1,720,975 research outputs found
Analysis and approximation of some shape-from-shading models for non-Lambertian surfaces
Full text linkThe reconstruction of a 3D object or a scene is a classical inverse problem in Computer Vision. In the case of a single image this is called the Shape-from-Shading (SfS) problem and it is known to be ill-posed even in a simplified version like the vertical light source case. A huge number of works deals with the orthographic SfS problem based on the Lambertian reflectance model, the most common and simplest model which leads to an eikonal-type equation when the light source is on the vertical axis. In this paper, we want to study non-Lambertian models since they are more realistic and suitable whenever one has to deal with different kind of surfaces, rough or specular. We will present a unified mathematical formulation of some popular orthographic non-Lambertian models, considering vertical and oblique light directions as well
as different viewer positions. These models lead to more complex stationary non-linear partial differential equations of Hamilton-Jacobi type which can be regarded as the generalization of the classical eikonal equation corresponding to the Lambertian case. However, all the equations corresponding to the models considered here (Oren-Nayar and Phong) have a similar structure so we can look for weak solutions to this class in the viscosity solution framework. Via this unified approach, we are able to develop a semi-Lagrangian approximation scheme for the Oren-Nayar and the Phong model and to prove a general convergence result. Numerical simulations on synthetic and real images will illustrate the effectiveness of this approach and the main features of the scheme, also comparing the results with previous results in the literature
A unified approach to the well-posedness of some non-lambertian models in shape-from-shading theory
No full textIn this paper we show that the introduction of an attenuation factor in the brightness equations relative to various perspective shape-from-shading models allows us to make the corresponding differential problems well-posed. We propose a unified approach based on the theory of viscosity solutions and we show that the brightness equations with the attenuation term admit a unique viscosity solution. We also discuss in detail the possible boundary conditions that we can use for the Hamilton–Jacobi equations associated to these models
A Semi-Lagrangian Approximation of the Oren-Nayar PDE for the Orthographic Shape–from–Shading Problem
No full textSeveral advances have been made in the last ten years to improve the Shape–from–Shading model in order to allow its use on real images. The classic Lambertian model, suitable to reconstruct 3D surfaces with uniform reflection properties has shown to be unsuitable for other types of surfaces, for example for rough objects consisting of materials such as clay. Other models have been proposed but it is still unclear what would be the best model. For this reason, we start our analysis for non-Lambertian surfaces. The goal being to find a unique model which should be flexible enough to deal with many kinds of real images. As a starting point for this big project, we consider the non-Lambertian Oren–Nayar reflectance model. In this paper we construct a semi-Lagrangian approximation scheme for its nonlinear partial differential equation and we compare its performances with the classical model in terms of some error indicators on series of benchmarks images
A discrete hughes model for pedestrian flow on graphs
Full text linkIn 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 whereas the minimization principle is described by a graph eikonal equation. We show that the discrete model is well-posed and the numerical examples reported confirm the validity of the proposed model and its applicability to describe real situations
A comparison of non-Lambertian models for the shape-from-shading problem
No full textIn 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
Height-from-polarisation with unknown lighting or albedo
Full text linkWe 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 estimation with only a single, uncalibrated illumination condition. We present results on real world data, including in uncontrolled, outdoor illumination
On the Segmentation of Astronomical Images via Level-Set Methods
No full textAstronomical images are of crucial importance for astronomers since they contain a lot of information about celestial bodies that can not be directly accessible. Most of the information available for the analysis of these objects starts with sky explorations via telescopes and satellites. Unfortunately, the quality of astronomical images is usually very low with respect to other real images and this is due to technical and physical features related to their acquisition process. This increases the percentage of noise and makes more difficult to use directly standard segmentation methods on the original image. In this work we will describe how to process astronomical images in two steps: in the first step we improve the image quality by a rescaling of light intensity whereas in the second step we apply level-set methods to identify the objects. Several experiments will show the effectiveness of this procedure and the results obtained via various discretization techniques for level-set equations
Shape Optimization for Thermal Insulation Problems
Full text link[EN] In this work we consider two domains: an external domain whose geometry varies,
and an internal fixed one. From the thermal insulation viewpoint, we are considering a body
to be insulated, enveloped in a layer of insulator, and we want to find the best shape for the
thermal insulator, in terms of heat dispersion. Mathematically, our problem is described by an
elliptic partial differential equation with Dirichlet-Robin boundary conditions.This research has been carried on within the PON R&I 2014-2020 - “AIM: Attraction and International Mobility” (Linea 2.1, project AIM1834118 - 2, CUP: E61G19000050001). The authors are members of the INdAM Research Group GNCS.Tozza, S.; Toraldo, G. (2022). Shape Optimization for Thermal Insulation Problems. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 11-15. https://doi.org/10.4995/YIC2021.2021.12288OCS111
Shape reconstruction of symmetric surfaces using photometric stereo
No full textThe reconstruction of a 3D surface through one gray scale digital image does not admit a unique solution in the orthographic Shape from Shading (SfS) framework. With the aim to make this type of problem well-posed it is possible to use the Photometric Stereo (PS) technique. It allows to add information about the surface introducing other images of the object taken from the same point of view but modifying, for each photo, the direction of the light source. The methods that use the PS technique with the orthographic model of SfS need of, at least, three images. However, even if three images are used, there is the possibility that the SfS-PS problem continues to be ill-posed. This is the case when the three images are taken using three coplanar light vectors. This work analyses this kind of illposedness in order to understand how it is possible to establish a connection among
the images that do not guarantee uniqueness. A further result in this paper is given by a geometrical characterization of the surfaces for which it is possible to solve the classic SfS problem
Uncalibrated, Two Source Photo-Polarimetric Stereo
Full text linkIn this paper we present methods for estimating shape from polarisation and shading information, i.e. photo-polarimetric shape estimation, under varying, but unknown, illumination, i.e. in an uncalibrated scenario. We propose several alternative photo-polarimetric constraints that depend upon the partial derivatives of the surface and show how to express them in a unified system of partial differential equations of which previous work is a special case. By careful combination and manipulation of the constraints, we show how to eliminate non-linearities such that a discrete version of the problem can be solved using linear least squares. We derive a minimal, combinatorial approach for two source illumination estimation which we use with RANSAC for robust light direction and intensity estimation. We also introduce a new method for estimating a polarisation image from multichannel data and provide methods for estimating albedo and refractive index. We evaluate lighting, shape, albedo and refractive index estimation methods on both synthetic and real-world data showing improvements over existing state-of-the-art
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