The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Photometric Invariants Related to Solid Shape
Abstract
An attempt is made to identify the structural invariants of the field of isophotes on lambertian surfaces of arbitrary shape under arbitrary illumination. It is a priori clear that such invariants play an important part in the perception of solid shape by means of chiaroscuro. We have found several such invariants. The topological structure of the field of isophotes is determined by the collection of nested, closed parabolic curves on the surface. An important class of stationary points of the field clings to these parabolic lines. The isophotes cut the parabolic lines at a constant angle, irrespective of the location of the light sources. For certain canonical surface undulations the field of isophotes is explicitly given.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
The Perception of the Visual World
Gibson, J. J. (1951) · The American Journal of Psychology · doi:10.2307/1419017 · Cited by 1,145
Cited by
Representing and Recognizing the Visual Appearance of Materials Using Three-Dimensional Textons
Leung, T., & Malik, J. (2001) · International Journal of Computer Vision · doi:10.1023/a:1011126920638 · Cited by 1,498
Height and gradient from shading
Horn, B. K. P. (1990) · International Journal of Computer Vision · doi:10.1007/bf00056771 · Cited by 469
Visual perception of materials and their properties
Fleming, R. W. (2014) · Vision Research · doi:10.1016/j.visres.2013.11.004 · Cited by 331
Hill, H., & Johnston, A. (2007) · Perception · doi:10.1068/p5523 · Cited by 70
Metadata
- Authors
- Koenderink, J. J., & van Doorn, A. J.
- Venue
- Optica Acta: International Journal of Optics
- Publisher
- Informa UK Limited
- Published
- 1980-07
- Volume
- 27
- Issue
- 7
- Pages
- 981-996
- ISSN
- 0030-3909 (ISSN-L)
- OpenAlex
- W1974638621
- Cited by
- 262
- References
- 1
- FWCI
- 1.10
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Photometric Invariants Related to Solid Shape. https://app.cochat.ai/papers/10.1080/713820338
- The paper
- Koenderink, J. J., & van Doorn, A. J. (1980). Photometric Invariants Related to Solid Shape. Optica Acta: International Journal of Optics. https://doi.org/10.1080/713820338
Data sources
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.
