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On Arrangements of Quadrics in Decomposing the Parameter Space of 3D Digitized Rigid Motions
No full textInternational audienceComputing the arrangement of quadrics in 3D is a fundamental problem in symbolic computation, with challenges arising when handling degenerate cases and asymptotic critical values. State-of-the-art methods typically require a generic change of coordinates to manage these asymptotes, rendering certain problems intractable. A specific instance of this challenge appears in digital geometry, where comparing 3D shapes up to isometry requires applying a 3D rigid motion on and mapping the result back to , a process typically achieved via a digitization operator. However, such motions do not preserve the topology of digital objects, making the analysis of digitized rigid motions crucial. Our main contribution is the decomposition of the 6D parameter space of digitized rigid motions for image patches of radius up to three. This problem reduces to computing the arrangement of up to 741 quadrics, some of which are degenerate. To address the computational challenges, we introduce and implement a new algorithm for computing arrangements of quadrics in 3D, specifically designed to handle degenerate directions and asymptotic critical values. This approach allows us to overcome the limitations of existing methods, making the problem tractable in the context of digital geometry
Concentration inequalities and cut-off phenomena for penalized model selection within a basic Rademacher framework
No full textThis article exists first and foremost to contribute to a tribute to Patrick Cattiaux. One of the two authors has known Patrick Cattiaux for a very long time, and owes him a great deal. If we are to illustrate the adage that life is made up of chance, then what could be better than the meeting of two young people in the 80s, both of whom fell in love with the mathematics of randomness, and one of whom changed the other's life by letting him in on a secret: if you really believe in it, you can turn this passion into a profession. By another happy coincidence, this tribute comes at just the right time, as Michel Talagrand has been awarded the Abel prize. The temptation was therefore great to do a double. Following one of the many galleries opened up by mathematics, we shall first draw a link between the mathematics of Patrick Cattiaux and that of Michel Talagrand. Then we shall show how the abstract probabilistic material on the concentration of product measures thus revisited can be used to shed light on cut-off phenomena in our field of expertise, mathematical statistics. Nothing revolutionary here, as everyone knows the impact that Talagrand's work has had on the development of mathematical statistics since the late 90s, but we've chosen a very simple framework in which everything can be explained with minimal technicality, leaving the main ideas to the fore
Is model selection possible for the -loss? PCO estimation for regression models
No full textThis paper addresses the problem of model selection in the sequence model , when is sub-Gaussian, for non-euclidian loss-functions. In this model, the Penalized Comparison to Overfitting procedure is studied for the weighted -loss, Several oracle inequalities are derived from concentration inequalities for sub-Weibull variables. Using judicious collections of models and penalty terms, minimax rates of convergence are stated for Besov bodies . These results are applied to the functional model of nonparametric regression
Revisiting CHAMPAGNE: Sparse Bayesian Learning as Reweighted Sparse Coding
No full textInternational audienceThis paper revisits the CHAMPAGNE algorithm within the Sparse Bayesian Learning (SBL) framework and establishes its connection to reweighted sparse coding. We demonstrate that the SBL objective can be reformulated as a reweighted ℓ21-minimization problem, providing a more straightforward interpretation of the sparsity mechanism and enabling the design of an efficient iterative algorithm. Additionally, we analyze the behavior of this reformulation in the low signal-to-noise ratio (SNR) regime, showing that it simplifies to a weighted ℓ21-regularized least squares problem. Numerical experiments validate the proposed approach, highlighting its improved computational efficiency and ability to produce exact sparse solutions, particularly in simulated MEG source localization tasks
X-ray simulations with gVirtualXray in medicine and life sciences
No full textInternational audiencegVirtualXray (gVXR) is a programming interface framework to simulate realistic X-ray projections in realtime on graphics processing units (GPUs). It solves the Beer-Lambert law (attenuation law) using a deterministic X-ray simulation algorithm based on 3D computer graphics, namely rasterisation. Implemented as multi-pass rendering makes it more computationally optimal than the more intuitive ray-tracing technique. Although written in C++ using OpenGL and its shading language (GLSL) to leverage the GPU, gVXR is available for other programming languages such as Python. Extensive validation studies, including comparisons with Monte Carlo simulations and real experimental data, have confirmed the accuracy of gVXR's simulations. gVXR was initially used in medical virtual reality (VR) for training purposes. It was then used in medical physics, and highthroughput data applications including mathematical optimisation and machine learning (ML). Micro-imaging studies on the C. elegans biological model are also reported
