| Texture modeling plays an important role in computer graphics, vision and image processing. Although various techniques have been developed for the study of texture analysis and synthesis, the mathematical definition of texture is still unclear. Due to the vague definition of texture, each technique has its own advantages and disadvantages, and thus fails to model certain types of textures.; This thesis presents a new unified mathematical framework for modeling textures using BGLAMs (Basic Gray Level Aura Matrices). The new framework will provide important understanding in texture modeling in both computer vision and computer graphics. It is proved that BGLAMs form a basis of GLAMs (Gray Level Aura Matrices), and that two images are identical if and only if their corresponding BGLAMs are the same. It is also proved that the number of different BGLAMs of a given image is no more than the number of pixels in the image. This work clarifies the relationship between BGLAMs, GLAMs, SGLAMs (Symmetric GLAMs), and GLCMs (Gray Level Cooccurrence Matrices), and demonstrates that BGLAMs outperform both SGLAMs and GLCMs in texture modeling.; Based on the theory, new techniques have developed new techniques for 2D and 3D texture synthesis, and a new method for classifying texture images using BGLAMs. The experimental results show that our new techniques can successfully apply to a wide range of textures and the results are either better or comparable to existing techniques. |
