Léo Lebrat

Léo Lebrat, Rodrigo Santa Cruz, Remi Chierchia et al.

Wound management poses a significant challenge, particularly for bedridden patients and the elderly. Accurate diagnostic and healing monitoring can significantly benefit from modern image analysis, providing accurate and precise measurements of wounds. Despite several existing techniques, the shortage of expansive and diverse training datasets remains a significant obstacle to constructing machine learning-based frameworks. This paper introduces Syn3DWound, an open-source dataset of high-fidelity simulated wounds with 2D and 3D annotations. We propose baseline methods and a benchmarking framework for automated 3D morphometry analysis and 2D/3D wound segmentation.

Rodrigo Santa Cruz, Léo Lebrat, Darren Fu et al.

The problem of Cortical Surface Reconstruction from magnetic resonance imaging has been traditionally addressed using lengthy pipelines of image processing techniques like FreeSurfer, CAT, or CIVET. These frameworks require very long runtimes deemed unfeasible for real-time applications and unpractical for large-scale studies. Recently, supervised deep learning approaches have been introduced to speed up this task cutting down the reconstruction time from hours to seconds. Using the state-of-the-art CorticalFlow model as a blueprint, this paper proposes three modifications to improve its accuracy and interoperability with existing surface analysis tools, while not sacrificing its fast inference time and low GPU memory consumption. First, we employ a more accurate ODE solver to reduce the diffeomorphic mapping approximation error. Second, we devise a routine to produce smoother template meshes avoiding mesh artifacts caused by sharp edges in CorticalFlow's convex-hull based template. Last, we recast pial surface prediction as the deformation of the predicted white surface leading to a one-to-one mapping between white and pial surface vertices. This mapping is essential to many existing surface analysis tools for cortical morphometry. We name the resulting method CorticalFlow$^{++}$. Using large-scale datasets, we demonstrate the proposed changes provide more geometric accuracy and surface regularity while keeping the reconstruction time and GPU memory requirements almost unchanged.

Frédéric de Gournay, Jonas Kahn, Léo Lebrat

This paper aims at determining under which conditions the semi-discrete optimal transport is twice differentiable with respect to the parameters of the discrete measure and exhibits numerical applications. The discussion focuses on minimal conditions on the background measure to ensure differentiability. We provide numerical illustrations in stippling and blue noise problems.

Frédéric de Gournay, Jonas Kahn, Léo Lebrat et al.

We propose a fast and scalable algorithm to project a given density on a set of structured measures defined over a compact 2D domain. The measures can be discrete or supported on curves for instance. The proposed principle and algorithm are a natural generalization of previous results revolving around the generation of blue-noise point distributions, such as Lloyd's algorithm or more advanced techniques based on power diagrams. We analyze the convergence properties and propose new approaches to accelerate the generation of point distributions. We also design new algorithms to project curves onto spaces of curves with bounded length and curvature or speed and acceleration. We illustrate the algorithm's interest through applications in advanced sampling theory, non-photorealistic rendering and path planning.

Frédéric de Gournay, Jonas Kahn, Léo Lebrat

This paper deals with the 3/4-discrete 2-Wasserstein optimal transport between two measures, where one is supported by a set of segment and the other one is supported by a set of Dirac masses. We select the most suitable optimization procedure that computes the optimal transport and provide numerical examples of approximation of cloud data by segments.

Léo Lebrat, Rodrigo Santa Cruz, Frédéric de Gournay et al.

In this paper we introduce CorticalFlow, a new geometric deep-learning model that, given a 3-dimensional image, learns to deform a reference template towards a targeted object. To conserve the template mesh's topological properties, we train our model over a set of diffeomorphic transformations. This new implementation of a flow Ordinary Differential Equation (ODE) framework benefits from a small GPU memory footprint, allowing the generation of surfaces with several hundred thousand vertices. To reduce topological errors introduced by its discrete resolution, we derive numeric conditions which improve the manifoldness of the predicted triangle mesh. To exhibit the utility of CorticalFlow, we demonstrate its performance for the challenging task of brain cortical surface reconstruction. In contrast to current state-of-the-art, CorticalFlow produces superior surfaces while reducing the computation time from nine and a half minutes to one second. More significantly, CorticalFlow enforces the generation of anatomically plausible surfaces; the absence of which has been a major impediment restricting the clinical relevance of such surface reconstruction methods.

Remi Chierchia, Léo Lebrat, David Ahmedt-Aristizabal et al.

Wound care is often challenged by the economic and logistical burdens that consistently afflict patients and hospitals worldwide. In recent decades, healthcare professionals have sought support from computer vision and machine learning algorithms. In particular, wound segmentation has gained interest due to its ability to provide professionals with fast, automatic tissue assessment from standard RGB images. Some approaches have extended segmentation to 3D, enabling more complete and precise healing progress tracking. However, inferring multi-view consistent 3D structures from 2D images remains a challenge. In this paper, we evaluate WoundNeRF, a NeRF SDF-based method for estimating robust wound segmentations from automatically generated annotations. We demonstrate the potential of this paradigm in recovering accurate segmentations by comparing it against state-of-the-art Vision Transformer networks and conventional rasterisation-based algorithms. The code will be released to facilitate further development in this promising paradigm.

