François Lauze

Rasmus Netterstrøm, Nikolay Kutuzov, Sune Darkner et al.

Tracking single molecules is instrumental for quantifying the transport of molecules and nanoparticles in biological samples, e.g., in brain drug delivery studies. Existing intensity-based localisation methods are not developed for imaging with a scanning microscope, typically used for in vivo imaging. Low signal-to-noise ratios, movement of molecules out-of-focus, and high motion blur on images recorded with scanning two-photon microscopy (2PM) in vivo pose a challenge to the accurate localisation of molecules. Using data-driven models is challenging due to low data volumes, typical for in vivo experiments. We developed a 2PM image simulator to supplement scarce training data. The simulator mimics realistic motion blur, background fluorescence, and shot noise observed in vivo imaging. Training a data-driven model with simulated data improves localisation quality in simulated images and shows why intensity-based methods fail.

Robin Bruneau, Baptiste Brument, Yvain Quéau et al.

Achieving high-fidelity 3D surface reconstruction while preserving fine details remains challenging, especially in the presence of materials with complex reflectance properties and without a dense-view setup. In this paper, we introduce a versatile framework that incorporates multi-view normal and optionally reflectance maps into radiance-based surface reconstruction. Our approach employs a pixel-wise joint re-parametrization of reflectance and surface normals, representing them as a vector of radiances under simulated, varying illumination. This formulation enables seamless incorporation into standard surface reconstruction pipelines, such as traditional multi-view stereo (MVS) frameworks or modern neural volume rendering (NVR) ones. Combined with the latter, our approach achieves state-of-the-art performance on multi-view photometric stereo (MVPS) benchmark datasets, including DiLiGenT-MV, LUCES-MV and Skoltech3D. In particular, our method excels in reconstructing fine-grained details and handling challenging visibility conditions. The present paper is an extended version of the earlier conference paper by Brument et al. (in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2024), featuring an accelerated and more robust algorithm as well as a broader empirical evaluation. The code and data relative to this article is available at https://github.com/RobinBruneau/RNb-NeuS2.

Jon Sporring, Peidi Xu, Jiahao Lu et al.

We present Locally Orderless Networks (LON) and its theoretic foundation which links it to Convolutional Neural Networks (CNN), to Scale-space histograms, and measurement theory. The key elements are a regular sampling of the bias and the derivative of the activation function. We compare LON, CNN, and Scale-space histograms on prototypical single-layer networks. We show how LON and CNN can emulate each other, how LON expands the set of functionals computable to non-linear functions such as squaring. We demonstrate simple networks which illustrate the improved performance of LON over CNN on simple tasks for estimating the gradient magnitude squared, for regressing shape area and perimeter lengths, and for explainability of individual pixels' influence on the result.

Sune Darkner, Jose D Tascon, Francois Lauze

First Order Locally Orderless Registration (FLOR) is a scale-space framework for image density estimation used for defining image similarity, mainly for Image Registration. The Locally Orderless Registration framework was designed in principle to use zeroth-order information, providing image density estimates over three scales: image scale, intensity scale, and integration scale. We extend it to take first-order information into account and hint at higher-order information. We show how standard similarity measures extend into the framework. We study especially Sum of Squared Differences (SSD) and Normalized Cross-Correlation (NCC) but present the theory of how Normalised Mutual Information (NMI) can be included.

Guan Wang, Francois Bernard Lauze, Aasa Feragen

We present a graph neural network model for solving graph-to-graph learning problems. Most deep learning on graphs considers ``simple'' problems such as graph classification or regressing real-valued graph properties. For such tasks, the main requirement for intermediate representations of the data is to maintain the structure needed for output, i.e., keeping classes separated or maintaining the order indicated by the regressor. However, a number of learning tasks, such as regressing graph-valued output, generative models, or graph autoencoders, aim to predict a graph-structured output. In order to successfully do this, the learned representations need to preserve far more structure. We present a conditional auto-regressive model for graph-to-graph learning and illustrate its representational capabilities via experiments on challenging subgraph predictions from graph algorithmics; as a graph autoencoder for reconstruction and visualization; and on pretraining representations that allow graph classification with limited labeled data.

Henrik Grønholt Jensen, François Lauze, Sune Darkner

We present an information-theoretic approach to the registration of images with directional information, and especially for diffusion-Weighted Images (DWI), with explicit optimization over the directional scale. We call it Locally Orderless Registration with Directions (LORD). We focus on normalized mutual information as a robust information-theoretic similarity measure for DWI. The framework is an extension of the LOR-DWI density-based hierarchical scale-space model that varies and optimizes the integration, spatial, directional, and intensity scales. As affine transformations are insufficient for inter-subject registration, we extend the model to non-rigid deformations. We illustrate that the proposed model deforms orientation distribution functions (ODFs) correctly and is capable of handling the classic complex challenges in DWI-registrations, such as the registration of fiber-crossings along with kissing, fanning, and interleaving fibers. Our experimental results clearly illustrate a novel promising regularizing effect, that comes from the nonlinear orientation-based cost function. We show the properties of the different image scales and, we show that including orientational information in our model makes the model better at retrieving deformations in contrast to standard scalar-based registration.

