Modern deep learning developments create new opportunities for 3D mapping technology, scene reconstruction pipelines, and virtual reality development. Despite advances in 3D deep learning technology, direct training of deep learning models on 3D data faces challenges due to the high dimensionality inherent in 3D data and the scarcity of labeled datasets. Structure-from-motion (SfM) and Simultaneous Localization and Mapping (SLAM) exhibit robust performance when applied to structured indoor environments but often struggle with ambiguous features in unstructured environments. These techniques often struggle to generate detailed geometric representations effective for downstream tasks such as rendering and semantic analysis. Current limitations require the development of 3D representation methods that combine traditional geometric techniques with deep learning capabilities to generate robust geometry-aware deep learning models. The dissertation provides solutions to the fundamental challenges in 3D vision by developing geometric deep learning methods tailored for essential tasks such as camera pose estimation, point cloud registration, depth prediction, and 3D reconstruction. The integration of geometric priors or constraints, such as including depth information, surface normals, and equivariance into deep learning models, enhances both the accuracy and robustness of geometric representations. This study systematically investigates key components of 3D vision, including camera pose estimation, point cloud registration, depth estimation, and high-fidelity 3D reconstruction, demonstrating their effectiveness across real-world applications such as digital cultural heritage preservation and immersive VR/AR environments.

Melanoma, a dangerous type of skin cancer resulting from abnormal skin cell growth, can be treated if detected early. Various approaches using Fully Convolutional Networks (FCNs) have been proposed, with the U-Net architecture being prominent To aid in its diagnosis through automatic skin lesion segmentation. However, the symmetrical U-Net model's reliance on convolutional operations hinders its ability to capture long-range dependencies crucial for accurate medical image segmentation. Several Transformer-based U-Net topologies have recently been created to overcome this limitation by replacing CNN blocks with different Transformer modules to capture local and global representations. Furthermore, the U-shaped structure is hampered by semantic gaps between the encoder and decoder. This study intends to increase the network's feature re-usability by carefully building the skip connection path. Integrating an already calculated attention affinity within the skip connection path improves the typical concatenation process utilized in the conventional skip connection path. As a result, we propose a U-shaped hierarchical Transformer-based structure for skin lesion segmentation and an Inter-scale Context Fusion (ISCF) method that uses attention correlations in each stage of the encoder to adaptively combine the contexts from each stage to mitigate semantic gaps. The findings from two skin lesion segmentation benchmarks support the ISCF module's applicability and effectiveness. The code is publicly available at \url{https://github.com/saniaesk/skin-lesion-segmentation}

Designing a synthetic crown is a time-consuming, inconsistent, and labor-intensive process. In this work, we present a fully automatic method that not only learns human design dental crowns, but also improves the consistency, functionality, and esthetic of the crowns. Following success in point cloud completion using the transformer-based network, we tackle the problem of the crown generation as a point-cloud completion around a prepared tooth. To this end, we use a geometry-aware transformer to generate dental crowns. Our main contribution is to add a margin line information to the network, as the accuracy of generating a precise margin line directly,determines whether the designed crown and prepared tooth are closely matched to allowappropriateadhesion.Using our ground truth crown, we can extract the margin line as a spline and sample the spline into 1000 points. We feed the obtained margin line along with two neighbor teeth of the prepared tooth and three closest teeth in the opposing jaw. We also add the margin line points to our ground truth crown to increase the resolution at the margin line. Our experimental results show an improvement in the quality of the designed crown when considering the actual context composed of the prepared tooth along with the margin line compared with a crown generated in an empty space as was done by other studies in the literature.

Deformable medical image registration plays an important role in clinical diagnosis and treatment. Recently, the deep learning (DL) based image registration methods have been widely investigated and showed excellent performance in computational speed. However, these methods cannot provide enough registration accuracy because of insufficient ability in representing both the global and local features of the moving and fixed images. To address this issue, this paper has proposed the transformer based image registration method. This method uses the distinctive transformer to extract the global and local image features for generating the deformation fields, based on which the registered image is produced in an unsupervised way. Our method can improve the registration accuracy effectively by means of self-attention mechanism and bi-level information flow. Experimental results on such brain MR image datasets as LPBA40 and OASIS-1 demonstrate that compared with several traditional and DL based registration methods, our method provides higher registration accuracy in terms of dice values.

Monocular visual odometry consists of the estimation of the position of an agent through images of a single camera, and it is applied in autonomous vehicles, medical robots, and augmented reality. However, monocular systems suffer from the scale ambiguity problem due to the lack of depth information in 2D frames. This paper contributes by showing an application of the dense prediction transformer model for scale estimation in monocular visual odometry systems. Experimental results show that the scale drift problem of monocular systems can be reduced through the accurate estimation of the depth map by this model, achieving competitive state-of-the-art performance on a visual odometry benchmark.