#### Eigenvalues and Eigenvectors – Recap

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If it’s been a while since you last dealt with eigenvalues and eigenvectors here’s a quick recap of the basics.

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If it’s been a while since you last dealt with eigenvalues and eigenvectors here’s a quick recap of the basics.

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As we did for the simple planar robots we can invert the Jacobian and perform resolved-rate motion control.

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By inverting the Jacobian matrix we can find the joint velocities required to achieve a particular end-effector velocity, so long as the Jacobian is not singular.

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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.

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We can also describe a blob by its contour or perimeter. Let’s look at how we determine the length of a blob’s perimeter using crack code and chain code. We can use the perimeter length to determine another scale and invariant shape parameter called circularity which indicates how compact, or circle-like, the blob is.

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We learn how to use information from three magnetometers to determine the direction of the Earth’s north magnetic pole.

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The image Jacobian depends not only on the image plane coordinates but also the distance from the camera to the points of interest. If this distance is not known, what can we do? Let’s look at how we can determine this distance, and how the optical flow equation can be rearranged to convert from observed […]

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Many technologies have been developed to determine the 3D-structure of the world. RGBD sensors such as the Kinect use structured light, projecting a pattern of light onto the scene and observing how it is distorted. Time of flight sensors measure the time it takes for a pulse of light to travel from the camera to […]

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Given two images of a scene taken from slightly different viewpoints, a stereo image pair, it’s possible to determine the disparity for every pixel using template matching. The disparity image is one where the value of each pixel is inversely related to the distance between that point in the scene and the camera.

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In order to determine the size and distance of objects in the scene our brain uses a number of highly evolved tricks. Let’s look at some of these.