Exploratory Methods for the Study of Incomplete and Intersecting Shape Boundaries from Landmark Data
Structured spatial point patterns appear in many applications within the natural sciences. The points often record the location of key features, called landmarks, on continuous object boundaries, such as anatomical features on a human face. In other situations, the points may simply be arbitrarily s...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2016/1285026 |
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| author | Fathi M. O. Hamed Robert G. Aykroyd |
| author_facet | Fathi M. O. Hamed Robert G. Aykroyd |
| author_sort | Fathi M. O. Hamed |
| collection | DOAJ |
| description | Structured spatial point patterns appear in many applications within the natural sciences. The points often record the location of key features, called landmarks, on continuous object boundaries, such as anatomical features on a human face. In other situations, the points may simply be arbitrarily spaced marks along a smooth curve, such as on handwritten numbers. This paper proposes novel exploratory methods for the identification of structure within point datasets. In particular, points are linked together to form curves which estimate the original shape from which the points are the only recorded information. Nonparametric regression methods are applied to polar coordinate variables obtained from the point locations and periodic modelling allows closed curves to be fitted even when data are available on only part of the boundary. Further, the model allows discontinuities to be identified to describe rapid changes in the curves. These generalizations are particularly important when the points represent shapes which are occluded or are intersecting. A range of real-data examples is used to motivate the modelling and to illustrate the flexibility of the approach. The method successfully identifies the underlying structure and its output could also be used as the basis for further analysis. |
| format | Article |
| id | doaj-art-66638edd3a7b457cbe64dc99f74195ac |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-66638edd3a7b457cbe64dc99f74195ac2025-02-03T01:12:06ZengWileyJournal of Probability and Statistics1687-952X1687-95382016-01-01201610.1155/2016/12850261285026Exploratory Methods for the Study of Incomplete and Intersecting Shape Boundaries from Landmark DataFathi M. O. Hamed0Robert G. Aykroyd1University of Benghazi, Benghazi, LibyaUniversity of Leeds, Leeds, UKStructured spatial point patterns appear in many applications within the natural sciences. The points often record the location of key features, called landmarks, on continuous object boundaries, such as anatomical features on a human face. In other situations, the points may simply be arbitrarily spaced marks along a smooth curve, such as on handwritten numbers. This paper proposes novel exploratory methods for the identification of structure within point datasets. In particular, points are linked together to form curves which estimate the original shape from which the points are the only recorded information. Nonparametric regression methods are applied to polar coordinate variables obtained from the point locations and periodic modelling allows closed curves to be fitted even when data are available on only part of the boundary. Further, the model allows discontinuities to be identified to describe rapid changes in the curves. These generalizations are particularly important when the points represent shapes which are occluded or are intersecting. A range of real-data examples is used to motivate the modelling and to illustrate the flexibility of the approach. The method successfully identifies the underlying structure and its output could also be used as the basis for further analysis.http://dx.doi.org/10.1155/2016/1285026 |
| spellingShingle | Fathi M. O. Hamed Robert G. Aykroyd Exploratory Methods for the Study of Incomplete and Intersecting Shape Boundaries from Landmark Data Journal of Probability and Statistics |
| title | Exploratory Methods for the Study of Incomplete and Intersecting Shape Boundaries from Landmark Data |
| title_full | Exploratory Methods for the Study of Incomplete and Intersecting Shape Boundaries from Landmark Data |
| title_fullStr | Exploratory Methods for the Study of Incomplete and Intersecting Shape Boundaries from Landmark Data |
| title_full_unstemmed | Exploratory Methods for the Study of Incomplete and Intersecting Shape Boundaries from Landmark Data |
| title_short | Exploratory Methods for the Study of Incomplete and Intersecting Shape Boundaries from Landmark Data |
| title_sort | exploratory methods for the study of incomplete and intersecting shape boundaries from landmark data |
| url | http://dx.doi.org/10.1155/2016/1285026 |
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