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.
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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 […]
We learn the mathematical relationship between angular velocity of a body and the time derivative of the rotation matrix describing the orientation of that body.
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.
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.
Let’s recap the important points from the topics we have covered in advanced image processing.
For a camera moving through the environment we frequently wish to track particular world points from one frame to the next. We’ll do a quick introduction to the very large field of feature detection and matching using Harris corner features.
When we look at an image we discern objects, and these tend to be groups of similar pixels surrounded by a distinctive edge. We look at intensity profiles in images and use spatial operators with kernels such as the Sobel kernel to find the intensity gradients in an image, and from these find edges in […]
We revisit the important points from this masterclass.
We will learn about the relationship, in 3D, between the velocity of the joints and the velocity of the end-effector — the velocity kinematics. This relationship is described by a Jacobian matrix which also provides information about how easily the end-effector can move in different Cartesian directions. To do this in 3D we need to […]