Summation Invariants Of Objects Under Projective Transformation Group With Application
Geometri tak varian adalah ciri geometri yang tidak berubah di bawah pelbagai jenis transformasi dan ia dapat digunakan dalam pemerihalan bentuk untuk mengatasi ber bagai kesukaran dalam pemasalahan pengecaman objek untuk visi komputer. Peranan parameter tak varian diiktiraf dalam beberapa aplik...
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my-usm-ep.316722019-04-12T05:25:25Z Summation Invariants Of Objects Under Projective Transformation Group With Application 2016-02 Azhir, Nasereh QA1 Mathematics (General) Geometri tak varian adalah ciri geometri yang tidak berubah di bawah pelbagai jenis transformasi dan ia dapat digunakan dalam pemerihalan bentuk untuk mengatasi ber bagai kesukaran dalam pemasalahan pengecaman objek untuk visi komputer. Peranan parameter tak varian diiktiraf dalam beberapa aplikasi seperti perwakilan bentuk, pemadanan bentuk, pengecaman objek dan aplikasi robotik. Tesis ini mengetengahkan penyelesaian permasalahan berkaitan terbitan tak varian objek dua dimensi untuk kumpulan transformasi unjuran. Di dalam tesis ini, satu kaedah diberikan untuk menentukan perjumlahan tak varian objek planar pada kumpulan transformasi unjuran dan satu algoritma telah dibangunkan untuk menggunapakai tak varian yang diterbitkan sebagai penyelesaian beberapa permasalahan pengecaman objek pada kumpulan transformasi. Kaedah Cartan dengan rangka bergerak digunakan untuk menerbitkan tak varian ini. Kamiran potensi baru untuk lengkung 2D dicadangkan untuk memperolehi kamiran tak varian di bawah tindakan suatu subkumpulan bagi transformasi unjuran dengan 6 darjah kebebasan. Geometric invariants are features which unchanged under a variety of transformations and they can be used as the shape descriptors to overcome many of problems of object recognition problems in computer vision. The role of invariants in computer vision has been advocated for various applications such as shape representation, shape matching, object recognition and robotic. This thesis solving problems associated with deriving invariants of two dimensional objects under projective transformation groups in Euclidean space. In this thesis, a method is given to determine projective invariants for planar objects under projective transformation groups and an algorithm is given to apply the derived invariants in order to solve some issues of object recognition under transformation groups. The Cartan’s method of moving frame is applied to derive these invariants. Novel integral potentials for 2D curves are proposed to derive integral invariants under the action of a subgroup of projective transformation with 6 degrees of freedom. 2016-02 Thesis http://eprints.usm.my/31672/ http://eprints.usm.my/31672/1/NASEREH_AZHIR_24.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Sains Matematik (School of Mathematical Sciences) |
| institution |
Universiti Sains Malaysia |
| collection |
USM Institutional Repository |
| language |
English |
| topic |
QA1 Mathematics (General) |
| spellingShingle |
QA1 Mathematics (General) Azhir, Nasereh Summation Invariants Of Objects Under Projective Transformation Group With Application |
| description |
Geometri tak varian adalah ciri geometri yang tidak berubah di bawah pelbagai
jenis transformasi dan ia dapat digunakan dalam pemerihalan bentuk
untuk mengatasi ber bagai kesukaran dalam pemasalahan pengecaman objek
untuk visi komputer. Peranan parameter tak varian diiktiraf dalam beberapa
aplikasi seperti perwakilan bentuk, pemadanan bentuk, pengecaman objek
dan aplikasi robotik. Tesis ini mengetengahkan penyelesaian permasalahan
berkaitan terbitan tak varian objek dua dimensi untuk kumpulan transformasi
unjuran. Di dalam tesis ini, satu kaedah diberikan untuk menentukan perjumlahan
tak varian objek planar pada kumpulan transformasi unjuran dan satu
algoritma telah dibangunkan untuk menggunapakai tak varian yang diterbitkan
sebagai penyelesaian beberapa permasalahan pengecaman objek pada
kumpulan transformasi. Kaedah Cartan dengan rangka bergerak digunakan
untuk menerbitkan tak varian ini. Kamiran potensi baru untuk lengkung 2D
dicadangkan untuk memperolehi kamiran tak varian di bawah tindakan suatu
subkumpulan bagi transformasi unjuran dengan 6 darjah kebebasan.
Geometric invariants are features which unchanged under a variety of transformations
and they can be used as the shape descriptors to overcome many of
problems of object recognition problems in computer vision. The role of invariants
in computer vision has been advocated for various applications such as
shape representation, shape matching, object recognition and robotic. This thesis
solving problems associated with deriving invariants of two dimensional
objects under projective transformation groups in Euclidean space. In this thesis,
a method is given to determine projective invariants for planar objects under
projective transformation groups and an algorithm is given to apply the
derived invariants in order to solve some issues of object recognition under
transformation groups. The Cartan’s method of moving frame is applied to
derive these invariants. Novel integral potentials for 2D curves are proposed
to derive integral invariants under the action of a subgroup of projective transformation
with 6 degrees of freedom. |
| format |
Thesis |
| qualification_name |
Doctor of Philosophy (PhD.) |
| qualification_level |
Doctorate |
| author |
Azhir, Nasereh |
| author_facet |
Azhir, Nasereh |
| author_sort |
Azhir, Nasereh |
| title |
Summation Invariants Of Objects Under Projective Transformation Group With Application |
| title_short |
Summation Invariants Of Objects Under Projective Transformation Group With Application |
| title_full |
Summation Invariants Of Objects Under Projective Transformation Group With Application |
| title_fullStr |
Summation Invariants Of Objects Under Projective Transformation Group With Application |
| title_full_unstemmed |
Summation Invariants Of Objects Under Projective Transformation Group With Application |
| title_sort |
summation invariants of objects under projective transformation group with application |
| granting_institution |
Universiti Sains Malaysia |
| granting_department |
Pusat Pengajian Sains Matematik (School of Mathematical Sciences) |
| publishDate |
2016 |
| url |
http://eprints.usm.my/31672/1/NASEREH_AZHIR_24.pdf |
| _version_ |
1747820476289253376 |