Abstract

Predicting a given pixel from surrounding neighboring pixels is of great interest for several image processing tasks. To model images, many researchers use Gaussian distributions. However, some data are obviously non-Gaussian, such as the image clutter and texture. In such cases, predictors are hard to derive and to obtain. In this
thesis, we analytically derive a new non-linear predictor based on an inverted Dirichlet mixture. The non-linear combination of the neighbouring pixels and the combination of the mixture parameters demonstrate a good efficiency in predicting pixels. In order
to prove the efficacy of our predictor, we use two challenging tasks, which are; object detection and image restoration.
We also develop a pixel prediction framework based on a finite generalized inverted Dirichlet (GID) mixture model that has proven its efficiency in several machine learning applications. We propose a GID optimal predictor, and we learn its parameters using a likelihood-based approach combined with the Newton-Raphson method. We demonstrate the efficiency of our proposed approach through a challenging application, namely image inpainting, and we compare the experimental results with related-work methods.
Finally, we build a new time series state space model based on inverted Dirichlet distribution. We use the power steady modeling approach and we derive an analytical expression of the model latent variable using the maximum a posteriori technique.
We also approximate the predictive density using local variational inference, and we validate our model on the electricity consumption time series dataset of Germany. A comparison with the Generalized Dirichlet state space model is conducted, and the results demonstrate the merits of our approach in modeling continuous positive vectors.