IEEE transactions on pattern analysis and machine intelligence, Jan 6, 2018
We present a method for estimating surface height directly from a single polarisation image simpl... more We present a method for estimating surface height directly from a single polarisation image simply by solving a large, sparse system of linear equations. To do so, we show how to express polarisation constraints as equations that are linear in the unknown height. The local ambiguity in the surface normal azimuth angle is resolved globally when the optimal surface height is reconstructed. Our method is applicable to dielectric objects exhibiting diffuse and specular reflectance, though lighting and albedo must be known. We relax this requirement by showing that either spatially varying albedo or illumination can be estimated from the polarisation image alone using nonlinear methods. In the case of illumination, the estimate can only be made up to a binary ambiguity which we show is a generalised Bas-relief transformation corresponding to the convex/concave ambiguity. We believe that our method is the first passive, monocular shape-from-x technique that enables well-posed height estim...
Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference
Thermal insulation represents one of the major challenges for energy efficiency. Problems related... more Thermal insulation represents one of the major challenges for energy efficiency. Problems related to insulation are well-known and widely studied in mathematical physics. Neverthless, mathematics involved is still very tricky especially when one looks at shape optimization issues [1, 2], and sometimes the answers are not so intuitive [3].In this talk we will consider two domains: an internal (fixed) ball of radius r and an external domain whose geometry varies. Physically, we are considering a domain of given temperature, thermally insulated by surrounding it with a constant thickness of thermal insulator. Our question is related to the best (or worst) shape for the external domain, in terms of heat dispersion (of course, under prescribed geometrical constraints). Mathematically, our problem is composed by an elliptic PDE with Robin-Dirichlet boundary conditions. This work is still in progress and we want to share someremarks and open questions, in addition to the results obtained ...
In this paper we propose a high-order accurate scheme for image segmentation based on the level-s... more In this paper we propose a high-order accurate scheme for image segmentation based on the level-set method. In this approach, the curve evolution is described as the 0-level set of a representation function but we modify the velocity that drives the curve to the boundary of the object in order to obtain a new velocity with additional properties that are extremely useful to develop a more stable high-order approximation with a small additional cost. The approximation scheme proposed here is the first 2D version of an adaptive "filtered" scheme recently introduced and analyzed by the authors in 1D. This approach is interesting since the implementation of the filtered scheme is rather efficient and easy. The scheme combines two building blocks (a monotone scheme and a high-order scheme) via a filter function and smoothness indicators that allow to detect the regularity of the approximate solution adapting the scheme in an automatic way. Some numerical tests on synthetic and r...
We consider a class of "filtered" schemes for first order time dependent Hamilton-Jacob... more We consider a class of "filtered" schemes for first order time dependent Hamilton-Jacobi equations and prove a general convergence result for this class of schemes. A typical filtered scheme is obtained mixing a high-order scheme and a monotone scheme according to a filter function F which decides where the scheme has to switch from one scheme to the other. A crucial role for this switch is played by a parameter ε=ε(Δ t,Δ x)>0 which goes to 0 as the time and space steps (Δ t,Δ x) are going to 0 and does not depend on the time t_n, for each iteration n. The tuning of this parameter in the code is rather delicate and has an influence on the global accuracy of the filtered scheme. Here we introduce an adaptive and automatic choice of ε=ε ^n (Δ t, Δ x) at every iteration modifying the classical set up. The adaptivity is controlled by a smoothness indicator which selects the regions where we modify the regularity threshold ε^n. A convergence result and some error estimates f...
Photometric 3D-reconstruction techniques aim at inferring the geometry of a scene from one or sev... more Photometric 3D-reconstruction techniques aim at inferring the geometry of a scene from one or several images, by inverting a physical model describing the image formation. This chapter presents an introductory overview of the main pho-tometric 3D-reconstruction techniques which are shape-from-shading, photometric stereo and shape-from-polarisation.
