A Novel Image Representation Method Under a Non-Standard Positional Numeral System
| العنوان: | A Novel Image Representation Method Under a Non-Standard Positional Numeral System |
|---|---|
| المؤلفون: | Zhanchuan Cai, Ting Lan |
| المصدر: | IEEE Transactions on Multimedia. 23:1301-1315 |
| بيانات النشر: | Institute of Electrical and Electronics Engineers (IEEE), 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Computer science, Gaussian integer, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Image processing, 02 engineering and technology, Decimal, Numerical digit, Computer Science Applications, Numeral system, Digital image, symbols.namesake, Computer Science::Computer Vision and Pattern Recognition, Signal Processing, 0202 electrical engineering, electronic engineering, information engineering, Media Technology, symbols, 020201 artificial intelligence & image processing, Multiplication, Binary code, Electrical and Electronic Engineering, Algorithm |
| الوصف: | Image representation is an active research area in the field of image processing. This paper proposes a novel image representation method under a non-standard positional numeral system, wherein complex numbers are used as bases in such non-standard positional numeral system. It is different with binary code and decimal code, where the digit 2 is used as the base in the binary system, and the digit 10 is used as the base in the decimal system. In the proposed image representation method, a two-dimensional image is transformed into a one-dimensional 0 $\sim$ 1 sequence, and its Gaussian integer is calculated based on the derived one-dimensional 0 $\sim$ 1 sequence. On the contrary, the original two-dimensional image can be recovered from its Gaussian integer. When images are represented as Gaussian integers, the classical geometrical operations are introduced into image processing. Then, the relationship of different images is established by the methods of plane geometry, i.e., the addition, subtraction, multiplication, division, conjugate, and inverse operations of images are defined. The experimental results show that the selection of complex number as base in the positional numeral system is a very special coding method, a given digital image is effectively converted to a Gaussian integer by using the proposed image representation method, and the image arithmetic is also successfully achieved. In addition, three applications based on the proposed image representation method including image camouflage, image sharing, and image scrambling are selected to demonstrate that the new image representation has good and potential practical applicability in the field of secure encryption of digital images. |
| تدمد: | 1941-0077 1520-9210 |
| الوصول الحر: | https://explore.openaire.eu/search/publication?articleId=doi_________::1d865274eb637360f527477e905936a4Test https://doi.org/10.1109/tmm.2020.2995258Test |
| حقوق: | CLOSED |
| رقم الانضمام: | edsair.doi...........1d865274eb637360f527477e905936a4 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 19410077 15209210 |
|---|