Image processing is a central theme in computer graphics. This book provides a modern introduction to both the underlying mathematics and the main concepts and techniques of the subject. It covers important modern techniques such as morphing and warping images as well as dithering, compositing, and other operations on images.
The book explores fundamental concepts of function spaces and operators, emphasizing both continuous and discrete perspectives. It introduces Fourier and Window Fourier Transforms, leading to the development of the Wavelet transform. Key discussions include multiresolution representation and its significance in function discretization and wavelet construction, providing a comprehensive foundation for understanding these essential mathematical tools.
Implicit definition and description of geometric objects and surfaces plays a critical role in the appearance and manipulation of computer graphics. In addition, the mathematical definition of shapes, using an implicit form, has pivotal applications for geometric modeling, visualization and animation.Until recently, the parametric form has been by far the most popular geometric representation used in computer graphics and computer-aided design. Whereas parametric objects and the techniques associated with them have been exhaustively developed, the implicit form has been used as a complementary geometric representation, mainly in the restricted context of specific applications. However, recent developments in graphics are changing this situation, and the community is beginning to draw its attention to implicit objects. This is reflected in the current research of aspects related to this subject. Employing a coherent conceptual framework, Implicit Objects in Computer Graphics addresses the role of implicitly defined objects in the following mathematical foundations of geometric models, implicit formulations for the specification of shapes, implicit primitives, techniques for constructing and manipulating implicit objects, modeling, rendering and animating implicit objects.