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“Computational Models for Texture Analysis and Texture Synthesis”
by David Donovan Garber
May 1981
Numerous computational methods for generating and simulating binary and grey-level natural digital-image textures are proposed using a variety of stochastic models. Pictorial results of each method are given and various aspects of each approach are discussed. The quality of the natural texture simulations depends on the computation time for data collection, computation time for generation, and storage used in each process. In most cases, as computation time and data storage increase, the visual match between the texture simulation and the parent texture improves. Many textures are adequately simulated using simple models thus providing a potentially great information compression for many applications.
In most of the texture synthesis methods presented in this thesis, pixel values are generated one-at-a-time according to both the given model and the values of pixels previously generated in the synthesis until the image space is completely filled. Nth-order joint density functions estimated from a natural texture sample were used for this purpose in one method. The results are excellent but the storage required, even for binary textures, is large. Therefore, a much simpler first-order linear, autoregressive model was applied to the texture synthesis problem. Using this model on both binary and continuous-tone textures, each pixel is generated as a linear combination of previously generated pixels plus stationary noise. The results indicate that many textures are satisfactorily simulated using this approach.
By adding cross-product terms, the first-order linear model is extended to a second-order linear model. The simulation results improve slightly but the number of computations required for the statistics collection process increases drastically. Non-stationary noise was then used in the synthesis process and further improvements in the quality of the simulations are achieved at the cost of increased storage.
Methods of texture simulation using more than one model are studied in this thesis. These multiple-model are useful for many textures, especially those with macro-structure. They also improve the fit of the model when applied to the parent texture data and therefore may produce improved simulations.
A final model, called the best-fit model, generates texture simulations directly from the parent texture itself. Each pixel in the synthesis image is generated based on the similarity of its previously-generated, neighboring pixel values to pixel values in all similarly-shaped neighborhoods in the parent texture. The measures of similarity at all points in the parent texture, along with a random variable, are used to generate the next pixel value in the synthesized image. The synthesis results using model are excellent but the synthesis process is very computationally demanding.
Although the success of texture synthesis is highly dependent on the texture itself and the modeling method chosen, general conclusions regarding the performance of various techniques are given. Methods of texture segmentation and identification based on texture synthesis results are also presented.