4. (a) For a pinhole-style camera with focal length f, provide the coordinates on the detector (x, y) as a function of the angular coordinates of observation (√x, Sy). The angular coordinates are defined with respect to the optical axis going through the center of the detector, where (x, y) = (0,0). (b) The coordinates on the detector in (a) are the undistorted coordinates (xu, yu). Express the distorted coordinates (xa, ya) in terms of the undistorted coordinates for a camera that suffers from radial distortion, quantified by distortion parameter k. (c) For a camera that suffers from pincushion distortion, i.e. the opposite of barrel distortion, is k smaller or larger than zero? Illustrate your explanation with a sketch.
4. (a) For a pinhole-style camera with focal length f, provide the coordinates on the detector (x, y) as a function of the angular coordinates of observation (√x, Sy). The angular coordinates are defined with respect to the optical axis going through the center of the detector, where (x, y) = (0,0). (b) The coordinates on the detector in (a) are the undistorted coordinates (xu, yu). Express the distorted coordinates (xa, ya) in terms of the undistorted coordinates for a camera that suffers from radial distortion, quantified by distortion parameter k. (c) For a camera that suffers from pincushion distortion, i.e. the opposite of barrel distortion, is k smaller or larger than zero? Illustrate your explanation with a sketch.
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Question
![4. (a)
For a pinhole-style camera with focal length f, provide the coordinates on
the detector (x, y) as a function of the angular coordinates of observation (√x, Sy).
The angular coordinates are defined with respect to the optical axis going through
the center of the detector, where (x, y) = (0,0).
(b)
The coordinates on the detector in (a) are the undistorted coordinates
(xu, yu). Express the distorted coordinates (xa, ya) in terms of the undistorted
coordinates for a camera that suffers from radial distortion, quantified by distortion
parameter k.
(c)
For a camera that suffers from pincushion distortion, i.e. the opposite of
barrel distortion, is k smaller or larger than zero? Illustrate your explanation with
a sketch.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3c33b0f-dd70-4092-8e70-53e8b5daa5fa%2F1d8c912a-2197-4280-913a-9265a0ab88c4%2Fyr9flcr_processed.png&w=3840&q=75)
Transcribed Image Text:4. (a)
For a pinhole-style camera with focal length f, provide the coordinates on
the detector (x, y) as a function of the angular coordinates of observation (√x, Sy).
The angular coordinates are defined with respect to the optical axis going through
the center of the detector, where (x, y) = (0,0).
(b)
The coordinates on the detector in (a) are the undistorted coordinates
(xu, yu). Express the distorted coordinates (xa, ya) in terms of the undistorted
coordinates for a camera that suffers from radial distortion, quantified by distortion
parameter k.
(c)
For a camera that suffers from pincushion distortion, i.e. the opposite of
barrel distortion, is k smaller or larger than zero? Illustrate your explanation with
a sketch.
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