#### 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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We live in a three-dimensional world but it’s taken humans a long time to learn how to realistically depict the illusion of depth on a flat surface.

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What are the consequences of representing a three-dimensional scene using only two-dimensions? The appearance of parallel lines converging and circular objects being elliptical should be surprising but we take this for granted.

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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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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.

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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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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.

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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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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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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 […]