Our method achieves advanced partialto-partial non-rigid point cloud registration results onthe4DMatch/4DLoMatch benchmark under both no-learned and supervised settings.

The high complexity of the unknown non-rigid motion make this task a challenging problem.

3D ultrasound (US) imaging has shown significant benefits in enhancing the outcomes of percutaneous liver tumour ablation. Its clinical integration is crucial for transitioning 3D US into the therapeutic domain. However, challenges of tumour identification in US images continue to hinder its broader adoption. In this work, we propose a novel framework for integrating 3D US into the standard ablation workflow. We present a key component, a clinically viable 2D US-CT/MRI registration approach, leveraging 3D US as an intermediary to reduce registration complexity. To facilitate efficient verification of the registration workflow, we also propose an intuitive multimodal image visualization technique. In our study, 2D US-CT/MRI registration achieved a landmark distance error of approximately 2-4 mm with a runtime of 0.22s per image pair. Additionally, non-rigid registration reduced the mean alignment error by approximately 40% compared to rigid registration. Results demonstrated the efficacy of the proposed 2D US-CT/MRI registration workflow. Our integration framework advanced the capabilities of 3D US imaging in improving percutaneous tumour ablation, demonstrating the potential to expand the therapeutic role of 3D US in clinical interventions.

Point cloud registration aims to provide estimated transformations to align point clouds, which plays a crucial role in pose estimation of various navigation systems, such as surgical guidance systems and autonomous vehicles. Despite the impressive performance of recent models on benchmark datasets, many rely on complex modules like KPConv and Transformers, which impose significant computational and memory demands. These requirements hinder their practical application, particularly in resource-constrained environments such as mobile robotics. In this paper, we propose a novel point cloud registration network that leverages a pure MLP architecture, constructing geometric information offline. This approach eliminates the computational and memory burdens associated with traditional complex feature extractors and significantly reduces inference time and resource consumption. Our method is the first to replace 3D coordinate inputs with offline-constructed geometric encoding, improving generalization and stability, as demonstrated by Maximum Mean Discrepancy (MMD) comparisons. This efficient and accurate geometric representation marks a significant advancement in point cloud analysis, particularly for applications requiring fast and reliability.

This paper presents a novel non-rigid point set registration method that is inspired by unsupervised clustering analysis. Unlike previous approaches that treat the source and target point sets as separate entities, we develop a holistic framework where they are formulated as clustering centroids and clustering members, separately. We then adopt Tikhonov regularization with an $\ell_1$-induced Laplacian kernel instead of the commonly used Gaussian kernel to ensure smooth and more robust displacement fields. Our formulation delivers closed-form solutions, theoretical guarantees, independence from dimensions, and the ability to handle large deformations. Subsequently, we introduce a clustering-improved Nystr\"om method to effectively reduce the computational complexity and storage of the Gram matrix to linear, while providing a rigorous bound for the low-rank approximation. Our method achieves high accuracy results across various scenarios and surpasses competitors by a significant margin, particularly on shapes with substantial deformations. Additionally, we demonstrate the versatility of our method in challenging tasks such as shape transfer and medical registration.

We present a novel method for intraoperative patient-to-image registration by learning Expected Appearances. Our method uses preoperative imaging to synthesize patient-specific expected views through a surgical microscope for a predicted range of transformations. Our method estimates the camera pose by minimizing the dissimilarity between the intraoperative 2D view through the optical microscope and the synthesized expected texture. In contrast to conventional methods, our approach transfers the processing tasks to the preoperative stage, reducing thereby the impact of low-resolution, distorted, and noisy intraoperative images, that often degrade the registration accuracy. We applied our method in the context of neuronavigation during brain surgery. We evaluated our approach on synthetic data and on retrospective data from 6 clinical cases. Our method outperformed state-of-the-art methods and achieved accuracies that met current clinical standards.

Autonomous ultrasound (US) imaging has gained increased interest recently, and it has been seen as a potential solution to overcome the limitations of free-hand US examinations, such as inter-operator variations. However, it is still challenging to accurately map planned paths from a generic atlas to individual patients, particularly for thoracic applications with high acoustic-impedance bone structures under the skin. To address this challenge, a graph-based non-rigid registration is proposed to enable transferring planned paths from the atlas to the current setup by explicitly considering subcutaneous bone surface features instead of the skin surface. To this end, the sternum and cartilage branches are segmented using a template matching to assist coarse alignment of US and CT point clouds. Afterward, a directed graph is generated based on the CT template. Then, the self-organizing map using geographical distance is successively performed twice to extract the optimal graph representations for CT and US point clouds, individually. To evaluate the proposed approach, five cartilage point clouds from distinct patients are employed. The results demonstrate that the proposed graph-based registration can effectively map trajectories from CT to the current setup for displaying US views through limited intercostal space. The non-rigid registration results in terms of Hausdorff distance (Mean$\pm$SD) is 9.48$\pm$0.27 mm and the path transferring error in terms of Euclidean distance is 2.21$\pm$1.11 mm.

Cortical surface registration plays a crucial role in aligning cortical functional and anatomical features across individuals. However, conventional registration algorithms are computationally inefficient. Recently, learning-based registration algorithms have emerged as a promising solution, significantly improving processing efficiency. Nonetheless, there remains a gap in the development of a learning-based method that exceeds the state-of-the-art conventional methods simultaneously in computational efficiency, registration accuracy, and distortion control, despite the theoretically greater representational capabilities of deep learning approaches. To address the challenge, we present SUGAR, a unified unsupervised deep-learning framework for both rigid and non-rigid registration. SUGAR incorporates a U-Net-based spherical graph attention network and leverages the Euler angle representation for deformation. In addition to the similarity loss, we introduce fold and multiple distortion losses, to preserve topology and minimize various types of distortions. Furthermore, we propose a data augmentation strategy specifically tailored for spherical surface registration, enhancing the registration performance. Through extensive evaluation involving over 10,000 scans from 7 diverse datasets, we showed that our framework exhibits comparable or superior registration performance in accuracy, distortion, and test-retest reliability compared to conventional and learning-based methods. Additionally, SUGAR achieves remarkable sub-second processing times, offering a notable speed-up of approximately 12,000 times in registering 9,000 subjects from the UK Biobank dataset in just 32 minutes. This combination of high registration performance and accelerated processing time may greatly benefit large-scale neuroimaging studies.

Physiological motion, such as cardiac and respiratory motion, during Magnetic Resonance (MR) image acquisition can cause image artifacts. Motion correction techniques have been proposed to compensate for these types of motion during thoracic scans, relying on accurate motion estimation from undersampled motion-resolved reconstruction. A particular interest and challenge lie in the derivation of reliable non-rigid motion fields from the undersampled motion-resolved data. Motion estimation is usually formulated in image space via diffusion, parametric-spline, or optical flow methods. However, image-based registration can be impaired by remaining aliasing artifacts due to the undersampled motion-resolved reconstruction. In this work, we describe a formalism to perform non-rigid registration directly in the sampled Fourier space, i.e. k-space. We propose a deep-learning based approach to perform fast and accurate non-rigid registration from the undersampled k-space data. The basic working principle originates from the Local All-Pass (LAP) technique, a recently introduced optical flow-based registration. The proposed LAPNet is compared against traditional and deep learning image-based registrations and tested on fully-sampled and highly-accelerated (with two undersampling strategies) 3D respiratory motion-resolved MR images in a cohort of 40 patients with suspected liver or lung metastases and 25 healthy subjects. The proposed LAPNet provided consistent and superior performance to image-based approaches throughout different sampling trajectories and acceleration factors.