Another non-linear operation on the pixels in the box around the input pixel is to test whether they match a reference shape. This is a very powerful and useful approach to cleaning up noisy binary images known as mathematical morphology and objects in the image are treated according to their compatibility with a structuring element. […]
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Mathematical morphology comprises operations such as erosion, dilation, opening and closing. Let’s look at how we can use different shaped structuring elements to solve complex problems.
In mathematical morphology the values of the structuring element were either zero or one. The hit and miss transform extends this to also include a ‘don’t care’ value. We can use this transform to solve complex problems like finding the skeleton of an object or the intersection point of lines.
Let’s recap the important points from the topics we have covered in advanced image processing.
We will extend our coverage of image processing. We will some previously discussed techniques in more depth, and introduce some additional ones.
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 […]
A problem arises when using three-angle sequences and particular values of the middle angle leads to a condition called a singularity. This mathematical phenomena is related to a problem that occurs in the physical world with mechanical gimbal systems. Note that in Robotics, Vision & Control (second edition) and RTB10.x the default definition of roll-pitch-yaw […]
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.
The orientation of a body in 3D can also be described by a unit-Quaternion, an unusual but very useful mathematical object. In the MATLAB example starting at 3:48 I use the Quaternion class. For Toolbox version 10 (2017) please use UnitQuaternion instead.
We summarise the important points from this lecture.