Invariance Of Geometry Of Planar Curves Using Atypical Wavelet Coefficients
The relationship between a curve and scaled, rotated and translated version is often not evident in terms of their sample points. However it is significant to note that the research fraternity working on linkage mechanism found this relationship useful for their study which they captured through Fou...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Tamkang University Press
2022-10-01
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| Series: | Journal of Applied Science and Engineering |
| Subjects: | |
| Online Access: | http://jase.tku.edu.tw/articles/jase-202305-26-5-0014 |
| _version_ | 1811343715308929024 |
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| author | D. Vignesh T. Palanisamy |
| author_facet | D. Vignesh T. Palanisamy |
| author_sort | D. Vignesh |
| collection | DOAJ |
| description | The relationship between a curve and scaled, rotated and translated version is often not evident in terms of their sample points. However it is significant to note that the research fraternity working on linkage mechanism found this relationship useful for their study which they captured through Fourier and wavelet transforms. This has been accomplished by using wavelet transform of a piecewise linear approximations of the given curve in
an earlier work. In our proposed work it is interesting to note that the desired relationship is found to be present
in a specific ratio of atypical wavelet detailed coefficients of sample points themselves. In fact, we employ a novel technique of wavelet transform using different wavelets unlike the previous attempt which is possible only by Haar wavelet. The results of this mathematical analysis are also supported by illustrated examples of continuous curves. Further the application of the proposed work to a real time image is found to suggest an useful feature which is invariant under certain transformations. |
| first_indexed | 2024-04-13T19:33:42Z |
| format | Article |
| id | doaj.art-bd0b2f454dd34e8c91fa8b3a27ce359f |
| institution | Directory Open Access Journal |
| issn | 2708-9967 2708-9975 |
| language | English |
| last_indexed | 2024-04-13T19:33:42Z |
| publishDate | 2022-10-01 |
| publisher | Tamkang University Press |
| record_format | Article |
| series | Journal of Applied Science and Engineering |
| spelling | doaj.art-bd0b2f454dd34e8c91fa8b3a27ce359f2022-12-22T02:33:06ZengTamkang University PressJournal of Applied Science and Engineering2708-99672708-99752022-10-0126573173710.6180/jase.202305_26(5).0014Invariance Of Geometry Of Planar Curves Using Atypical Wavelet CoefficientsD. Vignesh0T. Palanisamy1Department of Mathematics, Amrita school of Engineering Coimbatore, Amrita Vishwa Vidyapeetham, IndiaDepartment of Mathematics, Amrita school of Engineering Coimbatore, Amrita Vishwa Vidyapeetham, IndiaThe relationship between a curve and scaled, rotated and translated version is often not evident in terms of their sample points. However it is significant to note that the research fraternity working on linkage mechanism found this relationship useful for their study which they captured through Fourier and wavelet transforms. This has been accomplished by using wavelet transform of a piecewise linear approximations of the given curve in an earlier work. In our proposed work it is interesting to note that the desired relationship is found to be present in a specific ratio of atypical wavelet detailed coefficients of sample points themselves. In fact, we employ a novel technique of wavelet transform using different wavelets unlike the previous attempt which is possible only by Haar wavelet. The results of this mathematical analysis are also supported by illustrated examples of continuous curves. Further the application of the proposed work to a real time image is found to suggest an useful feature which is invariant under certain transformations.http://jase.tku.edu.tw/articles/jase-202305-26-5-0014planar curvessample pointsatypical wavelet transforminvariant feature vector |
| spellingShingle | D. Vignesh T. Palanisamy Invariance Of Geometry Of Planar Curves Using Atypical Wavelet Coefficients Journal of Applied Science and Engineering planar curves sample points atypical wavelet transform invariant feature vector |
| title | Invariance Of Geometry Of Planar Curves Using Atypical Wavelet Coefficients |
| title_full | Invariance Of Geometry Of Planar Curves Using Atypical Wavelet Coefficients |
| title_fullStr | Invariance Of Geometry Of Planar Curves Using Atypical Wavelet Coefficients |
| title_full_unstemmed | Invariance Of Geometry Of Planar Curves Using Atypical Wavelet Coefficients |
| title_short | Invariance Of Geometry Of Planar Curves Using Atypical Wavelet Coefficients |
| title_sort | invariance of geometry of planar curves using atypical wavelet coefficients |
| topic | planar curves sample points atypical wavelet transform invariant feature vector |
| url | http://jase.tku.edu.tw/articles/jase-202305-26-5-0014 |
| work_keys_str_mv | AT dvignesh invarianceofgeometryofplanarcurvesusingatypicalwaveletcoefficients AT tpalanisamy invarianceofgeometryofplanarcurvesusingatypicalwaveletcoefficients |