Vincent Jugnon

Laurent Demanet, Vincent Jugnon

This note formulates a deterministic recovery result for vectors $x$ from quadratic measurements of the form $(Ax)_i \overline{(Ax)_j}$ for some left-invertible $A$. Recovery is exact, or stable in the noisy case, when the couples $(i,j)$ are chosen as edges of a well-connected graph. One possible way of obtaining the solution is as a feasible point of a simple semidefinite program. Furthermore, we show how the proportionality constant in the error estimate depends on the spectral gap of a data-weighted graph Laplacian. Such quadratic measurements have found applications in phase retrieval, angular synchronization, and more recently interferometric waveform inversion.

Pierre-Louis Antonsanti, Thomas Benseghir, Vincent Jugnon et al.

Partial shapes correspondences is a problem that often occurs in computer vision (occlusion, evolution in time...). In medical imaging, data may come from different modalities and be acquired under different conditions which leads to variations in shapes and topologies. In this paper we use an asymmetric data dissimilarity term applicable to various geometric shapes like sets of curves or surfaces, assessing the embedding of a shape into another one without relying on correspondences. It is designed as a data attachment for the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework, allowing to compute a meaningful deformation of one shape onto a subset of the other. We refine it in order to control the resulting non-rigid deformations and provide consistent deformations of the shapes along with their ambient space. We show that partial matching can be used for robust multi-modal liver registration between a Computed Tomography (CT) volume and a Cone Beam Computed Tomography (CBCT) volume. The 3D imaging of the patient CBCT at point of care that we call live is truncated while the CT pre-intervention provides a full visualization of the liver. The proposed method allows the truncated surfaces from CBCT to be aligned non-rigidly, yet realistically, with surfaces from CT with an average distance of 2.6mm(+/- 2.2). The generated deformations extend consistently to the liver volume, and are evaluated on points of interest for the physicians, with an average distance of 5.8mm (+/- 2.7) for vessels bifurcations and 5.13mm (+/- 2.5) for tumors landmarks. Such multi-modality volumes registrations would help the physicians in the perspective of navigating their tools in the patient's anatomy to locate structures that are hardly visible in the CBCT used during their procedures. Our code is available at https://github.com/plantonsanti/PartialMatchingVarifolds.

Gauthier Miralles, Loïc Le Folgoc, Vincent Jugnon et al.

In interventional radiology, Cone-Beam Computed Tomography (CBCT) is a helpful imaging modality that provides guidance to practicians during minimally invasive procedures. CBCT differs from traditional Computed Tomography (CT) due to its limited reconstructed field of view, specific artefacts, and the intra-arterial administration of contrast medium. While CT benefits from abundant publicly available annotated datasets, interventional CBCT data remain scarce and largely unannotated, with existing datasets focused primarily on radiotherapy applications. To address this limitation, we leverage a proprietary collection of unannotated interventional CBCT scans in conjunction with annotated CT data, employing domain adaptation techniques to bridge the modality gap and enhance liver segmentation performance on CBCT. We propose a novel unsupervised domain adaptation (UDA) framework based on the formalism of Margin Disparity Discrepancy (MDD), which improves target domain performance through a reformulation of the original MDD optimization framework. Experimental results on CT and CBCT datasets for liver segmentation demonstrate that our method achieves state-of-the-art performance in UDA, as well as in the few-shot setting.

Gonzalo Iñaki Quintana, Laurence Vancamberg, Vincent Jugnon et al.

This work studies the relationship between Contrastive Learning and Domain Adaptation from a theoretical perspective. The two standard contrastive losses, NT-Xent loss (Self-supervised) and Supervised Contrastive loss, are related to the Class-wise Mean Maximum Discrepancy (CMMD), a dissimilarity measure widely used for Domain Adaptation. Our work shows that minimizing the contrastive losses decreases the CMMD and simultaneously improves class-separability, laying the theoretical groundwork for the use of Contrastive Learning in the context of Domain Adaptation. Due to the relevance of Domain Adaptation in medical imaging, we focused the experiments on mammography images. Extensive experiments on three mammography datasets - synthetic patches, clinical (real) patches, and clinical (real) images - show improved Domain Adaptation, class-separability, and classification performance, when minimizing the Supervised Contrastive loss.

Pierre-Louis Antonsanti, Joan Glaunès, Thomas Benseghir et al.

In computer vision and medical imaging, the problem of matching structures finds numerous applications from automatic annotation to data reconstruction. The data however, while corresponding to the same anatomy, are often very different in topology or shape and might only partially match each other. We introduce a new asymmetric data dissimilarity term for various geometric shapes like sets of curves or surfaces. This term is based on the Varifold shape representation and assesses the embedding of a shape into another one without relying on correspondences between points. It is designed as data attachment for the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework, allowing to compute meaningful deformation of one shape onto a subset of the other. Registrations are illustrated on sets of synthetic 3D curves, real vascular trees and livers' surfaces from two different modalities: Computed Tomography (CT) and Cone Beam Computed Tomography (CBCT). All experiments show that this data dissimilarity term leads to coherent partial matching despite the topological differences.

Pierre-Louis Antonsanti, Thomas Benseghir, Vincent Jugnon et al.

Automatic annotation of anatomical structures can help simplify workflow during interventions in numerous clinical applications but usually involves a large amount of annotated data. The complexity of the labeling task, together with the lack of representative data, slows down the development of robust solutions. In this paper, we propose a solution requiring very few annotated cases to label 3D pelvic arterial trees of patients with benign prostatic hyperplasia. We take advantage of Large Deformation Diffeomorphic Metric Mapping (LDDMM) to perform registration based on meaningful deformations from which we build an atlas. Branch pairing is then computed from the atlas to new cases using optimal transport to ensure one-to-one correspondence during the labeling process. To tackle topological variations in the tree, which usually degrades the performance of atlas-based techniques, we propose a simple bottom-up label assignment adapted to the pelvic anatomy. The proposed method achieves 97.6\% labeling precision with only 5 cases for training, while in comparison learning-based methods only reach 82.2\% on such small training sets.