Lecture Notes in Computational Science and Engineering, 2019
In this paper we consider a class of “filtered” schemes for some first order time dependent Hamil... more In this paper we consider a class of “filtered” schemes for some first order time dependent Hamilton-Jacobi equations. A typical feature of a filtered scheme is that at the node xj the scheme is obtained as a mixture of a high-order scheme and a monotone scheme according to a filter function F. The mixture is usually governed by F and by a fixed parameter e = e(Δt, Δx) > 0 which goes to 0 as (Δt, Δx) is going to 0 and does not depend on n. Here we improve the standard filtered scheme introducing an adaptive and automatic choice of the parameter e = en(Δt, Δx) at every iteration. To this end, we use a smoothness indicator in order to select the regions where we can compute the regularity threshold en. The numerical tests presented confirms the effectiveness of the adaptive scheme.
In this paper we present in a unified approach Shape-from-Shading models under orthographic proje... more In this paper we present in a unified approach Shape-from-Shading models under orthographic projection for non-Lambertian surfaces and compare them with the classical Lambertian model. Those non-Lambertian models have been proposed in the literature by various authors in order to take into account more realistic surfaces such as rough and specular surfaces. The advantage of our unified mathematical model is the possibility to easily modify a single differential model to various situations just changing some control parameters. Moreover, the numerical approximation we propose is valid for that general model and can be easily adapted to the real situation. Finally, we compare the models on some benchmarks including real and synthetic images.
In this paper, we introduce a discrete time-finite state model for pedestrian flow on a graph in ... more In this paper, we introduce a discrete time-finite state model for pedestrian flow on a graph in the spirit of the Hughes dynamic continuum model. The pedestrians, represented by a density function, move on the graph choosing a route to minimize the instantaneous travel cost to the destination. The density is governed by a conservation law while the minimization principle is described by a graph eikonal equation. We show that the model is well posed and we implement some numerical examples to demonstrate the validity of the proposed model.
IEEE transactions on pattern analysis and machine intelligence, Jan 6, 2018
We present a method for estimating surface height directly from a single polarisation image simpl... more We present a method for estimating surface height directly from a single polarisation image simply by solving a large, sparse system of linear equations. To do so, we show how to express polarisation constraints as equations that are linear in the unknown height. The local ambiguity in the surface normal azimuth angle is resolved globally when the optimal surface height is reconstructed. Our method is applicable to dielectric objects exhibiting diffuse and specular reflectance, though lighting and albedo must be known. We relax this requirement by showing that either spatially varying albedo or illumination can be estimated from the polarisation image alone using nonlinear methods. In the case of illumination, the estimate can only be made up to a binary ambiguity which we show is a generalised Bas-relief transformation corresponding to the convex/concave ambiguity. We believe that our method is the first passive, monocular shape-from-x technique that enables well-posed height estim...
Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference
Thermal insulation represents one of the major challenges for energy efficiency. Problems related... more Thermal insulation represents one of the major challenges for energy efficiency. Problems related to insulation are well-known and widely studied in mathematical physics. Neverthless, mathematics involved is still very tricky especially when one looks at shape optimization issues [1, 2], and sometimes the answers are not so intuitive [3].In this talk we will consider two domains: an internal (fixed) ball of radius r and an external domain whose geometry varies. Physically, we are considering a domain of given temperature, thermally insulated by surrounding it with a constant thickness of thermal insulator. Our question is related to the best (or worst) shape for the external domain, in terms of heat dispersion (of course, under prescribed geometrical constraints). Mathematically, our problem is composed by an elliptic PDE with Robin-Dirichlet boundary conditions. This work is still in progress and we want to share someremarks and open questions, in addition to the results obtained ...
