  Capsule networks (CapsNets) were introduced to address convolutional neural
networks limitations, learning object-centric representations that are more
robust, pose-aware, and interpretable. They organize neurons into groups called
capsules, where each capsule encodes the instantiation parameters of an object
or one of its parts. Moreover, a routing algorithm connects capsules in
different layers, thereby capturing hierarchical part-whole relationships in
the data.
  This thesis investigates the intriguing aspects of CapsNets and focuses on
three key questions to unlock their full potential. First, we explore the
effectiveness of the routing algorithm, particularly in small-sized networks.
We propose a novel method that anneals the number of routing iterations during
training, enhancing performance in architectures with fewer parameters.
  Secondly, we investigate methods to extract more effective first-layer
capsules, also known as primary capsules. By exploiting pruned backbones, we
aim to improve computational efficiency by reducing the number of capsules
while achieving high generalization. This approach reduces CapsNets memory
requirements and computational effort.
  Third, we explore part-relationship learning in CapsNets. Through extensive
research, we demonstrate that capsules with low entropy can extract more
concise and discriminative part-whole relationships compared to traditional
capsule networks, even with reasonable network sizes.
  Lastly, we showcase how CapsNets can be utilized in real-world applications,
including autonomous localization of unmanned aerial vehicles, quaternion-based
rotations prediction in synthetic datasets, and lung nodule segmentation in
biomedical imaging.
  The findings presented in this thesis contribute to a deeper understanding of
CapsNets and highlight their potential to address complex computer vision
challenges.
