Lennart Bastian

Lennart Bastian, Tony Danjun Wang, Tobias Czempiel et al.

Purpose: Recent advances in Surgical Data Science (SDS) have contributed to an increase in video recordings from hospital environments. While methods such as surgical workflow recognition show potential in increasing the quality of patient care, the quantity of video data has surpassed the scale at which images can be manually anonymized. Existing automated 2D anonymization methods under-perform in Operating Rooms (OR), due to occlusions and obstructions. We propose to anonymize multi-view OR recordings using 3D data from multiple camera streams. Methods: RGB and depth images from multiple cameras are fused into a 3D point cloud representation of the scene. We then detect each individual's face in 3D by regressing a parametric human mesh model onto detected 3D human keypoints and aligning the face mesh with the fused 3D point cloud. The mesh model is rendered into every acquired camera view, replacing each individual's face. Results: Our method shows promise in locating faces at a higher rate than existing approaches. DisguisOR produces geometrically consistent anonymizations for each camera view, enabling more realistic anonymization that is less detrimental to downstream tasks. Conclusion: Frequent obstructions and crowding in operating rooms leaves significant room for improvement for off-the-shelf anonymization methods. DisguisOR addresses privacy on a scene level and has the potential to facilitate further research in SDS.

Lennart Bastian, Alexander Baumann, Emily Hoppe et al.

Statistical shape models (SSMs) are an established way to represent the anatomy of a population with various clinically relevant applications. However, they typically require domain expertise, and labor-intensive landmark annotations to construct. We address these shortcomings by proposing an unsupervised method that leverages deep geometric features and functional correspondences to simultaneously learn local and global shape structures across population anatomies. Our pipeline significantly improves unsupervised correspondence estimation for SSMs compared to baseline methods, even on highly irregular surface topologies. We demonstrate this for two different anatomical structures: the thyroid and a multi-chamber heart dataset. Furthermore, our method is robust enough to learn from noisy neural network predictions, potentially enabling scaling SSMs to larger patient populations without manual segmentation annotation.

Lennart Bastian, Tobias Czempiel, Christian Heiliger et al.

The surgical operating room (OR) presents many opportunities for automation and optimization. Videos from various sources in the OR are becoming increasingly available. The medical community seeks to leverage this wealth of data to develop automated methods to advance interventional care, lower costs, and improve overall patient outcomes. Existing datasets from OR room cameras are thus far limited in size or modalities acquired, leaving it unclear which sensor modalities are best suited for tasks such as recognizing surgical action from videos. This study demonstrates that surgical action recognition performance can vary depending on the image modalities used. We perform a methodical analysis on several commonly available sensor modalities, presenting two fusion approaches that improve classification performance. The analyses are carried out on a set of multi-view RGB-D video recordings of 18 laparoscopic procedures.

Yizheng Xie, Lennart Bastian, Congyue Deng et al.

Deep functional maps, leveraging learned feature extractors and spectral correspondence solvers, are fundamental to non-rigid 3D shape matching. Based on an analysis of open-source implementations, we find that standard functional map implementations solve k independent linear systems serially, which is a computational bottleneck at higher spectral resolution. We thus propose a vectorized reformulation that solves all systems in a single kernel call, achieving up to a 33x speedup while preserving the exact solution. Furthermore, we identify and document a previously unnoticed implementation divergence in the spatial gradient features of the mainstay DiffusionNet: two variants that parameterize distinct families of tangent-plane transformations, and present experiments analyzing their respective behaviors across diverse benchmarks. We additionally revisit overlap prediction evaluation for partial-to-partial matching and show that balanced accuracy provides a useful complementary metric under varying overlap ratios. To share these advancements with the wider community, we present an open-source codebase, DeepShapeMatchingKit, that incorporates these improvements and standardizes training, evaluation, and data pipelines for common deep shape matching methods. The codebase is available at: https://github.com/xieyizheng/DeepShapeMatchingKit

Tony Danjun Wang, Ka Young Kim, Tolga Birdal et al.

