Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.26162

A Matlab/Octave package for photometric stereo 3D reconstruction

Alessandro Buccini·Elisa Crabu·Federica Pes·Giuseppe Rodriguez
View original source ↗Read source document ↗Export metadata ↓

Abstract

The photometric stereo model allows the construction of 3D virtual replicas of real objects from images acquired under different light conditions. The assumptions of this model are strongly restrictive and are seldom fully satisfied in applications. Indeed, the surface of the observed objects may deviate from ideal conditions, and the geometry of the scene is often only an approximation of the one assumed by the model. Additionally, real-world surfaces may present reflection phenomena, which introduce distortions in reconstructions. In this paper, we present a revised version of the Matlab package \ttt{\small ps3d}~\cite{cdfrv21}, developed to implement the photometric stereo model under various conditions. The new package contains various extensions, the most notable one is the presence of an alternative model to address the presence of a reflective object surface. In addition, it implements particular metrics to analyze the compliance of a dataset to model assumptions, and it is compatible with GNU Octave. The tool allows users to test the model under different observation configurations, also in presence of reflection, using either synthetic or experimental data.

Explore related subjects

math.NAcs.NA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Alessandro Buccini, Elisa Crabu, Federica Pes, Giuseppe Rodriguez. 2026-10-19. A Matlab/Octave package for photometric stereo 3D reconstruction. https://arxiv.org/abs/2610.26162

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Shape calculus and automatic differentiation for multi-phase level-set topology optimisation with unfitted finite elements

We present shape calculus techniques and a scalable automatic shape differentiation framework for multi-phase topology optimisation on unfitted discretisations defined by several level-set functions. First we establish general, exact shape calculus expressions in the discrete case for multi-phase systems by leveraging concepts from convex geometry. To complement this theoretical foundation, we introduce an open-source multi-phase automatic shape differentiation framework based on polytopal cutting. This computational framework is validated against both finite differences and our established exact expressions, matching the latter to near machine precision. Furthermore, the proposed automatic shape differentiation is scalable across distributed computing environments, demonstrating near ideal weak scaling up to 1.65 billion finite elements across 13,824 computer cores. We demonstrate our implementation by solving unfitted multi-phase topology optimisation problems for anisotropic diffusion, linear elasticity, and fluid--structure interaction. