arXiv subjects

Florian Bernard

Publications and source records attributed to Florian Bernard.

At least 37 records · Page 2Linked to original sources

arXiv2025

TwoSquared: 4D Generation from 2D Image Pairs

Despite the astonishing progress in generative AI, 4D dynamic object generation remains an open challenge. With limited high-quality training data and heavy computing requirements, the combination of hallucinating unseen geometry together with unseen movement poses great challenges to generative models. In this work, we propose TwoSquared as a method to obtain a 4D physically plausible sequence starting from only two 2D RGB images corresponding to the beginning and end of the action. Instead of directly solving the 4D generation problem, TwoSquared decomposes the problem into two steps: 1) an image-to-3D module generation based on the existing generative model trained on high-quality 3D assets, and 2) a physically inspired deformation module to predict intermediate movements. To this end, our method does not require templates or object-class-specific prior knowledge and can take in-the-wild images as input. In our experiments, we demonstrate that TwoSquared is capable of producing texture-consistent and geometry-consistent 4D sequences only given 2D images.

cs.CV↗

arXiv2025

Abdominal aortic aneurysm wall stress: A 7-line code in MATLAB and a one-click software application

An abdominal aortic aneurysm (AAA) is a life-threatening condition characterized by the irreversible dilation of the lower aorta, usually detected incidentally during imaging for other health issues. Current clinical practice for managing AAA relies on a one-size-fits-all approach, based on the aneurysm's maximum diameter and growth rate, which can lead to underestimation or overestimation of AAA rupture risk. Patient-specific AAA wall stress, computed using biomechanical models derived from medical images without needing patient-specific material properties, has been widely investigated for developing individualized AAA rupture risk predictors. Therefore, AAA wall stress, determined reliably and quickly, has the potential to enhance patient-specific treatment plans. This paper presents a 7-line code, written in MATLAB using the Partial Differential Equation Toolbox, for AAA wall stress computations via finite element analysis. The code takes AAA wall geometry as input and outputs stress components over the AAA wall domain. Additionally, we present a one-click standalone software application for AAA wall stress computation, developed based on our 7-line code using MATLAB Compiler. After verification, we used our code to compute AAA wall stress in ten patients. Our analysis indicated that the 99th percentile of maximum principal stress across all patients ranged from 0.307 MPa to 0.466 MPa, with an average of 0.380 MPa and a standard deviation of 0.048 MPa. Moreover, for every case, the MATLAB simulation time was less than a minute on a laptop workstation.

cs.CE↗

arXiv2025

4Deform: Neural Surface Deformation for Robust Shape Interpolation

Generating realistic intermediate shapes between non-rigidly deformed shapes is a challenging task in computer vision, especially with unstructured data (e.g., point clouds) where temporal consistency across frames is lacking, and topologies are changing. Most interpolation methods are designed for structured data (i.e., meshes) and do not apply to real-world point clouds. In contrast, our approach, 4Deform, leverages neural implicit representation (NIR) to enable free topology changing shape deformation. Unlike previous mesh-based methods that learn vertex-based deformation fields, our method learns a continuous velocity field in Euclidean space. Thus, it is suitable for less structured data such as point clouds. Additionally, our method does not require intermediate-shape supervision during training; instead, we incorporate physical and geometrical constraints to regularize the velocity field. We reconstruct intermediate surfaces using a modified level-set equation, directly linking our NIR with the velocity field. Experiments show that our method significantly outperforms previous NIR approaches across various scenarios (e.g., noisy, partial, topology-changing, non-isometric shapes) and, for the first time, enables new applications like 4D Kinect sequence upsampling and real-world high-resolution mesh deformation.

cs.CV↗

arXiv2025

Towards Full Automation of Geometry Extraction for Biomechanical Analysis of Abdominal Aortic Aneurysm; Neural Network-Based versus Classical Methodologies

