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Local shape from mirror reflections

Savarese, Silvio and Chen, Min and Perona, Pietro (2005) Local shape from mirror reflections. International Journal of Computer Vision, 64 (1). pp. 31-67. ISSN 0920-5691. https://resolver.caltech.edu/CaltechAUTHORS:20140730-101718448

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Abstract

We study the problem of recovering the 3D shape of an unknown smooth specular surface from a single image. The surface reflects a calibrated pattern onto the image plane of a calibrated camera. The pattern is such that points are available in the image where position, orientations, and local scale may be measured (e.g. checkerboard). We first explore the differential relationship between the local geometry of the surface around the point of reflection and the local geometry in the image. We then study the inverse problem and give necessary and sufficient conditions for recovering surface position and shape. We prove that surface position and shape up to third order can be derived as a function of local position, orientation and local scale measurements in the image when two orientations are available at the same point (e.g. a corner). Information equivalent to scale and orientation measurements can be also extracted from the reflection of a planar scene patch of arbitrary geometry, provided that the reflections of (at least) 3 distinctive points may be identified. We validate our theoretical results with both numerical simulations and experiments with real surfaces.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s11263-005-1086-xDOIArticle
https://rdcu.be/btl6tPublisherFree ReadCube access
ORCID:
AuthorORCID
Perona, Pietro0000-0002-7583-5809
Additional Information:© 2005 Springer Science + Business Media. Received May 3, 2004; Revised February 2, 2005; Accepted February 2, 2005; First online version published in April, 2005. This work is supported by the NSF Engineering Research Center for Neuromorphic Systems Engineering (CNSE) at Caltech (EEC-9402726). We wish to thank Gabriel Taubin, Jean Ponce, Marzia Polito, Jerry Marsden and Jim Arvo for helpful feedback as well as Matthew Cook, Fei-Fei Li and Massimo Franceschetti for many fruitful discussions.
Funders:
Funding AgencyGrant Number
NSFEEC-9402726
Center for Neuromorphic Systems Engineering, CaltechUNSPECIFIED
Subject Keywords:Artificial Intelligence (incl. Robotics), Computer Imaging, Graphics and Computer Vision, Image Processing, Automation and Robotics Artificial Intelligence (incl. Robotics) Computer Imaging, Graphics and Computer Vision Image Processing Automation and Robotics
Issue or Number:1
Record Number:CaltechAUTHORS:20140730-101718448
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140730-101718448
Official Citation:Savarese, S., Chen, M. & Perona, P. Int J Comput Vision (2005) 64: 31. https://doi.org/10.1007/s11263-005-1086-x
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:47607
Collection:CaltechAUTHORS
Deposited By: Caroline Murphy
Deposited On:19 Aug 2014 17:37
Last Modified:03 Oct 2019 06:55

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