A Unified Approach to the Well-Posedness of Some Non-Lambertian Models in Shape-from-Shading Theory

Camilli, Fabio; Tozza, Silvia

doi:10.1137/16m1066397

Cited by 10 publications

(19 citation statements)

References 26 publications

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“…Because of their nonlinearity and the degeneration of coefficients, HJB equations do not always have smooth solutions that are defined in a classical sense, while they admit solutions with lower regularity called viscosity solutions . Due to their rich mathematical properties, HJB equations and viscosity solutions have been analyzed from both analytical and numerical viewpoints . To our knowledge, PV systems have not been mathematically analyzed from the viewpoint of stochastic control and viscosity solutions, although they are potential mathematical tools for efficiently analyzing the systems.…”

Section: Introductionmentioning

confidence: 99%

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

Yoshioka

Yano

2019

Appl Stoch Models Bus & Ind

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The operation of a stand‐alone photovoltaic (PV) system ultimately aims for the optimization of its energy storage. We present a mathematical model for cost‐effective control of a stand‐alone system based on a PV panel equipped with an angle adjustment device. The model is based on viscosity solutions to partial differential equations, which serve as a new and mathematically rigorous tool for modeling, analyzing, and controlling PV systems. We formulate a stochastic optimal switching problem of the panel angle, which is here a binary variable to be dynamically controlled under stochastic weather condition. The stochasticity comes from cloud cover dynamics, which is modeled with a nonlinear stochastic differential equation. In finding the optimal control policy of the panel angle, switching the angle is subject to impulsive cost and reduces to solving a system of Hamilton‐Jacobi‐Bellman quasi‐variational inequalities (HJBQVIs). We show that the stochastic differential equation is well posed and that the HJBQVIs admit a unique viscosity solution. In addition, a finite‐difference scheme is proposed for the numerical discretization of HJBQVIs. A demonstrative computational example of the HJBQVIs, with emphasis on a stand‐alone experimental system, is finally presented with practical implications for its cost‐effective operation.

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Section: Introductionmentioning

confidence: 99%

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

Yoshioka

Yano

2019

Appl Stoch Models Bus & Ind

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“…Recently, the introduction of an attenuation factor in the brightness equations relative to various perspective SfS models allowed to make the corresponding differential problems well-posed. In [18], a unified approach based on the theory of viscosity solutions has been proposed, showing that the brightness equations coming from different non-Lambertian reflectance models with the attenuation term admit a unique viscosity solution.…”

Section: -C)mentioning

confidence: 99%

A Comprehensive Introduction to Photometric 3D-Reconstruction

Durou

Falcone

Quéau

et al. 2020

Advances in Computer Vision and Pattern Recognition

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“…Liu et al () perform a careful analysis of the effect of the direction of illumination on the final solved shape slope errors (assuming the Lambertian model). Camilli and Tozza () studied how to make the SfS problem well‐posed for some non‐Lambertian models.…”

Section: Comparison With Related Workmentioning

confidence: 99%

Multiview Shape‐From‐Shading for Planetary Images

Alexandrov

Beyer

2018

Earth and Space Science

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We propose and validate an algorithm for shape‐from‐shading that works for planetary data, with multiple input images, realistic camera models, non‐Lambertian reflectance, variable albedo, uncertain camera positions and orientations, low angles of illumination, and shadows. The algorithm begins with images and existing terrain data (provided by stereogrammetry, lidar data, or even just a flat surface) which is then optimized. We show that shape‐from‐shading is able to recover more detail than obtained from stereo alone while eliminating stereo numerical artifacts and improving the terrain accuracy. Our software implementation is released under an open‐source license as part of the NASA Ames Stereo Pipeline.

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A Unified Approach to the Well-Posedness of Some Non-Lambertian Models in Shape-from-Shading Theory

Cited by 10 publications

References 26 publications

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

A Comprehensive Introduction to Photometric 3D-Reconstruction

Multiview Shape‐From‐Shading for Planetary Images

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