Background: For the clinical adoption of stress-based rupture risk estimation in abdominal aortic aneurysms (AAAs), a fully automated pipeline, from clinical imaging to biomechanical stress computation, is essential. To this end, we investigated the impact of AI-based image segmentation methods on stress computation results in the walls of AAAs. We compared wall stress distributions and magnitudes calculated from geometry models obtained from classical semi-automated segmentation versus automated neural network-based segmentation. Method: 16 different AAA contrast-enhanced computed tomography (CT) images were semi-automatically segmented by an analyst, taking between 15 and 40 minutes of human effort per patient, depending on image quality. The same images were automatically segmented using PRAEVAorta2 commercial software by NUREA (https://www.nurea-soft.com/), developed based on artificial intelligence (AI) algorithms, and automatically post-processed with an in-house MATLAB code, requiring only 1-2 minutes of computer time per patient. Aneurysm wall stress calculations were automatically performed using the BioPARR software (https://bioparr.mech.uwa.edu.au/). Results: Compared to the classical semi-automated segmentation, the automatic neural network-based segmentation leads to equivalent stress distributions, and slightly higher peak and 99th percentile maximum principal stress values. However, our statistical analysis indicated that the differences in AAA wall stress obtained using the two segmentation methods are not statistically significant and fall well within the typical range of inter-analyst and intra-analyst variability. Conclusions: Our findings are a steppingstone toward a fully automated pipeline for biomechanical analysis of AAAs, starting with CT scans and concluding with wall stress assessment.

cs.CE↗

arXiv2025

Implicit Neural Surface Deformation with Explicit Velocity Fields

In this work, we introduce the first unsupervised method that simultaneously predicts time-varying neural implicit surfaces and deformations between pairs of point clouds. We propose to model the point movement using an explicit velocity field and directly deform a time-varying implicit field using the modified level-set equation. This equation utilizes an iso-surface evolution with Eikonal constraints in a compact formulation, ensuring the integrity of the signed distance field. By applying a smooth, volume-preserving constraint to the velocity field, our method successfully recovers physically plausible intermediate shapes. Our method is able to handle both rigid and non-rigid deformations without any intermediate shape supervision. Our experimental results demonstrate that our method significantly outperforms existing works, delivering superior results in both quality and efficiency.

cs.CV↗

arXiv2024

DiscoMatch: Fast Discrete Optimisation for Geometrically Consistent 3D Shape Matching

In this work we propose to combine the advantages of learningbased and combinatorial formalisms for 3D shape matching. While learningbased methods lead to state-of-the-art matching performance, they do not ensure geometric consistency, so that obtained matchings are locally non-smooth. On the contrary, axiomatic, optimisation-based methods allow to take geometric consistency into account by explicitly constraining the space of valid matchings. However, existing axiomatic formalisms do not scale to practically relevant problem sizes, and require user input for the initialisation of non-convex optimisation problems. We work towards closing this gap by proposing a novel combinatorial solver that combines a unique set of favourable properties: our approach (i) is initialisation free, (ii) is massively parallelisable and powered by a quasi-Newton method, (iii) provides optimality gaps, and (iv) delivers improved matching quality with decreased runtime and globally optimal results for many instances.

cs.CV↗

arXiv2024

$C^2M^3$: Cycle-Consistent Multi-Model Merging

In this paper, we present a novel data-free method for merging neural networks in weight space. Differently from most existing works, our method optimizes for the permutations of network neurons globally across all layers. This allows us to enforce cycle consistency of the permutations when merging $N \geq 3$ models, allowing circular compositions of permutations to be computed without accumulating error along the path. We qualitatively and quantitatively motivate the need for such a constraint, showing its benefits when merging sets of models in scenarios spanning varying architectures and datasets. We finally show that, when coupled with activation renormalization, our approach yields the best results in the task.

cs.LG↗

arXiv2024

Synchronous Diffusion for Unsupervised Smooth Non-Rigid 3D Shape Matching

Most recent unsupervised non-rigid 3D shape matching methods are based on the functional map framework due to its efficiency and superior performance. Nevertheless, respective methods struggle to obtain spatially smooth pointwise correspondences due to the lack of proper regularisation. In this work, inspired by the success of message passing on graphs, we propose a synchronous diffusion process which we use as regularisation to achieve smoothness in non-rigid 3D shape matching problems. The intuition of synchronous diffusion is that diffusing the same input function on two different shapes results in consistent outputs. Using different challenging datasets, we demonstrate that our novel regularisation can substantially improve the state-of-the-art in shape matching, especially in the presence of topological noise.

