Gaussian Representation for Deformable Image Registration

Deformable image registration (DIR) is a fundamental task in radiotherapy, with existing methods often struggling to balance computational efficiency, registration accuracy, and speed effectively. We introduce a novel DIR approach employing parametric 3D Gaussian control points achieving a better tradeoff. It provides an explicit and flexible representation for spatial deformation fields between 3D volumetric medical images, producing a displacement vector field (DVF) across all volumetric positions. The movement of individual voxels is derived using linear blend skinning (LBS) through localized interpolation of transformations associated with neighboring Gaussians. This interpolation strategy not only simplifies the determination of voxel motions but also acts as an effective regularization technique. Our approach incorporates a unified optimization process through backpropagation, enabling iterative learning of both the parameters of the 3D Gaussians and their transformations. Additionally, the density of Gaussians is adjusted adaptively during the learning phase to accommodate varying degrees of motion complexity. We validated our approach on the 4D-CT lung DIR-Lab and cardiac ACDC datasets, achieving an average target registration error (TRE) of 1.06 mm within a much-improved processing time of 2.43 seconds for the DIR-Lab dataset over existing methods, demonstrating significant advancements in both accuracy and efficiency.

CPT-Interp: Continuous sPatial and Temporal Motion Modeling for 4D Medical Image Interpolation

Motion information from 4D medical imaging offers critical insights into dynamic changes in patient anatomy for clinical assessments and radiotherapy planning and, thereby, enhances the capabilities of 3D image analysis. However, inherent physical and technical constraints of imaging hardware often necessitate a compromise between temporal resolution and image quality. Frame interpolation emerges as a pivotal solution to this challenge. Previous methods often suffer from discretion when they estimate the intermediate motion and execute the forward warping. In this study, we draw inspiration from fluid mechanics to propose a novel approach for continuously modeling patient anatomic motion using implicit neural representation. It ensures both spatial and temporal continuity, effectively bridging Eulerian and Lagrangian specifications together to naturally facilitate continuous frame interpolation. Our experiments across multiple datasets underscore the method's superior accuracy and speed. Furthermore, as a case-specific optimization (training-free) approach, it circumvents the need for extensive datasets and addresses model generalization issues.

Continuous sPatial-Temporal Deformable Image Registration (CPT-DIR) for motion modelling in radiotherapy: beyond classic voxel-based methods

Background and purpose: Deformable image registration (DIR) is a crucial tool in radiotherapy for extracting and modelling organ motion. However, when significant changes and sliding boundaries are present, it faces compromised accuracy and uncertainty, determining the subsequential contour propagation and dose accumulation procedures. Materials and methods: We propose an implicit neural representation (INR)-based approach modelling motion continuously in both space and time, named Continues-sPatial-Temporal DIR (CPT-DIR). This method uses a multilayer perception (MLP) network to map 3D coordinate (x,y,z) to its corresponding velocity vector (vx,vy,vz). The displacement vectors (dx,dy,dz) are then calculated by integrating velocity vectors over time. The MLP's parameters can rapidly adapt to new cases without pre-training, enhancing optimisation. The DIR's performance was tested on the DIR-Lab dataset of 10 lung 4DCT cases, using metrics of landmark accuracy (TRE), contour conformity (Dice) and image similarity (MAE). Results: The proposed CPT-DIR can reduce landmark TRE from 2.79mm to 0.99mm, outperforming B-splines' results for all cases. The MAE of the whole-body region improves from 35.46HU to 28.99HU. Furthermore, CPT-DIR surpasses B-splines for accuracy in the sliding boundary region, lowering MAE and increasing Dice coefficients for the ribcage from 65.65HU and 90.41% to 42.04HU and 90.56%, versus 75.40HU and 89.30% without registration. Meanwhile, CPT-DIR offers significant speed advantages, completing in under 15 seconds compared to a few minutes with the conventional B-splines method. Conclusion: Leveraging the continuous representations, the CPT-DIR method significantly enhances registration accuracy, automation and speed, outperforming traditional B-splines in landmark and contour precision, particularly in the challenging areas.

Neural Graphics Primitives-based Deformable Image Registration for On-the-fly Motion Extraction

Intra-fraction motion in radiotherapy is commonly modeled using deformable image registration (DIR). However, existing methods often struggle to balance speed and accuracy, limiting their applicability in clinical scenarios. This study introduces a novel approach that harnesses Neural Graphics Primitives (NGP) to optimize the displacement vector field (DVF). Our method leverages learned primitives, processed as splats, and interpolates within space using a shallow neural network. Uniquely, it enables self-supervised optimization at an ultra-fast speed, negating the need for pre-training on extensive datasets and allowing seamless adaptation to new cases. We validated this approach on the 4D-CT lung dataset DIR-lab, achieving a target registration error (TRE) of 1.15\pm1.15 mm within a remarkable time of 1.77 seconds. Notably, our method also addresses the sliding boundary problem, a common challenge in conventional DIR methods.

Kickback cuts Backprop's red-tape: Biologically plausible credit assignment in neural networks

Error backpropagation is an extremely effective algorithm for assigning credit in artificial neural networks. However, weight updates under Backprop depend on lengthy recursive computations and require separate output and error messages -- features not shared by biological neurons, that are perhaps unnecessary. In this paper, we revisit Backprop and the credit assignment problem. We first decompose Backprop into a collection of interacting learning algorithms; provide regret bounds on the performance of these sub-algorithms; and factorize Backprop's error signals. Using these results, we derive a new credit assignment algorithm for nonparametric regression, Kickback, that is significantly simpler than Backprop. Finally, we provide a sufficient condition for Kickback to follow error gradients, and show that Kickback matches Backprop's performance on real-world regression benchmarks.

Coupled Clustering: a Method for Detecting Structural Correspondence

This paper proposes a new paradigm and computational framework for identification of correspondences between sub-structures of distinct composite systems. For this, we define and investigate a variant of traditional data clustering, termed coupled clustering, which simultaneously identifies corresponding clusters within two data sets. The presented method is demonstrated and evaluated for detecting topical correspondences in textual corpora.