Surgical Scene Graphs abstract the complexity of surgical operating rooms (OR) into a structure of entities and their relations, but existing paradigms suffer from strictly dyadic structural limitations. Frameworks that predominantly rely on pairwise message passing or tokenized sequences flatten the manifold geometry inherent to relational structures and lose structure in the process. We introduce TopoOR, a new paradigm that models multimodal operating rooms as a higher-order structure, innately preserving pairwise and group relationships. By lifting interactions between entities into higher-order topological cells, TopoOR natively models complex dynamics and multimodality present in the OR. This topological representation subsumes traditional scene graphs, thereby offering strictly greater expressivity. We also propose a higher-order attention mechanism that explicitly preserves manifold structure and modality-specific features throughout hierarchical relational attention. In this way, we circumvent combining 3D geometry, audio, and robot kinematics into a single joint latent representation, preserving the precise multimodal structure required for safety-critical reasoning, unlike existing methods. Extensive experiments demonstrate that our approach outperforms traditional graph and LLM-based baselines across sterility breach detection, robot phase prediction, and next-action anticipation

Aleksei Zhuravlev, Lennart Bastian, Dongliang Cao et al.

Estimating correspondences between deformed shape instances is a long-standing problem in computer graphics; numerous applications, from texture transfer to statistical modelling, rely on recovering an accurate correspondence map. Many methods have thus been proposed to tackle this challenging problem from varying perspectives, depending on the downstream application. This state-of-the-art report is geared towards researchers, practitioners, and students seeking to understand recent trends and advances in the field. We categorise developments into three paradigms: spectral methods based on functional maps, combinatorial formulations that impose discrete constraints, and deformation-based methods that directly recover a global alignment. Each school of thought offers different advantages and disadvantages, which we discuss throughout the report. Meanwhile, we highlight the latest developments in each area and suggest new potential research directions. Finally, we provide an overview of emerging challenges and opportunities in this growing field, including the recent use of vision foundation models for zero-shot correspondence and the particularly challenging task of matching partial shapes.

Lennart Bastian, Mohammad Rashed, Nassir Navab et al.

Modeling the rotation of moving objects is a fundamental task in computer vision, yet $SO(3)$ extrapolation still presents numerous challenges: (1) unknown quantities such as the moment of inertia complicate dynamics, (2) the presence of external forces and torques can lead to non-conservative kinematics, and (3) estimating evolving state trajectories under sparse, noisy observations requires robustness. We propose modeling trajectories of noisy pose estimates on the manifold of 3D rotations in a physically and geometrically meaningful way by leveraging Neural Controlled Differential Equations guided with $SO(3)$ Savitzky-Golay paths. Existing extrapolation methods often rely on energy conservation or constant velocity assumptions, limiting their applicability in real-world scenarios involving non-conservative forces. In contrast, our approach is agnostic to energy and momentum conservation while being robust to input noise, making it applicable to complex, non-inertial systems. Our approach is easily integrated as a module in existing pipelines and generalizes well to trajectories with unknown physical parameters. By learning to approximate object dynamics from noisy states during training, our model attains robust extrapolation capabilities in simulation and various real-world settings. Code is available at https://github.com/bastianlb/forecasting-rotational-dynamics

Tony Danjun Wang, Tolga Birdal, Nassir Navab et al.

3D pose estimation from sparse multi-views is a critical task for numerous applications, including action recognition, sports analysis, and human-robot interaction. Optimization-based methods typically follow a two-stage pipeline, first detecting 2D keypoints in each view and then associating these detections across views to triangulate the 3D pose. Existing methods rely on mere pairwise associations to model this correspondence problem, treating global consistency between views (i.e., cycle consistency) as a soft constraint. Yet, reconciling these constraints for multiple views becomes brittle when spurious associations propagate errors. We thus propose COMPOSE, a novel framework that formulates multi-view pose correspondence matching as a hypergraph partitioning problem rather than through pairwise association. While the complexity of the resulting integer linear program grows exponentially in theory, we introduce an efficient geometric pruning strategy to substantially reduce the search space. COMPOSE achieves improvements of up to 23% in average precision over previous optimization-based methods and up to 11% over self-supervised end-to-end learned methods, offering a promising solution to a widely studied problem.

Lennart Bastian, Vincent Bürgin, Ha Young Kim et al.