cs.CV↗

arXiv2024

Partial-to-Partial Shape Matching with Geometric Consistency

Finding correspondences between 3D shapes is an important and long-standing problem in computer vision, graphics and beyond. A prominent challenge are partial-to-partial shape matching settings, which occur when the shapes to match are only observed incompletely (e.g. from 3D scanning). Although partial-to-partial matching is a highly relevant setting in practice, it is rarely explored. Our work bridges the gap between existing (rather artificial) 3D full shape matching and partial-to-partial real-world settings by exploiting geometric consistency as a strong constraint. We demonstrate that it is indeed possible to solve this challenging problem in a variety of settings. For the first time, we achieve geometric consistency for partial-to-partial matching, which is realized by a novel integer non-linear program formalism building on triangle product spaces, along with a new pruning algorithm based on linear integer programming. Further, we generate a new inter-class dataset for partial-to-partial shape-matching. We show that our method outperforms current SOTA methods on both an established intra-class dataset and our novel inter-class dataset.

cs.CV↗

arXiv2024

Isometric Multi-Shape Matching

Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence methods aim to find a solution between pairs of shapes, even if multiple instances of the same class are available. While isometries are often studied in shape correspondence problems, they have not been considered explicitly in the multi-matching setting. This paper closes this gap by proposing a novel optimisation formulation for isometric multi-shape matching. We present a suitable optimisation algorithm for solving our formulation and provide a convergence and complexity analysis. Our algorithm obtains multi-matchings that are by construction provably cycle-consistent. We demonstrate the superior performance of our method on various datasets and set the new state-of-the-art in isometric multi-shape matching.

cs.CV↗

arXiv2024

SIGMA: Scale-Invariant Global Sparse Shape Matching

We propose a novel mixed-integer programming (MIP) formulation for generating precise sparse correspondences for highly non-rigid shapes. To this end, we introduce a projected Laplace-Beltrami operator (PLBO) which combines intrinsic and extrinsic geometric information to measure the deformation quality induced by predicted correspondences. We integrate the PLBO, together with an orientation-aware regulariser, into a novel MIP formulation that can be solved to global optimality for many practical problems. In contrast to previous methods, our approach is provably invariant to rigid transformations and global scaling, initialisation-free, has optimality guarantees, and scales to high resolution meshes with (empirically observed) linear time. We show state-of-the-art results for sparse non-rigid matching on several challenging 3D datasets, including data with inconsistent meshing, as well as applications in mesh-to-point-cloud matching.

cs.CV↗

arXiv2024

Neural Implicit Representations for Physical Parameter Inference from a Single Video

Neural networks have recently been used to analyze diverse physical systems and to identify the underlying dynamics. While existing methods achieve impressive results, they are limited by their strong demand for training data and their weak generalization abilities to out-of-distribution data. To overcome these limitations, in this work we propose to combine neural implicit representations for appearance modeling with neural ordinary differential equations (ODEs) for modelling physical phenomena to obtain a dynamic scene representation that can be identified directly from visual observations. Our proposed model combines several unique advantages: (i) Contrary to existing approaches that require large training datasets, we are able to identify physical parameters from only a single video. (ii) The use of neural implicit representations enables the processing of high-resolution videos and the synthesis of photo-realistic images. (iii) The embedded neural ODE has a known parametric form that allows for the identification of interpretable physical parameters, and (iv) long-term prediction in state space. (v) Furthermore, the photo-realistic rendering of novel scenes with modified physical parameters becomes possible.

cs.CV↗

arXiv2024

Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation

Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified framework to predict both point-wise correspondences and shape interpolation between 3D shapes. To this end, we combine the deep functional map framework with classical surface deformation models to map shapes in both spectral and spatial domains. On the one hand, by incorporating spatial maps, our method obtains more accurate and smooth point-wise correspondences compared to previous functional map methods for shape matching. On the other hand, by introducing spectral maps, our method gets rid of commonly used but computationally expensive geodesic distance constraints that are only valid for near-isometric shape deformations. Furthermore, we propose a novel test-time adaptation scheme to capture both pose-dominant and shape-dominant deformations. Using different challenging datasets, we demonstrate that our method outperforms previous state-of-the-art methods for both shape matching and interpolation, even compared to supervised approaches.

