#### Perspective Projection – Recap

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We recap the basics of perspective projection.

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We recap the basics of perspective projection.

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Let’s look at how light rays reflected from an object can form an image. We use the simple geometry of a pinhole camera to describe how points in a three-dimensional scene are projected on to a two-dimensional image plane.

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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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Let’s recap the important points from the topics we have covered about homogeneous coordinates, image formation, camera modeling and planar homographies.

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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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An image is a two dimensional projection of a three dimensional world. The big problem with this projection is that big distant objects appear the same size as small close objects. For people, and robots, it’s important to distinguish these different situations. Let’s look at how humans and robots can determine the scale of objects […]

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Let’s recap the important points from the topics we have covered about image formation and perspective projection.

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Let’s recap the important points from the topics we have covered about human depth perception, display of 3D images and estimating 3D scene structure using stereo and other types of sensors.

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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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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.