Thyroid disorders are most commonly diagnosed using high-resolution Ultrasound (US). Longitudinal nodule tracking is a pivotal diagnostic protocol for monitoring changes in pathological thyroid morphology. This task, however, imposes a substantial cognitive load on clinicians due to the inherent challenge of maintaining a mental 3D reconstruction of the organ. We thus present a framework for automated US image slice localization within a 3D shape representation to ease how such sonographic diagnoses are carried out. Our proposed method learns a common latent embedding space between US image patches and the 3D surface of an individual's thyroid shape, or a statistical aggregation in the form of a statistical shape model (SSM), via contrastive metric learning. Using cross-modality registration and Procrustes analysis, we leverage features from our model to register US slices to a 3D mesh representation of the thyroid shape. We demonstrate that our multi-modal registration framework can localize images on the 3D surface topology of a patient-specific organ and the mean shape of an SSM. Experimental results indicate slice positions can be predicted within an average of 1.2 mm of the ground-truth slice location on the patient-specific 3D anatomy and 4.6 mm on the SSM, exemplifying its usefulness for slice localization during sonographic acquisitions. Code is publically available: \href{https://github.com/vuenc/slice-to-shape}{https://github.com/vuenc/slice-to-shape}

Lennart Bastian, Yizheng Xie, Nassir Navab et al.

Non-isometric shape correspondence remains a fundamental challenge in computer vision. Traditional methods using Laplace-Beltrami operator (LBO) eigenmodes face limitations in characterizing high-frequency extrinsic shape changes like bending and creases. We propose a novel approach of combining the non-orthogonal extrinsic basis of eigenfunctions of the elastic thin-shell hessian with the intrinsic ones of the LBO, creating a hybrid spectral space in which we construct functional maps. To this end, we present a theoretical framework to effectively integrate non-orthogonal basis functions into descriptor- and learning-based functional map methods. Our approach can be incorporated easily into existing functional map pipelines across varying applications and is able to handle complex deformations beyond isometries. We show extensive evaluations across various supervised and unsupervised settings and demonstrate significant improvements. Notably, our approach achieves up to 15% better mean geodesic error for non-isometric correspondence settings and up to 45% improvement in scenarios with topological noise.

Tony Danjun Wang, Lennart Bastian, Tobias Czempiel et al.

Surgical domain models improve workflow optimization through automated predictions of each staff member's surgical role. However, mounting evidence indicates that team familiarity and individuality impact surgical outcomes. We present a novel staff-centric modeling approach that characterizes individual team members through their distinctive movement patterns and physical characteristics, enabling long-term tracking and analysis of surgical personnel across multiple procedures. To address the challenge of inter-clinic variability, we develop a generalizable re-identification framework that encodes sequences of 3D point clouds to capture shape and articulated motion patterns unique to each individual. Our method achieves 86.19% accuracy on realistic clinical data while maintaining 75.27% accuracy when transferring between different environments - a 12% improvement over existing methods. When used to augment markerless personnel tracking, our approach improves accuracy by over 50%. Through extensive validation across three datasets and the introduction of a novel workflow visualization technique, we demonstrate how our framework can reveal novel insights into surgical team dynamics and space utilization patterns, advancing methods to analyze surgical workflows and team coordination.

Mustafa Hajij, Lennart Bastian, Sarah Osentoski et al.

We introduce copresheaf topological neural networks (CTNNs), a powerful unifying framework that encapsulates a wide spectrum of deep learning architectures, designed to operate on structured data, including images, point clouds, graphs, meshes, and topological manifolds. While deep learning has profoundly impacted domains ranging from digital assistants to autonomous systems, the principled design of neural architectures tailored to specific tasks and data types remains one of the field's most persistent open challenges. CTNNs address this gap by formulating model design in the language of copresheaves, a concept from algebraic topology that generalizes most practical deep learning models in use today. This abstract yet constructive formulation yields a rich design space from which theoretically sound and practically effective solutions can be derived to tackle core challenges in representation learning, such as long-range dependencies, oversmoothing, heterophily, and non-Euclidean domains. Our empirical results on structured data benchmarks demonstrate that CTNNs consistently outperform conventional baselines, particularly in tasks requiring hierarchical or localized sensitivity. These results establish CTNNs as a principled multi-scale foundation for the next generation of deep learning architectures.

Tony Danjun Wang, Tobias Czempiel, Nassir Navab et al.

