Stanford University

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• Stanford University
• EE 362 / PSYCH 221
• Applied Vision and Imaging Systems
• Winter 2007
• "Measurements and Correction of Geometric
  Distortion"
• Athanasios Bismpigiannis
• thanosb_at_stanford.edu

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• Image Distortion
• Models of Image Distortion
• Measurements
• Distortion Simulation

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Image Distortion

• A perfect lens in a camera would render straight
  lines as straight, no matter where they occur.
• Unfortunately, low cost cameras are equipped with
  lenses that are not that good.
• This results to changes in the geometry of the
  image.

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Image Distortion - Lenses
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Image Distortion

• Two types of distortion
• Internal distortion
• External distortion

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Internal Distortion
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External Distortion
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Radial Distortion

• The most severe and the most common type of
  distortion
• straight lines in the subject curve in the image
  taken by the camera
• Straight lines that run through the image center
  remain straight
• The most typical cases are the barrel and the
  pin-cushion distortion

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Radial Distortion

• Original grid Barrel
  distortion Pin-cushion distortion

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Models of image distortion

• The removal of radial distortion is commonly
• performed by
• Applying a parametric radial distortion model
• Estimating the distortion coefficients
• Correcting the distortion

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Models of image distortion

• Generally, the radial distortion is governed by
  the following polynomial equation
• Which can be written also as

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Models of image distortion

• We can model the radial distortion using one
• of the following functions

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Measurements

• 
  

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Measurements

• Original Image Distorted Image

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Measurements

• Original Image Distorted Image

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Measurements

Original Image Distorted Image
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Measurements

• Original Image Distorted Image

A
A
B
B
E (AB)-(AB) Error Mean_Squae_Value(E)
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Distortion Simulation
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• Thank you!