- Application period: 01 Nov. – 15 Dec. 2017.
- This offer has been approved (25 Oct. 2017), and is now part of the
website of the German Academic Exchange Service: https://www.daad.de/rise/en/rise-worldwide/
- Please make this offer widely known to your students in Germany! Please post it on your university notice boards.
DAAD RISE Internship Project Description: Hypercomplex Color Image Processing
I work with Sir William Rowan Hamilton’s quaternion algebra since over 10 years. The British Royal Astronomer Hamilton (1805-1865) introduced quaternions (in 1843) with three imaginary units, in order to describe rotations in three dimensions, similar to the complex description of rotations in two dimensions. Quaternions are now mainly applied in robotics, computer graphics, virtual reality and aero-space engineering. But the three imaginary units have proved also ideal for assigning colors RGB and for processing color images. Advantage of this method is holistic color processing, as opposed to separate color channel wise processing. The quaternionic approach showed to have further advantages, including the definition of a robust color edge filter, a natural luminosity/chromaticity decomposition, and more.
Image structure and image features, filtering, light paths in optics, etc. all use the Fourier transformation as a fundamental tool. Its natural extension for color images is the quaternionic Fourier transform (QFT), which I researched during the past ten years. Its implementation in software is very similar to the standard complex Fourier transform and families of hypercomplex of Clifford Fourier transforms. For the latter there exists a well documented and illustrated free Python implementation using a Jyputer notebook .
The proposed internship project envisions to use the Jyputer notebook  as a starting template and implement the QFT of color images, and begin testing it for a variety of color images. The first step would be to render the (quaternionic) spectrum, further steps would be to try various filters, etc. At the be beginning the intern will get a thorough introduction to the concept of QFT, compared to the standard complex Fourier transform. Then he would be free to begin adapting the Jyputer notebook for Python, or write his own notebook. I will help him to become confident in using quaternions instead of complex numbers, and we would discuss the results after several runs of the algorithm, and how to further develop and enhance it.
The student needs to know complex numbers well, and needs to have some previous experience with the programming language Python. Students from mathematics, computer science, electric engineering, physics, etc. would all be welcome for this internship. At the end of the internship period, the intern will be given an opportunity to present his work to natural science students from physics, chemistry, biology, computer science and mathematics.
The International Christian University (http://www.icu.ac.jp/en/) was founded over 60 years ago as a joint Japanese-American venture with global participation. The university is fully bilingual in English and Japanese. The intern will have no communication problems when he/she masters basic English communication. The location is in the western suburbs of Tokyo on a wide spacious green park land forest campus. It does not feel at all like being in Tokyo, but it is well connected to the city center by public transport. Events, exhibitions in the city center are easy to take advantage of in the evenings or on the weekends. Daytrips or weekend trips to interesting regions like Kamakura, Kyoto, Nara, Mt. Fuji, etc. are possible. Meals (breakfast, lunch and dinner) are available in the university restaurant (both western and Japanese cuisine). There are many student clubs, including sports, arts, tea ceremony, music, … The campus has excellent sports facilities, including gyms, field and track, etc. All enrolled Japanese students get two years of intensive English training, international students get two years of intensive Japanese training instead.
For further request of information, please do not hesitate to contact me by email.
Eckhard Hitzer, Dr. rer. nat., Senior Associate Professor, College of Liberal Arts,
International Christian University, Tokyo, Japan,
URL: http://erkenntnis.icu.ac.jp/, GA-Net: http://erkenntnis.icu.ac.jp/GA-Net/
Source: Email from Your RISE Worldwide Team, German Academic Exchange Service (DAAD), rise-worlwide_AT_daad.de, 25/10/2017 18:29