Slotted E-Graphs: First-Class Support for (Bound) Variables in E-Graphs
No full textInternational audienceEquality saturation has gained significant interest as a powerful optimization and reasoning technique. At its heart is the e-graph data structure, that space-efficiently represents equal sub-terms uniquely. An important open problem in this context is extending this efficient representation to languages featuring (bound) variables. Independent of how we represent variables in e-graphs, either as names or nameless (using de Bruijn indices), sharing is broken as sub-terms that differ only in the names of their variables are represented separately. This results in aggressive e-graph growth, bad performance, as well as reduced expressiveness. In this paper, we present a novel approach to representing bound variables in e-graphs by making them a first-class built-in feature of the data structure. Our slotted e-graph represents terms that differ only by (bound or free) variable names uniquely. To do so, e-classes that represent equivalent terms via e-nodes are parameterized by slots , abstracting over free variables of the represented terms. Referring to an e-class from an e-node now requires relating the variables from its context to the slots of the e-class. Our evaluation of slotted e-graph uses two case studies from compiler optimization and theorem proving to show that performing equality saturation for languages with bound variables is greatly simplified and that we can solve practically relevant problems that cannot be solved with e-graphs using de Bruijn indices
Strategies for the Reconciliation of Artistic Intent and Technical Constraints in Mixed Reality Performances
No full textInternational audienceAs immersive technologies advance, Mixed Reality Performances (MRP) increasingly integrate them but often face technical challenges that must balance artistic vision and practical constraints. These constraints sometimes lead to unavoidable limitations. The diversity of technologies and artistic goals in MRP prevents a onesize-fits-all solution to such dilemmas. This paper presents a model unifying strategies for addressing compromises between artistic intent and technological feasibility. Using reflexive thematic analysis of a performance-led case study, interviews, and independent case studies, we identify recurring strategies in Mixed Reality experiences with varying constraints. These strategies fall on an axis based on the audience's awareness of limitations and are categorized into five approaches: Avoid, Disguise, Tolerate, Integrate, or Leverage. We argue that this framework helps designers better navigate the limitations inherent in creating MRPs, offering practical pathways to align technological capabilities with creative objectives
Dynamic off-the-grid untangling of curves with Reeds-Shepp metric.
No full textWe propose an improved strategy for point sources tracking in a temporal stack through an off-the-grid fashion, inspired by the Benamou-Brenier regularisation in the literature. We define a lifting of the problem in the higher-dimensional space of the roto-translation group. This allows us to overcome the theoretical limitation of the off-the-grid method towards tangled point source trajectories, thus enabling the reconstruction and untangling even from the numerical standpoint. We define accordingly a new regularisation based on the relaxed Reeds-Shepp metric, an approximation of the sub-Riemannian Reeds-Shepp metric, further allowing control on the local curvature of the recovered trajectories. Then, we derive some properties of the discretisation and prove a Γ-convergence result, fostering interest for practical applications of polygonal, Bézier, and piecewise geodesic discretisation. We finally test our proposed method on a localisation problem example, and give a fair comparison with the state-of-the-art off-the-grid method.</div
Variable and extended precision (VRP) accelerator implemented in a 22 nm SoC
No full textInternational audienceLinear solvers and eigensolvers are the heart of HPC scientific applications. Among them, iterative projection methods are preferred to direct algorithms for large problems because of their lower memory usage, but they are prone to roundoff errors. Using an enhanced working precision inside the linear computing kernels mitigates this issue and accelerates convergence. However, only software libraries support variable and extended precision Floating Point (FP) computations beyond 80 bits.We introduce the VaRiable and extended Precision Accelerator (VRP), a RISC-V accelerator implemented on a System-on-Chip (SoC) using GF22FDX technology. The VRP supports FP computations with a range of significand bits from 2 to 512. This accelerator delivers an average 19.25x application speedup compared to the well-known MPFR software library running on a 2400+ MHz Intel Xeon processor. Additionally, extended precision facilitates the convergence of linear solvers for problems that would otherwise fail to converge and reduces energy-to-solution