cs.CV↗

arXiv2023

FIRe: Fast Inverse Rendering using Directional and Signed Distance Functions

Neural 3D implicit representations learn priors that are useful for diverse applications, such as single- or multiple-view 3D reconstruction. A major downside of existing approaches while rendering an image is that they require evaluating the network multiple times per camera ray so that the high computational time forms a bottleneck for downstream applications. We address this problem by introducing a novel neural scene representation that we call the directional distance function (DDF). To this end, we learn a signed distance function (SDF) along with our DDF model to represent a class of shapes. Specifically, our DDF is defined on the unit sphere and predicts the distance to the surface along any given direction. Therefore, our DDF allows rendering images with just a single network evaluation per camera ray. Based on our DDF, we present a novel fast algorithm (FIRe) to reconstruct 3D shapes given a posed depth map. We evaluate our proposed method on 3D reconstruction from single-view depth images, where we empirically show that our algorithm reconstructs 3D shapes more accurately and it is more than 15 times faster (per iteration) than competing methods.

cs.CV↗

arXiv2023

Structured Prediction Problem Archive

Structured prediction problems are one of the fundamental tools in machine learning. In order to facilitate algorithm development for their numerical solution, we collect in one place a large number of datasets in easy to read formats for a diverse set of problem classes. We provide archival links to datasets, description of the considered problems and problem formats, and a short summary of problem characteristics including size, number of instances etc. For reference we also give a non-exhaustive selection of algorithms proposed in the literature for their solution. We hope that this central repository will make benchmarking and comparison to established works easier. We welcome submission of interesting new datasets and algorithms for inclusion in our archive.

cs.LG↗

arXiv2023

Non-Negative Spherical Relaxations for Universe-Free Multi-Matching and Clustering

We propose a novel non-negative spherical relaxation for optimization problems over binary matrices with injectivity constraints, which in particular has applications in multi-matching and clustering. We relax respective binary matrix constraints to the (high-dimensional) non-negative sphere. To optimize our relaxed problem, we use a conditional power iteration method to iteratively improve the objective function, while at same time sweeping over a continuous scalar parameter that is (indirectly) related to the universe size (or number of clusters). Opposed to existing procedures that require to fix the integer universe size before optimization, our method automatically adjusts the analogous continuous parameter. Furthermore, while our approach shares similarities with spectral multi-matching and spectral clustering, our formulation has the strong advantage that we do not rely on additional post-processing procedures to obtain binary results. Our method shows compelling results in various multi-matching and clustering settings, even when compared to methods that use the ground truth universe size (or number of clusters).

stat.ML↗

arXiv2023

Geometrically Consistent Partial Shape Matching

Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property of matchings is geometric consistency, which means that neighboring triangles in one shape are consistently matched to neighboring triangles in the other shape. Moreover, while in practice one often has only access to partial observations of a 3D shape (e.g. due to occlusion, or scanning artifacts), there do not exist any methods that directly address geometrically consistent partial shape matching. In this work we fill this gap by proposing to integrate state-of-the-art deep shape features into a novel integer linear programming partial shape matching formulation. Our optimization yields a globally optimal solution on low resolution shapes, which we then refine using a coarse-to-fine scheme. We show that our method can find more reliable results on partial shapes in comparison to existing geometrically consistent algorithms (for which one first has to fill missing parts with a dummy geometry). Moreover, our matchings are substantially smoother than learning-based state-of-the-art shape matching methods.

cs.CV↗

arXiv2023

Adaptive Certified Training: Towards Better Accuracy-Robustness Tradeoffs

As deep learning models continue to advance and are increasingly utilized in real-world systems, the issue of robustness remains a major challenge. Existing certified training methods produce models that achieve high provable robustness guarantees at certain perturbation levels. However, the main problem of such models is a dramatically low standard accuracy, i.e. accuracy on clean unperturbed data, that makes them impractical. In this work, we consider a more realistic perspective of maximizing the robustness of a model at certain levels of (high) standard accuracy. To this end, we propose a novel certified training method based on a key insight that training with adaptive certified radii helps to improve both the accuracy and robustness of the model, advancing state-of-the-art accuracy-robustness tradeoffs. We demonstrate the effectiveness of the proposed method on MNIST, CIFAR-10, and TinyImageNet datasets. Particularly, on CIFAR-10 and TinyImageNet, our method yields models with up to two times higher robustness, measured as an average certified radius of a test set, at the same levels of standard accuracy compared to baseline approaches.

cs.LG↗