#### Spatial Operators

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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.

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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.

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We run into problems when we take all of the pixels in a box around an input pixel and that pixel is close to one of the edges of the image. Let’s look at some strategies to deal with edge pixels.

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When a camera moves in the world, points in the image move in a very specific way. The image plane or pixel velocity is a function of the camera’s motion and the position of the points in the world. This is known as optical flow. Let’s explore the link between camera and image motion.

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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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An important problem in robotic vision is moving a camera so that the view it sees matches the view we want it to have. To achieve this we exploit knowledge about how an image changes as a camera moves. Then we invert that and compute how the camera should move so the image changes in […]

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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.

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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.

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For a simple 2-link planar robot we introduce and derive its Jacobian matrix, and also introduce the concept of spatial velocity.

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We summarise the important points from this lecture.

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Time varying coordinate frames are required to describe how the end-effector of a robot should move to grab an object, or to describe objects that are moving in the world. We make an important distinction between a path and a trajectory.