The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
Application of affine-invariant Fourier descriptors to recognition of 3-D objects
Abstract
The method of Fourier descriptors is extended to produce a set of normalized coefficients which are invariant under any affine transformation (translation, rotation, scaling, and shearing). The method is based on a parameterized boundary description which is transformed to the Fourier domain and normalized there to eliminate dependencies on the affine transformation and on the starting point. Invariance to affine transforms allows considerable robustness when applied to images of objects which rotate in all three dimensions, as is demonstrated by processing silhouettes of aircraft maneuvering in three-space.>
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
(1973) · CERN Document Server (European Organization for Nuclear Research) · Cited by 12,895
Pattern Classification and Scene Analysis
Thompson, M., Duda, R. O., & Hart, P. E. (1974) · Leonardo · doi:10.2307/1573081 · Cited by 4,495
Fourier Descriptors for Plane Closed Curves
Zahn, C. T., & Roskies, R. Z. (1972) · IEEE Transactions on Computers · doi:10.1109/tc.1972.5008949 · Cited by 1,860
Elliptic Fourier features of a closed contour
Kuhl, F. P., & Giardina, C. R. (1982) · Computer Graphics and Image Processing · doi:10.1016/0146-664x(82)90034-x · Cited by 1,839
The Fourier integral and its applications
Papoulis, A. (1962) · CERN Document Server (European Organization for Nuclear Research) · Cited by 1,650
Shape Discrimination Using Fourier Descriptors
Persoon, E., & Fu, K.-S. (1977) · IEEE Transactions on Systems, Man, and Cybernetics · doi:10.1109/tsmc.1977.4309681 · Cited by 1,073
Fourier Preprocessing for Hand Print Character Recognition
Granlund, G. H. (1972) · IEEE Transactions on Computers · doi:10.1109/tc.1972.5008926 · Cited by 580
Three-dimensional model matching from an unconstrained viewpoint
Thompson, D., & Mundy, J. (2005) · Proceedings. 1987 IEEE International Conference on Robotics and Automation · doi:10.1109/robot.1987.1088004 · Cited by 232
Identification of Three-Dimensional Objects Using Fourier Descriptors of the Boundary Curve
Richard, C. W., & Hemami, H. (1974) · IEEE Transactions on Systems Man and Cybernetics · doi:10.1109/tsmc.1974.5408458 · Cited by 148
Cited by
Funkhouser, T., Min, P., Kazhdan, M., Chen, J., Halderman, A., Dobkin, D., & Jacobs, D. (2003) · ACM Transactions on Graphics · doi:10.1145/588272.588279 · Cited by 935
Kauppinen, H., Seppanen, T., & Pietikainen, M. (1995) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.368168 · Cited by 386
A novel approach for quantitative assessment of mucosal damage in inflammatory bowel disease
Matalka, I. I., Al-Omari, F. A., Salama, R. M., & Mohtaseb, A. H. (2013) · Diagnostic Pathology · doi:10.1186/1746-1596-8-156 · Cited by 25
“Assume that K boundary point samples are collected to represent the curve, then the Discrete Fourier Transform (DFT) can be used to calculate the K complex values representing the Fourier Transform of the closed curve in the frequency domain, such that, [18] z uð Þ ¼ 1 K XK−1 k¼0 r kð Þe−2πuk=K ; ∀u ¼ 0; 1;…;K−1; ð1Þ…”
Influential
Metadata
- Authors
- Arbter, K., Snyder, W. E., Burkhardt, H., & Hirzinger, G.
- Venue
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- Published
- 1990-07
- Volume
- 12
- Issue
- 7
- Pages
- 640-647
- ISSN
- 0162-8828 (ISSN-L)
- OpenAlex
- W2105664606
- Cited by
- 396
- References
- 9
- FWCI
- 9.58
- 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: Application of affine-invariant Fourier descriptors to recognition of 3-D objects. https://app.cochat.ai/papers/10.1109/34.56206
- The paper
- Arbter, K., Snyder, W. E., Burkhardt, H., & Hirzinger, G. (1990). Application of affine-invariant Fourier descriptors to recognition of 3-D objects. IEEE Transactions on Pattern Analysis and Machine Intelligence. https://doi.org/10.1109/34.56206
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.