Remi Chierchia, Léo Lebrat, David Ahmedt-Aristizabal et al.

Neural Surface Reconstruction has become a standard methodology for indoor 3D reconstruction, with Signed Distance Functions (SDFs) proving particularly effective for representing scene geometry. A variety of applications require a detailed understanding of the scene context, driving the need for object-level semantic signals. While recent methods successfully integrate semantic labels, they often inherit the slow training time and limited scalability of multi-SDF learning. In this paper, we introduce FSTM, a unified approach for learning geometry and semantics through a two-step process: a geometry warm-up using RGB inputs and geometric cues, followed by semantic field estimation. By first optimising geometry without semantic supervision, we observe substantial improvements compared to the standard joint optimisation. Rather than relying on specialised modules or complex multi-SDF designs, FSTM shows that a streamlined formulation is sufficient to achieve strong geometric and semantic reconstructions. Experiments on both synthetic and real-world indoor datasets show that our method outperforms multi-SDF approaches. It trains 2.3x faster on Replica, improves robustness to real-world imperfections on ScanNet++, and achieves higher recall by recovering the surfaces of more objects in the scene. The code will be made available at https://remichierchia.github.io/FSTM.

Ines Vati, Pierrick Bourgeat, Rodrigo Santa Cruz et al.

We introduce neural cortical maps, a continuous and compact neural representation for cortical feature maps, as an alternative to traditional discrete structures such as grids and meshes. It can learn from meshes of arbitrary size and provide learnt features at any resolution. Neural cortical maps enable efficient optimization on the sphere and achieve runtimes up to 30 times faster than classic barycentric interpolation (for the same number of iterations). As a proof of concept, we investigate rigid registration of cortical surfaces and propose NC-Reg, a novel iterative algorithm that involves the use of neural cortical feature maps, gradient descent optimization and a simulated annealing strategy. Through ablation studies and subject-to-template experiments, our method demonstrates sub-degree accuracy ($<1^\circ$ from the global optimum), and serves as a promising robust pre-alignment strategy, which is critical in clinical settings.

Remi Chierchia, Rodrigo Santa Cruz, Léo Lebrat et al.

Managing chronic wounds remains a major healthcare challenge, with clinical assessment often relying on subjective and time-consuming manual documentation methods. Although 2D digital videometry frameworks aided the measurement process, these approaches struggle with perspective distortion, a limited field of view, and an inability to capture wound depth, especially in anatomically complex or curved regions. To overcome these limitations, we present Wound3DAssist, a practical framework for 3D wound assessment using monocular consumer-grade videos. Our framework generates accurate 3D models from short handheld smartphone video recordings, enabling non-contact, automatic measurements that are view-independent and robust to camera motion. We integrate 3D reconstruction, wound segmentation, tissue classification, and periwound analysis into a modular workflow. We evaluate Wound3DAssist across digital models with known geometry, silicone phantoms, and real patients. Results show that the framework supports high-quality wound bed visualization, millimeter-level accuracy, and reliable tissue composition analysis. Full assessments are completed in under 20 minutes, demonstrating feasibility for real-world clinical use.

Léo Lebrat, Rodrigo Santa Cruz, Clinton Fookes et al.

Recent advances in geometric deep-learning introduce complex computational challenges for evaluating the distance between meshes. From a mesh model, point clouds are necessary along with a robust distance metric to assess surface quality or as part of the loss function for training models. Current methods often rely on a uniform random mesh discretization, which yields irregular sampling and noisy distance estimation. In this paper we introduce MongeNet, a fast and optimal transport based sampler that allows for an accurate discretization of a mesh with better approximation properties. We compare our method to the ubiquitous random uniform sampling and show that the approximation error is almost half with a very small computational overhead.

Rodrigo Santa Cruz, Léo Lebrat, Pierrick Bourgeat et al.

Brain morphometry from magnetic resonance imaging (MRI) is a consolidated biomarker for many neurodegenerative diseases. Recent advances in this domain indicate that deep convolutional neural networks can infer morphometric measurements within a few seconds. Nevertheless, the accuracy of the devised model for insightful bio-markers (mean curvature and thickness) remains unsatisfactory. In this paper, we propose a more accurate and efficient neural network model for brain morphometry named HerstonNet. More specifically, we develop a 3D ResNet-based neural network to learn rich features directly from MRI, design a multi-scale regression scheme by predicting morphometric measures at feature maps of different resolutions, and leverage a robust optimization method to avoid poor quality minima and reduce the prediction variance. As a result, HerstonNet improves the existing approach by 24.30% in terms of intraclass correlation coefficient (agreement measure) to FreeSurfer silver-standards while maintaining a competitive run-time.