Deep neural networks are prone to learning spurious correlations, exploiting dataset-specific artifacts rather than meaningful features for prediction. In surgical operating rooms (OR), these manifest through the standardization of smocks and gowns that obscure robust identifying landmarks, introducing model bias for tasks related to modeling OR personnel. Through gradient-based saliency analysis on two public OR datasets, we reveal that CNN models succumb to such shortcuts, fixating on incidental visual cues such as footwear beneath surgical gowns, distinctive eyewear, or other role-specific identifiers. Avoiding such biases is essential for the next generation of intelligent assistance systems in the OR, which should accurately recognize personalized workflow traits, such as surgical skill level or coordination with other staff members. We address this problem by encoding personnel as 3D point cloud sequences, disentangling identity-relevant shape and motion patterns from appearance-based confounders. Our experiments demonstrate that while RGB and geometric methods achieve comparable performance on datasets with apparent simulation artifacts, RGB models suffer a 12% accuracy drop in realistic clinical settings with decreased visual diversity due to standardizations. This performance gap confirms that geometric representations capture more meaningful biometric features, providing an avenue to developing robust methods of modeling humans in the OR.

Tony Danjun Wang, Christian Heiliger, Nassir Navab et al.

Providing intelligent support to surgical teams is a key frontier in automated surgical scene understanding, with the long-term goal of improving patient outcomes. Developing personalized intelligence for all staff members requires maintaining a consistent state of who is located where for long surgical procedures, which still poses numerous computational challenges. We propose TrackOR, a framework for tackling long-term multi-person tracking and re-identification in the operating room. TrackOR uses 3D geometric signatures to achieve state-of-the-art online tracking performance (+11% Association Accuracy over the strongest baseline), while also enabling an effective offline recovery process to create analysis-ready trajectories. Our work shows that by leveraging 3D geometric information, persistent identity tracking becomes attainable, enabling a critical shift towards the more granular, staff-centric analyses required for personalized intelligent systems in the operating room. This new capability opens up various applications, including our proposed temporal pathway imprints that translate raw tracking data into actionable insights for improving team efficiency and safety and ultimately providing personalized support.

Mario Tuci, Lennart Bastian, Benjamin Dupuis et al.

Providing generalization guarantees for stochastic optimization algorithms is a major challenge in modern learning theory. Recently, several studies highlighted the impact of the geometry of training trajectories on the generalization error, both theoretically and empirically. Among these works, a series of topological generalization bounds have been proposed, relating the generalization error to notions of topological complexity that stem from topological data analysis (TDA). Despite their empirical success, these bounds rely on intricate information-theoretic (IT) terms that can be bounded in specific cases but remain intractable for practical algorithms (such as ADAM), potentially reducing the relevance of the derived bounds. In this paper, we seek to formulate comprehensive and interpretable topological generalization bounds free of intractable mutual information terms. To this end, we introduce a novel learning theoretic framework that departs from the existing strategies via proof techniques rooted in algorithmic stability. By extending an existing notion of \textit{hypothesis set stability}, to \textit{trajectory stability}, we prove that the generalization error of trajectory-stable algorithms can be upper bounded in terms of (i) TDA quantities describing the complexity of the trajectory of the optimizer in the parameter space, and (ii) the trajectory stability parameter of the algorithm. Through a series of experimental evaluations, we demonstrate that the TDA terms in the bound are of great importance, especially as the number of training samples grows. This ultimately forms an explanation of the empirical success of the topological generalization bounds.

Viktoria Ehm, Nafie El Amrani, Yizheng Xie et al.

Finding correspondences between 3D shapes is an important and long-standing problem in computer vision, graphics and beyond. While approaches based on machine learning dominate modern 3D shape matching, almost all existing (learning-based) methods require that at least one of the involved shapes is complete. In contrast, the most challenging and arguably most practically relevant setting of matching partially observed shapes, is currently underexplored. One important factor is that existing datasets contain only a small number of shapes (typically below 100), which are unable to serve data-hungry machine learning approaches, particularly in the unsupervised regime. In addition, the type of partiality present in existing datasets is often artificial and far from realistic. To address these limitations and to encourage research on these relevant settings, we provide a generic and flexible framework for the procedural generation of challenging partial shape matching scenarios. Our framework allows for a virtually infinite generation of partial shape matching instances from a finite set of shapes with complete geometry. Further, we manually create cross-dataset correspondences between seven existing (complete geometry) shape matching datasets, leading to a total of 2543 shapes. Based on this, we propose several challenging partial benchmark settings, for which we evaluate respective state-of-the-art methods as baselines.