Quaternion and Octonion color image processing with MATLAB / Artyom M. Grigoryan and Sos S. Agaian.

Format:

Book

Author/Creator:

Grigoryan, Artyom M., author.

Agaian, S. S., author.

Contributor:

Society of Photo-Optical Instrumentation Engineers, publisher.

Series:

SPIE monograph ; PM279.

SPIE digital library

SPIE Press monograph ; PM279

Language:

English

Subjects (All):

MATLAB.

Image processing--Digital techniques--Mathematics.

Image processing.

Quaternions.

Color vision.

Color.

Image processing--Digital techniques.

Genre:

Electronic books.

Physical Description:

1 online resource (404 pages).

Place of Publication:

Bellingham, Washington : SPIE, 2018.

System Details:

Mode of access: World Wide Web.

text file

Summary:

"Color image processing has involved much interest in the recent years. The use of color in image processing is motivated by the facts that 1) the human eyes can discern thousands of colors, and image processing is used both for human interaction and computer interpretation; 2) the color image comprises more information than the gray-level image; 3) the color features are robust to several image processing procedures (for example, to the translation and rotation of the regions of interest); 4) the color features are efficiently used in many vision tasks, including object recognition and tracking, image segmentation and retrieval, image registration etc.; 5) the color is necessary in many real life applications such as visual communications, multimedia systems, fashion and food industries, computer vision, entertainment, consumer electronics, production printing and proofing, digital photography, biometrics, digital artwork reproduction, industrial inspection, and biomedical applications. Finally, the enormous number of color images that constantly are uploaded into Internet require new approaches and challenges of big visual media creation, retrieval, processing, and applications. It also gives us new opportunities to create a number of big visual data-driven applications. Three independent quantities are used to describe any particular color; the human eyes are seen all colors as variable combinations of primary colors of red, green, and blue. Many methods of the modern color image processing are based on dealing out each primary color"-- Provided by publisher.

Contents:

Preface

1. Complex and hypercomplex numbers: 1.1. Complex and hypercomplex numbers; 1.2. Vector space and pure quaternions; 1.3. Quaternion multiplication and rotation; 1.4. The quaternion exponential function; 1.5. Quaternion trigonometric and hyperbolic functions; 1.6. Quaternion-type numbers; References

2. Octonion numbers: 2.1. Octonion arithmetic; 2.2. Functions on octonions; References

3. Quaternions and color images: 3.1. Digital grayscale images; 3.2. Model 1: (2x2)-mapping; 3.3. Color models; 3.4. Image models with octonions; References

4. Color images as 2-D grayscale images: 4.1. 2-D DFT of the image; 4.2. The (3x2) color-to-gray model; 4.3. The (3x1) color-to-gray model; 4.4. The (1x3) color-to-gray model; 4.5. Model of color-to-octonion image; 4.6. Color images and quaternion multiplication; References

5. 1-D quaternion and octonion discrete Fourier transforms: 5.1. Discrete Fourier transform; 5.2. 1-D right-side QDFT; 5.3. 1-D left-side QDFT; 5.4. Octonion discrete Fourier transform; References

6. 2-D quaternion and octonion discrete Fourier transforms: 6.1. Tensor representation of the image; 6.2. Mapping of 2-D DFTs in quaternion algebra; 6.3. 2-D two-side QDFT; 6.4. 2-D right-side QDFT; 6.5. Method of symplectic decomposition; 6.6. Tensor representation of the 2-D right-side QDFT; 6.7. Tensor representation of grayscale and color images; 6.8. Direction components of quaternion images; 6.9. 2-D left-side QDFT and tensor transform; 6.10. 2-D QDFT on the hexagonal lattice; 6.11. 2-D two-side octonion DFT; 6.12. 2-D right-side ODFT; 6.13. 2-D left-side ODFT; References

7. Color image enhancement and QDFT: 7.1. Transform-based image enhancement; 7.2. Quantitative measure of image enhancement; 7.3. New color image quality measure; 7.4. Enhancement of images by colors; 7.5. 2-D Quaternion DFT in image enhancement; References

8. Gradients, face recognition, visualization, and quaternions: 8.1. Correlation function and gradients; 8.2. Laplacian gradient; 8.3. Weber-Fechner visibility images; 8.4. Image visualization by the Michelson contrast; 8.5. EME-type measures and visibility; 8.6. Multiplicative visibility images; 8.7. Two-window gradient operators; 8.8. Facial image representation; 8.9. Color visibility images; 8.10. Quaternion image gradients; 8.11. Color facial image representation; References

9. Color image restoration and QDFT: 9.1. Problem of image restoration; 9.3. Optimal filtration of color images; References

Index.

Notes:

"SPIE Digital Library."--Website.

Includes bibliographical references and index.

Title from PDF title page (SPIE eBooks Website, viewed 2018-04-04).

Other Format:

Print version

ISBN:

9781510611368

1510611363

OCLC:

1030945325

Access Restriction:

Restricted for use by site license.