# 19 - Auto-Calibration  pp. 458-501

By Richard Hartley and Andrew Zisserman

Image View

Auto-calibration is the process of determining internal camera parameters directly from multiple uncalibrated images. Once this is done, it is possible to compute a metric reconstruction from the images. Auto-calibration avoids the onerous task of calibrating cameras using special calibration objects. This gives great flexibility since, for example, a camera can be calibrated directly from an image sequence despite unknown motion and changes in some of the internal parameters.

The root of the method is that a camera moves rigidly, so the absolute conic is fixed under the motion. Conversely, then, if a unique fixed conic in 3-space can be determined in some way from the images, this identifies Ω∞. As we have seen in earlier chapters, once Ω∞ is identified, the metric geometry can be computed. An array of auto-calibration methods are available for this task of identifying Ω∞.

This chapter has four main parts. First we lay out the algebraic structure of the autocalibration problem, and show how the auto-calibration equations are generated from constraints on the internal or external parameters. Second, we describe several direct methods for auto-calibration which involve computing the absolute conic or its image. These include estimating the absolute dual quadric over many views, or the Kruppa equations from view pairs. Third, are stratified methods for auto-calibration which involve two steps – first solving for the plane at infinity, then using this to solve for the absolute conic.

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