Abstracts

Pierre Louis Antonsanti How to Register a Live onto a Liver ? Partial Matching in the Space of Varifolds

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 an asymmetric data dissimilarity term applicable to 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. 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 first illustrate the diffeomorphic registrations with partial matching on sets of synthetic 3D curves and real vascular trees. We qualitatively show with two real vascular trees that despite the target's complexity, partial matching guides consistent registrations of the atlas. We also 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. Evaluating the LDDMM guided by partial matching of the liver surfaces on the volume registrations with points of interest for the physicians, we obtain an average distance of 6.21mm for vessels bifurcations and 5.56mm for tumors landmarks.

 Sylvain Arguillère ResNet-LDDMM: A new LDDMM-like Framework Using Deep Residual Networks

In this talk, we introduce a new kind of possible registration through diffeomorphisms, where the velocity fields are generated by a simple residual neural network in two or three dimensions. We will discuss the geometric interpretation of such a network, and its advantage compared to traditional LDDMM. We will also discuss its limits and drawbacks, both theoretical and empirical.

Malte Brunn High-Speed Image Registration for Large-Scale Applications with CLAIRE

3D image registration is a fundamental and computationally expensive operation in biomedical image analysis. We present an effective Gauss-Newton-Krylov solver for large deformation diffeomorphic registration of two images. Our work [1] extends the publicly available CLAIRE library [2, 3] to a multi-node multi-graphics processing units (GPUs) environment. We introduce several novel algorithmic modifications that significantly improve computational performance on the target architecture and allow us to tackle large-scale applications in biomedical imaging. Only few implementations of large deformation diffeomorphic registration packages are optimized for GPUs. Our contributions are the following: (i) efficient schemes for preconditioning the reduced-space Hessian system to further accelerate each Newton iteration using an approximate multi-level inverse Hessian; (ii) highly-optimized multi-node multi-GPU implementation exploiting direct device communication (i.e., CUDA-aware Message Passing Interface) for the main computational kernels - interpolation, high-order finite difference operators and Fast-Fourier-Transform; (iii) algorithmic options to adapt for available hardware resources to optimize utilization and runtime; and (iv) comparison with state-of-the-art CPU and GPU implementations an previous implementations of CLAIRE. We demonstrate the efficiency and scalability of our implementation on multiple NVIDIA Tesla V100 GPUs for a variety of test-cases, including high-resolution real-world biomedical imaging data for neuroimaging datasets of humans and CLARITY imaging datasets for murine neuroimaging. Most notably, we demonstrate that we can solve clinically relevant problem sizes (50M unknowns) in less than 5s on a single NVIDIA Tesla V100 and less than 3.5s on modern consumer grade hardware, with a peak performance speedup of 2x compared to the state-of-the-art [3]. We show scalability results for images with resolutions up to 2048³ (25B unknowns; ~152x larger than the single GPU implementation) on 64 nodes with 256 GPUs on TACC's Longhorn system.

[1] M. Brunn et al. "Multi-node multi-gpu diffeomorphic image registration for large-scale imaging problems", Conference on Supercomputing 2020.
[2] A. Mang and G. Biros, "Constrained large deformation diffeomorphic image registration (CLAIRE)", 2019, https://andreasmang.github.io/claire
[3] M. Brunn et al., "Fast GPU 3D diffeomorphic image registration", Journal of Parallel and Distributed Computing 149 (2021): 149-162.

Ninon Burgos On the interplay between medical image registration and synthesis

Many medical image synthesis works have for objective to improve subsequent image processing steps such as registration. For example, computed tomography (CT) images can be synthesised from magnetic resonance (MR) images to ease registration between MR and X-ray images. Inversely, registration can be used to synthesise medical images of a particular modality from images of another modality. This can be done using an atlas composed of a pair of images: an image of the source modality and an image of the target modality. The atlas' source image is registered to the subject's source image and the resulting transformation is applied to the atlas' target image to generate the subject's target image.
This presentation will describe in more detail the interplay that exists between medical image registration and synthesis. It will take as use case the synthesis/registration of CT and MR images in the brain, head & neck, and pelvis regions.

