94 citations · 287 across the 29 of their papers we have counts for
33 papers
Computing Smooth Geodesics under Two-Sided Curvature Bounds with Applications to Robotics and Image Analysis
Da Chen, Zhenjiang Li, Jean-Marie Mirebeau +4
Curvature of planar curves serves as a key regularization term for computing second-order minimal paths, due to its tight relevance to desirable geometric properties such as smooth…
Discretization and convergence of the ballistic Benamou-Brenier formulation of the porous medium and Burgers equations
Jean-Marie Mirebeau, Erwan Stampfli
We study the discretization, convergence, and numerical implementation of recent reformulations of the quadratic porous medium equation (multidimensional and anisotropic) and Burge…
Dynamic Exploration on Segment-Proposal Graphs for Tubular Centerline Tracking
Chong Di, Jinglin Zhang, Zhenjiang Li +3
Optimal curve methods provide a fundamental framework for tubular centerline tracking. Point-wise approaches, such as minimal paths, are theoretically elegant but often suffer from…
Unbalanced L1 optimal transport for vector valued measures and application to Full Waveform Inversion
Gabriele Todeschi, Ludovic Métivier, Jean-Marie Mirebeau
Optimal transport has recently started to be successfully employed to define misfit or loss functions in inverse problems. However, it is a problem intrinsically defined for positi…
Computing Geodesic Paths Encoding a Curvature Prior
Da Chen, Jean-Marie Mirebeau, Minglei Shu +1
In this paper, we introduce an efficient method for computing curves minimizing a variant of the Euler-Mumford elastica energy, with fixed endpoints and tangents at these endpoints…
Geodesic Tracking via New Data-driven Connections of Cartan Type for Vascular Tree Tracking
Nicky van den Berg, Bart Smets, Gautam Pai +2
We introduce a data-driven version of the plus Cartan connection on the homogeneous space of 2D positions and orientations. We formulate a theorem that describes all…
Geodesic Models with Convexity Shape Prior
Da Chen, Jean-Marie Mirebeau, Minglei Shu +2
The minimal geodesic models based on the Eikonal equations are capable of finding suitable solutions in various image segmentation scenarios. Existing geodesic-based segmentation a…
A Generalized Asymmetric Dual-front Model for Active Contours and Image Segmentation
Da Chen, Jack Spencer, Jean-Marie Mirebeau +3
The Voronoi diagram-based dual-front active contour models are known as a powerful and efficient way for addressing the image segmentation and domain partitioning problems. In the…
A Region-based Randers Geodesic Approach for Image Segmentation
Da Chen, Jean-Marie Mirebeau, Huazhong Shu +1
The geodesic model based on the eikonal partial differential equation (PDE) has served as a fundamental tool for the applications of image segmentation and boundary detection in th…
Automatic differentiation of non-holonomic fast marching for computing most threatening trajectories under sensors surveillance
Jean-Marie Mirebeau, Johann Dreo
We consider a two player game, where a first player has to install a surveillance system within an admissible region. The second player needs to enter the the monitored area, visit…
Optimal Paths for Variants of the 2D and 3D Reeds-Shepp Car with Applications in Image Analysis
Remco Duits, Stephan P. L. Meesters, Jean-Marie Mirebeau +1
We present a PDE-based approach for finding optimal paths for the Reeds-Shepp car. In our model we minimize a (data-driven) functional involving both curvature and length penalizat…
Global Minimum for a Finsler Elastica Minimal Path Approach
Da Chen, Jean-Marie Mirebeau, Laurent D. Cohen
In this paper, we propose a novel curvature-penalized minimal path model via an orientation-lifted Finsler metric and the Euler elastica curve. The original minimal path model comp…
Sub-Riemannian Fast Marching in SE(2)
Gonzalo Sanguinetti, Erik Bekkers, Remco Duits +3
We propose a Fast Marching based implementation for computing sub-Riemanninan (SR) geodesics in the roto-translation group SE(2), with a metric depending on a cost induced by the i…
Minimal geodesics along volume preserving maps, through semi-discrete optimal transport
Quentin Mérigot, Jean-Marie Mirebeau
We introduce a numerical method for extracting minimal geodesics along the group of volume preserving maps, equipped with the L2 metric, which as observed by Arnold solve Euler's e…
Anisotropic Diffusion in ITK
Jean-Marie Mirebeau, Jérôme Fehrenbach, Laurent Risser +1
Anisotropic Non-Linear Diffusion is a powerful image processing technique, which allows to simultaneously remove the noise and enhance sharp features in two or three dimensional im…
Discretization of the 3D Monge-Ampere operator, between Wide Stencils and Power Diagrams
Jean-Marie Mirebeau
We introduce a monotone (degenerate elliptic) discretization of the Monge-Ampere operator, on domains discretized on cartesian grids. The scheme is consistent provided the solution…
A -Convergence Result for the Upper Bound Limit Analysis of Plates
Jérémy Bleyer, Guillaume Carlier, Vincent Duval +2
Upper bound limit analysis allows one to evaluate directly the ultimate load of structures without performing a cumbersome incremental analysis. In order to numerically apply this…
Monotone and Consistent discretization of the Monge-Ampere operator
Jean-David Benamou, Francis Collino, Jean-Marie Mirebeau
We introduce a novel discretization of the Monge-Ampere operator, simultaneously consistent and degenerate elliptic, hence accurate and robust in applications. These properties are…
Adaptive, Anisotropic and Hierarchical cones of Discrete Convex functions
Jean-Marie Mirebeau
We address the discretization of optimization problems posed on the cone of convex functions, motivated in particular by the principal agent problem in economics, which models the…
Sparse Non-Negative Stencils for Anisotropic Diffusion
Jérôme Fehrenbach, Jean-Marie Mirebeau
We introduce a new discretization scheme for Anisotropic Diffusion, AD-LBR, on two and three dimensional cartesian grids. The main features of this scheme is that it is non-negativ…
Efficient Fast Marching with Finsler metrics
Jean-Marie Mirebeau
We study the discretization of the Escape Time problem: find the length of the shortest path joining an arbitrary point of a domain, to the domain's boundary. Path length is measur…
On the Accuracy of Anisotropic Fast Marching
J. -M. Mirebeau
The fast marching algorithm, and its variants, solves numerically the generalized eikonal equation associated to an underlying riemannian metric. A major challenge for these algori…
Anisotropic Fast-Marching on cartesian grids using Lattice Basis Reduction
Jean-Marie Mirebeau
We introduce a modification of the Fast Marching Algorithm, which solves the generalized eikonal equation associated to an arbitrary continuous riemannian metric, on a two or three…
Adaptive and anisotropic finite element approximation : Theory and algorithms
Jean-Marie Mirebeau
Mesh adaption procedures for finite element approximation allows one to adapt the resolution, by local refinement in the regions of strong variation of the function of interest. Th…