The Generic Bilinear Calibration-Estimation Problem

  • Authors:

  • Jan J. Koenderink;Andrea J. Van Doorn

  • Affiliations:

  • Helmholtz Instituut, Buys Ballot Laboratory, Universiteit Utrecht, PO Box 80 000, 3508 TA Utrecht, The Netherlands;Helmholtz Instituut, Buys Ballot Laboratory, Universiteit Utrecht, PO Box 80 000, 3508 TA Utrecht, The Netherlands

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1997

Quantified Score

Hi-index 0.01

Visualization

Abstract

We identify a very general, recurring pattern in a number of wellknown problems in biological and machine vision. Many problems are ofa peculiar double-sided nature: One attempts to estimate certainproperties of the environment using a certain type of equipment andsimultaneously one attempts to calibrate the same equipment on thestructure of the environment. At first sight this appears the kind ofthe chicken and the egg problem that might well prove to beinsoluble. However, due to basic constraints that universally apply(e.g., the world is only three-dimensional), a solution—up to acertain class of ambiguity transformations—often exists. The morecomplicated the problem is, the less important the remainingambiguity will be, at least in a relative sense. Many well knownproblems are special in that they can be cast in bilinear form,sometimes after transformation or the introduction of dummyvariables. Instances include photometric stereo, photometricestimations (e.g., of lightness), local (differential) imageoperators, a variety of photogrammetric problems, etc. It turns outthat many of these problems—and together these make up a largefraction of the generic problems in machine vision today—can becast in a simple universal framework. This framework enables one tohandle arbitrarily large (that is, not minimal, consistentconfigurations), noisy (thus inconsistent) date setsautomatically. The level at which prior information (either of adeterministic or a statistical nature) is used (assumptions such asconstant albedo, rigidity, uniform distributions, etc.) is clearlyseparated as an additional, typically nonlinear, stage.