#### Point Correspondence in Image-Based Visual Servoing

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A critical part of a visual servoing system is establishing correspondence between points in the scene observed by the camera, and points in our desired image of the scene.

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A critical part of a visual servoing system is establishing correspondence between points in the scene observed by the camera, and points in our desired image of the scene.

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The linear algebra approach we’ve discussed is very well suited to MATLAB implementation. Let’s look at some toolbox functions that can simulate what cameras do. If you are using a more recent version of MVTB, ie. MVTB 4.x then please change>> cam.project(PW ‘Tcam’, transl(0.1, 0, 0)) to >> cam.project(PW ‘pose’, transl(0.1, 0, 0)).

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The pinhole camera simplifies the geometry but in practice it results in very dark images. Cameras, as well as our eyes, use a lens to form a brighter image but there are consequences.

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Let’s learn how to import a color image into MATLAB and see how the data is organized as a matrix with three dimensions.

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It is common to think about an assembly task being specified in terms of coordinates in the 3D world. An alternative approach is to consider the task in terms of the relative position of objects in one or more views of the task — visual servoing.

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We can describe the relationship between a 3D world point and a 2D image plane point, both expressed in homogeneous coordinates, using a linear transformation – a 3×4 matrix. Then we can extend this to account for an image plane which is a regular grid of discrete pixels.

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How is an image formed? The real world has three dimensions but an image has only two. We can use linear algebra and homogeneous coordinates to understand what’s going on. This more general approach allows us to model the positions of pixels in the sensor array and to derive relationships between points on the image […]

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We consider a robot with three joints that moves its end-effector on a plane.

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To fully describe an object on the plane we need to not only describe its position, but also which direction it is pointing. This combination is referred to as pose. 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 learn how to describe the position and orientation of objects on a 2-dimensional plane. We introduce the notion of reference frames as a basis for describing the position of objects in two dimensions.