special properties.
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.
We summarise the important points from this lecture.