In computer vision, image segmentation is one of the most critical problems. A wide range of applications, including medical imaging and robotics, make it highly appealing. Additionally, it is used extensively for automatic microscopy image analysis. As deep learning models have gained considerable traction across a range of vision applications, a substantial amount of research has been conducted on developing deep learning approaches to image segmentation. Deep learning architectures based on Convolutional Neural Networks have succeeded and are widely used, particularly for computer vision tasks.

Compared with state-of-the-art classifiers, the Gaussian process classifier offers several noticeable advantages. For example, its Bayesian nature allows any prior information to be used in the classification process. They allow the estimation of the hyper-parameters to be completed automatically. By using appropriate kernels, feature selection can be part of the learning process. They yield a posterior probability estimate as well as a variance estimate, which can be exploited as a confidence value for the predicted decision. By definition, a Gaussian process (GP) is a distribution over functions determined by its mean and kernel function. Therefore, it is essential for GP modeling to select an appropriate kernel function for a particular problem. Thus many research developed a connection between Convolutional Neural Networks and GP with a particular kernel.

The first aspect of this thesis will explain Gaussian processes, how they can be deduced from Convolutional Neural Networks, and how they can be used for classification. As segmentation is a form of labeling in which every pixel is assigned to a label, we will first train a Gaussian Process Classifier to perform pixel-level classification and then use the classifier to generate semantic segmentation. To illustrate the GP-CNN kernel's capability, we perform semantic segmentation of several images from the MNIST data set. Then, we focus on the light microscopy images.