The DOI matches its Crossref record.
A Viscosity Solutions Approach to Shape-From-Shading
Abstract
The problem of recovering a Lambertian surface from a single two-dimensional image may be written as a first-order nonlinear equation which presents the disadvantage of having several continuous and even smooth solutions. A new approach based on Hamilton–Jacobi–Bellman equations and viscosity solutions theories enables one to study non-uniqueness phenomenon and thus to characterize the surface among the various solutions. A consistent and monotone scheme approximating the surface is constructed thanks to the dynamic programming principle, and numerical results are presented.
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Cited by
Zhang, R., Tsai, P.-S., Cryer, J. E., & Shah, M. (1999) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.784284 · Cited by 1,731
Path Planning for Autonomous Underwater Vehicles
Petres, C., Pailhas, Y., Patron, P., Petillot, Y., Evans, J., & Lane, D. (2007) · IEEE Transactions on Robotics · doi:10.1109/tro.2007.895057 · Cited by 433
Metadata
- Authors
- Rouy, E., & Tourin, A.
- Venue
- SIAM Journal on Numerical Analysis
- Published
- 1992-06
- Volume
- 29
- Issue
- 3
- Pages
- 867-884
- ISSN
- 0036-1429 (ISSN-L)
- 1095-7170
- OpenAlex
- W2012872284
- Cited by
- 657
- References
- 0
- FWCI
- 7.96
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: A Viscosity Solutions Approach to Shape-From-Shading. https://app.cochat.ai/papers/10.1137/0729053
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- Rouy, E., & Tourin, A. (1992). A Viscosity Solutions Approach to Shape-From-Shading. SIAM Journal on Numerical Analysis. https://doi.org/10.1137/0729053
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
