Large training datasets have played a vital role in the success of modern deep learning methods in computer vision. But, obtaining sufficient amount of training data is challenging, specially when annotating volumetric images. This is because fully annotating a single image volume require annotating a whole stack of images which is costly. Moreover, majority of volumetric images originate from niche domains that require expert knowledge to annotate and it further increase the associated cost. Therefore, designing models for volumetric image segmentation that can work with small training datasets is of great importance. One way to address this challenge is to use prior knowledge in segmentation model design. There are many forms of prior knowledge and in this thesis, we focus on using object priors which defines prior knowledge related to the properties of the object being segmented. We begin by proposing an end-to-end differentiable architecture that produce surface meshes from input image volumes which enable easy integration of object priors related to topology and surface properties. With that we demonstrate how the priors help achieve better accuracy and quality in predictions compared to state-of-the-art methods that do not use them. Then we focus on surface priors and propose a methodology based on Active Surface models to achieve better trade-offs between the accuracy of the surfaces produced by the segmentation models and their quality. Afterwards, we apply the Active Surface model proposed earlier to develop an interactive annotation tool that significantly reduce the effort necessary to annotate image volumes. Along with that, a volumetric image segmentation model that best utilize annotations produced with the tool is also proposed. Finally we focus on object priors related to overall shape. We use Probabilistic Atlases (PAs) to introduce this prior knowledge into the segmentation model and demonstrate its ability to improve the accuracy in predictions. Overall, we use object prior to improve the accuracy, quality and the speed of annotation in volumetric image segmentation. To demonstrate their effectiveness, we use volumetric images produced by Magnetic Resonance Imaging (MRI), Computed Tomography (CT) and Electron Microscopy (EMs).