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TECHNICAL PAPERS

Camera Calibration Based on Snell’s Law

[+] Author and Article Information
Psang Dain Lin1

 National Cheng Kung University, Department of Mechanical Engineering, Tainan, Taiwan 70101

Chi-Kuen Sung

 National Cheng Kung University, Department of Mechanical Engineering, Tainan, Taiwan 70101

1

Author to whom all correspondence should be addressed.

J. Dyn. Sys., Meas., Control 128(3), 548-557 (Aug 24, 2005) (10 pages) doi:10.1115/1.2192824 History: Received November 03, 2004; Revised August 24, 2005

In this paper we present a camera calibration method using Snell’s Law. Traditional camera calibration is based on the pinhole model, which is an approximation algorithm using untrue geometrical assumptions and giving a single lumped result for the various optical elements in the camera system. Using full modeling of lens geometry, the proposed method establishes the geometric relationship between images and objects via Snell’s Law. A matrix equation that relates the intrinsic/extrinsic parameters of image the plane and six pose parameters of each element is determined from sensitivity analysis. These parameters can be identified using the least square method by observing points with known coordinates. An illustrative example using a two-camera stereo coordinate measurement system demonstrates that system performance via the proposed method is better than the pinhole model.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Skew ray-tracing along a flat boundary surface

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Figure 2

Skew ray tracing along a spherical boundary surface

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Figure 3

General notation for ray-traction through a camera with k elements and n boundary surfaces

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Figure 4

The jth lens is a convex-convex element

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Figure 5

The jth lens is a convex-concave element

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Figure 6

The jth lens is a convex-flat element

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Figure 7

The jth lens is a concave-convex element

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Figure 8

The jth lens is a concave-concave element

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Figure 9

The jth lens is a concave-flat element

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Figure 10

The jth lens is a flat-convex element

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Figure 11

The jth lens is a flat-concave element

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Figure 12

The jth lens is a flat-flat element

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Figure 13

Effects of pose changes on ray tracing

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Figure 14

Binocular stereo coordinate measurement system

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