Noémie Debroux Multiscale Image Registration

In the seminal paper  E. Tadmor, S. Nezzar and L. Vese, {\it{A multiscale image representation using hierarchical (BV, L^2) decompositions}}, Multiscale Model. Simul., 2(4), 554--579, (2004), the authors introduce a multiscale image decomposition model providing a hierarchical decomposition of a given image into the sum of scale-varying components. In line with this framework, we extend the approach to the case of registration, task which consists of mapping salient features of an image onto the corresponding ones in another, the underlying goal being to obtain such a kind of hierarchical decomposition of the deformation relating the two considered images (from the coarser one that encodes the main structural/geometrical deformation, to the more refined one). To achieve this goal, we introduce a functional minimisation problem in a hyperelasticity setting by viewing the shapes to be matched as Ogden materials. This approach is complemented by hard constraints on the L^∞-norm of both the Jacobian and its inverse, ensuring that the deformation is a bi-Lipschitz homeomorphism. Theoretical results emphasising the mathematical soundness of the model are provided, among which the existence of minimisers, a $\Gamma$-convergence result and an ana\-lysis of a suitable numerical algorithm, along with numerical simulations demonstrating the ability of the model to produce accurate hierarchical representations of deformations.

Jean Feydy Fast geometric libraries for vision and data sciences

From 3D point clouds to high-dimensional samples, sparse representations have a key position in the computer vision toolbox. They complement 2D images and 3D volumes effectively, enabling fast geometric computations for e.g. shape registration.
In this talk, I will present extensions for PyTorch, NumPy, Matlab and R that speed up fundamental computations on (generalized) point clouds by several orders of magnitude — compared with PyTorch, TF and JAX GPU baselines. These software tools allow researchers to break through major computational bottlenecks in the field and have been downloaded more than 100k times over the last few years.
The presentation may be of interest to all researchers who deal with point clouds, time series and segmentation maps, with a special focus on:
1. Fast and scalable computations with (generalized) distance matrices.
2. Efficient and robust solvers for the optimal transport (= “Earth Mover’s”) problem.
3. Applications to shape analysis and geometric deep learning, with a case study on the “pixel-perfect” registration of lung vessel trees.

- “Geometric data analysis, beyond convolutions”: https://www.jeanfeydy.com/geometric_data_analysis.pdf
- “Fast geometric learning with symbolic matrices”: http://jeanfeydy.com/Papers/KeOps_NeurIPS_2020.pdf
- KeOps library (geometric computations): http://kernel-operations.io/keops/index.html
- GeomLoss library (optimal transport): https://www.kernel-operations.io/geomloss/

Anton François An implementation of metamorphosis and its limits

We recently proposed an implementation of both Large Deformation Diffeomorphic Metric Mapping (LDDMM) and Metamorphosis image registration using a semi-Lagrangian scheme for geodesic shooting. Metamorphosis extends the image diffeomorphic registration taking into account the topological differences. In this talk we will first present the PyTorch implementation and some applications of the method. We will also discuss the limits of the method on how it fails to disentangle intensity changes from image variation and actual topological additions. We will finally present the locally weighted metamorphosis using prior segmentation masks which is an ongoing work.

Hicham Janati Optimal transport in brain imaging: modeling inter-subject spatial variability.

Magnetoencephalography and electroencephalography (M/EEG) are non-invasive modalities that measure the weak electromagnetic fields generated by neural activity. Estimating the location and magnitude of the current sources that generated these electromagnetic fields is a challenging ill-posed inverse problem known as source imaging. We propose to jointly solve the inverse problems of multiple subjects in a single multi-task regression with a binding regularization. This regularization is defined through an Optimal transport penalty that promotes spatial proximity between sources across subjects. We show that a problem combining OT with sparsifying priors can be optimized efficiently and lead to a decrease of the source localization error by up to 4 mm per source compared to individual solutions. Our analysis of a multimodal dataset shows how multi-subject source localization closes the gap between MEG and fMRI for brain mapping.