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Concept
Pinhole camera model
Summary
The pinhole camera model describes the mathematical relationship between the coordinates of a point in three-dimensional space and its projection onto the image plane of an ideal pinhole camera, where the camera aperture is described as a point and no lenses are used to focus light. The model does not include, for example, geometric distortions or blurring of unfocused objects caused by lenses and finite sized apertures. It also does not take into account that most practical cameras have only discrete image coordinates. This means that the pinhole camera model can only be used as a first order approximation of the mapping from a 3D scene to a 2D . Its validity depends on the quality of the camera and, in general, decreases from the center of the image to the edges as lens distortion effects increase.
Some of the effects that the pinhole camera model does not take into account can be compensated, for example by applying suitable coordinate transformations on the image coordinates; other effects are sufficiently small to be neglected if a high quality camera is used. This means that the pinhole camera model often can be used as a reasonable description of how a camera depicts a 3D scene, for example in computer vision and computer graphics.
The geometry related to the mapping of a pinhole camera is illustrated in the figure. The figure contains the following basic objects:
A 3D orthogonal coordinate system with its origin at O. This is also where the camera aperture is located. The three axes of the coordinate system are referred to as X1, X2, X3. Axis X3 is pointing in the viewing direction of the camera and is referred to as the optical axis, principal axis, or principal ray. The plane which is spanned by axes X1 and X2 is the front side of the camera, or principal plane.
An image plane, where the 3D world is projected through the aperture of the camera. The image plane is parallel to axes X1 and X2 and is located at distance from the origin O in the negative direction of the X3 axis, where f is the focal length of the pinhole camera.
Official source
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