Search Results for: second derivative

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.

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.

A number of strategies exist to reduce the effect of these coupling torques between the joints, from introducing a gearbox between the motor and the joint, to advanced feedforward strategies.

The relationship between world coordinates, image coordinates and camera spatial velocity is elegantly summed up by a single matrix equation that involves what we call the image Jacobian.

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 recap the important points from this masterclass.

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.

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 […]

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.