Reflection alignment on analysis of planar shape†
Jun Yeong Park1 · Hyeongseok Lee2 · Min Ho Cho3
123Department of Statistics, Inha University
Correspondence to: † This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2022-00167077).
1 Undergraduate student, Department of Statistics, Incheon 22212, Korea.
2 Master student, Department of Statistics, Incheon 22212, Korea.
3 Assistant professor, Department of Statistics, Incheon 22212, Korea. E-mail: mcho@inha.ac.kr
1 Undergraduate student, Department of Statistics, Incheon 22212, Korea.
2 Master student, Department of Statistics, Incheon 22212, Korea.
3 Assistant professor, Department of Statistics, Incheon 22212, Korea. E-mail: mcho@inha.ac.kr
Received July 29, 2024; Revised August 18, 2024; Accepted August 19, 2024.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Abstract
- Shape data analysis involves comparing the differences in shape of objects. It is widely used in various application fields such as computer vision and medical imaging, where recognition and detection of objects in images or videos via their shape are needed. To analyze unique shapes, it is necessary to ensure that the shape is invariant to several nuisance transformations such as location, size, and rotation. However, relatively few studies have been conducted on the reflection transformation when extracting planar curves on the boundary of the objects. For instance, when an object is captured from the opposite direction, conventional shape analysis treats the object which has different shape from the original one. In many areas, it requires the removal of this reflection variation in shape analysis. Hence, we propose a shape distance and corresponding analysis tools, accompanied by symmetric reflection alignment. The proposed framework for shape analysis is based on planar curves and an elastic metric. Some visual explorations of our procedure are provided, and its performance of clustering and classification is compared to the existing method through toy and real data examples.
- Keywords : Clustering and classification, elastic metric, reflection alignment, shape data, symmetric reflection
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