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Recovering Local Shape of a Mirror Surface from Reflection of a Regular Grid

  • Silvio Savarese
  • Min Chen
  • Pietro Perona
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3023)

Abstract

We present a new technique to recover the shape of an unknown smooth specular surface from a single image. A calibrated camera faces a specular surface reflecting a calibrated scene (for instance a checkerboard or grid pattern). The mapping from the scene pattern to its reflected distorted image in the camera changes the local geometrical structure of the scene pattern. We show that if measurements of both local orientation and scale of the distorted scene in the image plane are available, this mapping can be inverted. Specifically, we prove that surface position and shape up to third order can be derived as a function of such local measurements when two orientations are available at the same point (e.g. a corner). Our results generalize previous work [1, 2] where the mirror surface geometry was recovered only up to first order from at least three intersecting lines. We validate our theoretical results with both numerical simulations and experiments with real surfaces.

Keywords

Image Plane Mirror Surface Checkerboard Pattern Scene Point Specular Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Silvio Savarese
    • 1
  • Min Chen
    • 2
  • Pietro Perona
    • 1
  1. 1.California Institute of TechnologyPasadenaUSA
  2. 2.Oracle ParkwayRedwood CityUSA

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