Rotation Symmetry DetectionMembers: Seungkyu Lee, Yanxi Liu, Robert T. Collins |
Project Descriptions
"Rotation Symmetry Group Detection Via Frequency Analysis of Frieze-Expansions"We present a novel and effective algorithm for rotation symmetry group detection from real-world images. We propose a frieze-expansion method that transforms rotation symmetry group detection into a simple translation symmetry detection problem. We define and construct a dense symmetry strength map from a given image, and search for potential rotational symmetry centers automatically. Frequency analysis, using Discrete Fourier Transform (DFT), is applied to the frieze-expansion patterns to uncover the types and the cardinality of multiple rotation symmetry groups in an image, concentric or otherwise. Furthermore, our detection algorithm can discriminate discrete versus continuous and cyclic versus dihedral symmetry groups, and identify the corresponding supporting regions in the image. Experimental results on over 80 synthetic and natural images demonstrate superior performance of our rotation detection algorithm in accuracy and in speed over the state of the art rotation detection algorithms.
(b) Frieze-expansion; each diameter of the circle.
corresponds to a column of the frieze-expansion.
(c) 1D DFT results; horizontal axis is the index of DFT basis and vertical axis is the same as the vertical axis of the frieze pattern. (a)~(c) are repeated for all image pixels to build RSS map.
(d) Rotation symmetry strength (RSS) map overlaid on the original image. Once a center is detected, the corresponding DFT segmentation is performed on (c).
(e)(f)(g) are the sum of absolute DFT coefficients of the segmented regions.
(h)(i)(j) are the segmented frieze patterns from (b).
(k) Final rotation symmetry group detection result.
Publications
- S. Lee, R. Collins and Y. Liu, "Rotation Symmetry Group Detection Via Frequency Analysis of Frieze-Expansions", Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2008).(to appear).
Related Links
Experimental results.Test image set.
Movie 1 (Real image multiple centers)
Movie 2 (Synthetic image multiple centers)