Francois Lauze, Mads Nielsen

We develop in this paper a generic Bayesian framework for the joint estimation of motion and recovery of missing data in a damaged video sequence. Using standard maximum a posteriori to variational formulation rationale, we derive generic minimum energy formulations for the estimation of a reconstructed sequence as well as motion recovery. We instantiate these energy formulations and from their Euler-Lagrange Equations, we propose a full multiresolution algorithms in order to compute good local minimizers for our energies and discuss their numerical implementations, focusing on the missing data recovery part, i.e. inpainting. Experimental results for synthetic as well as real sequences are presented. Image sequences and extra material is available at http://image.diku.dk/francois/seqinp.php.

Marco Loog, François Lauze

We start out by demonstrating that an elementary learning task, corresponding to the training of a single linear neuron in a convolutional neural network, can be solved for feature spaces of very high dimensionality. In a second step, acknowledging that such high-dimensional learning tasks typically benefit from some form of regularization and arguing that the problem of scale has not been taken care of in a very satisfactory manner, we come to a combined resolution of both of these shortcomings by proposing a form of scale regularization. Moreover, using variational method, this regularization problem can also be solved rather efficiently and we demonstrate, on an artificial filter learning problem, the capabilities of our basic linear neuron. From a more general standpoint, we see this work as prime example of how learning and variational methods could, or even should work to their mutual benefit.

Yvain Quéau, Bastien Durix, Tao Wu et al.

We conduct a thorough study of photometric stereo under nearby point light source illumination, from modeling to numerical solution, through calibration. In the classical formulation of photometric stereo, the luminous fluxes are assumed to be directional, which is very difficult to achieve in practice. Rather, we use light-emitting diodes (LEDs) to illuminate the scene to reconstruct. Such point light sources are very convenient to use, yet they yield a more complex photometric stereo model which is arduous to solve. We first derive in a physically sound manner this model, and show how to calibrate its parameters. Then, we discuss two state-of-the-art numerical solutions. The first one alternatingly estimates the albedo and the normals, and then integrates the normals into a depth map. It is shown empirically to be independent from the initialization, but convergence of this sequential approach is not established. The second one directly recovers the depth, by formulating photometric stereo as a system of PDEs which are partially linearized using image ratios. Although the sequential approach is avoided, initialization matters a lot and convergence is not established either. Therefore, we introduce a provably convergent alternating reweighted least-squares scheme for solving the original system of PDEs, without resorting to image ratios for linearization. Finally, we extend this study to the case of RGB images.

Aasa Feragen, Francois Lauze, Søren Hauberg

We consider kernel methods on general geodesic metric spaces and provide both negative and positive results. First we show that the common Gaussian kernel can only be generalized to a positive definite kernel on a geodesic metric space if the space is flat. As a result, for data on a Riemannian manifold, the geodesic Gaussian kernel is only positive definite if the Riemannian manifold is Euclidean. This implies that any attempt to design geodesic Gaussian kernels on curved Riemannian manifolds is futile. However, we show that for spaces with conditionally negative definite distances the geodesic Laplacian kernel can be generalized while retaining positive definiteness. This implies that geodesic Laplacian kernels can be generalized to some curved spaces, including spheres and hyperbolic spaces. Our theoretical results are verified empirically.

Aasa Feragen, Pechin Lo, Marleen de Bruijne et al.

In order to develop statistical methods for shapes with a tree-structure, we construct a shape space framework for tree-like shapes and study metrics on the shape space. This shape space has singularities, corresponding to topological transitions in the represented trees. We study two closely related metrics on the shape space, TED and QED. QED is a quotient Euclidean distance arising naturally from the shape space formulation, while TED is the classical tree edit distance. Using Gromov's metric geometry we gain new insight into the geometries defined by TED and QED. We show that the new metric QED has nice geometric properties which facilitate statistical analysis, such as existence and local uniqueness of geodesics and averages. TED, on the other hand, does not share the geometric advantages of QED, but has nice algorithmic properties. We provide a theoretical framework and experimental results on synthetic data trees as well as airway trees from pulmonary CT scans. This way, we effectively illustrate that our framework has both the theoretical and qualitative properties necessary to build a theory of statistical tree-shape analysis.