In this paper we propose a high-order accurate scheme for image segmentation based on the level-s... more In this paper we propose a high-order accurate scheme for image segmentation based on the level-set method. In this approach, the curve evolution is described as the 0-level set of a representation function but we modify the velocity that drives the curve to the boundary of the object in order to obtain a new velocity with additional properties that are extremely useful to develop a more stable high-order approximation with a small additional cost. The approximation scheme proposed here is the first 2D version of an adaptive "filtered" scheme recently introduced and analyzed by the authors in 1D. This approach is interesting since the implementation of the filtered scheme is rather efficient and easy. The scheme combines two building blocks (a monotone scheme and a high-order scheme) via a filter function and smoothness indicators that allow to detect the regularity of the approximate solution adapting the scheme in an automatic way. Some numerical tests on synthetic and r...
We consider a class of "filtered" schemes for first order time dependent Hamilton-Jacob... more We consider a class of "filtered" schemes for first order time dependent Hamilton-Jacobi equations and prove a general convergence result for this class of schemes. A typical filtered scheme is obtained mixing a high-order scheme and a monotone scheme according to a filter function F which decides where the scheme has to switch from one scheme to the other. A crucial role for this switch is played by a parameter ε=ε(Δ t,Δ x)>0 which goes to 0 as the time and space steps (Δ t,Δ x) are going to 0 and does not depend on the time t_n, for each iteration n. The tuning of this parameter in the code is rather delicate and has an influence on the global accuracy of the filtered scheme. Here we introduce an adaptive and automatic choice of ε=ε ^n (Δ t, Δ x) at every iteration modifying the classical set up. The adaptivity is controlled by a smoothness indicator which selects the regions where we modify the regularity threshold ε^n. A convergence result and some error estimates f...
Photometric 3D-reconstruction techniques aim at inferring the geometry of a scene from one or sev... more Photometric 3D-reconstruction techniques aim at inferring the geometry of a scene from one or several images, by inverting a physical model describing the image formation. This chapter presents an introductory overview of the main pho-tometric 3D-reconstruction techniques which are shape-from-shading, photometric stereo and shape-from-polarisation.
Lecture Notes in Computational Science and Engineering, 2019
In this paper we consider a class of “filtered” schemes for some first order time dependent Hamil... more In this paper we consider a class of “filtered” schemes for some first order time dependent Hamilton-Jacobi equations. A typical feature of a filtered scheme is that at the node xj the scheme is obtained as a mixture of a high-order scheme and a monotone scheme according to a filter function F. The mixture is usually governed by F and by a fixed parameter e = e(Δt, Δx) > 0 which goes to 0 as (Δt, Δx) is going to 0 and does not depend on n. Here we improve the standard filtered scheme introducing an adaptive and automatic choice of the parameter e = en(Δt, Δx) at every iteration. To this end, we use a smoothness indicator in order to select the regions where we can compute the regularity threshold en. The numerical tests presented confirms the effectiveness of the adaptive scheme.
In this paper we present in a unified approach Shape-from-Shading models under orthographic proje... more In this paper we present in a unified approach Shape-from-Shading models under orthographic projection for non-Lambertian surfaces and compare them with the classical Lambertian model. Those non-Lambertian models have been proposed in the literature by various authors in order to take into account more realistic surfaces such as rough and specular surfaces. The advantage of our unified mathematical model is the possibility to easily modify a single differential model to various situations just changing some control parameters. Moreover, the numerical approximation we propose is valid for that general model and can be easily adapted to the real situation. Finally, we compare the models on some benchmarks including real and synthetic images.
In this paper, we introduce a discrete time-finite state model for pedestrian flow on a graph in ... more In this paper, we introduce a discrete time-finite state model for pedestrian flow on a graph in the spirit of the Hughes dynamic continuum model. The pedestrians, represented by a density function, move on the graph choosing a route to minimize the instantaneous travel cost to the destination. The density is governed by a conservation law while the minimization principle is described by a graph eikonal equation. We show that the model is well posed and we implement some numerical examples to demonstrate the validity of the proposed model.
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