This dissertation presents novel solutions for improving the generalization capabilities of deep learning based computer vision models. Neural networks are known to suffer a large drop in performance when tested on samples from a different distribution than the one on which they were trained. The proposed solutions, based on latent space geometry and meta-learning, address this issue by improving the robustness of these models to distribution shifts. Through the use of geometrical alignment, state-of-the-art domain adaptation and source-free test-time adaptation strategies are developed. Additionally, geometrical alignment can allow classifiers to be progressively adapted to new, unseen test domains without requiring retraining of the feature extractors. The dissertation also presents algorithms for enabling in-the-wild generalization without needing access to any samples from the target domain. Other causes of poor generalization, such as data scarcity in critical applications and training data with high levels of noise and variance, are also explored. To address data scarcity in fine-grained computer vision tasks such as object detection, novel context-aware augmentations are suggested. While the first four chapters focus on general-purpose computer vision models, strategies are also developed to improve robustness in specific applications. The efficiency of training autonomous agents for visual navigation is improved by incorporating semantic knowledge, and the integration of domain experts' knowledge allows for the realization of a low-cost, minimally invasive generalizable automated rehabilitation system. Lastly, new tools for explainability and model introspection using counter-factual explainers trained through interval-based uncertainty calibration objectives are presented.

Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision: including view-point in activity analysis, articulation in shape analysis, and measurement invariance in non-linear dynamical modeling. The increasing success of these methods is attributed to the complementary information that topology provides, as well as availability of tools for computing topological summaries such as persistence diagrams. However, persistence diagrams are multi-sets of points and hence it is not straightforward to fuse them with features used for contemporary machine learning tools like deep-nets. In this paper theoretically well-grounded approaches to develop novel perturbation robust topological representations are presented, with the long-term view of making them amenable to fusion with contemporary learning architectures. The proposed representation lives on a Grassmann manifold and hence can be efficiently used in machine learning pipelines.

The proposed representation.The efficacy of the proposed descriptor was explored on three applications: view-invariant activity analysis, 3D shape analysis, and non-linear dynamical modeling. Favorable results in both high-level recognition performance and improved performance in reduction of time-complexity when compared to other baseline methods are obtained.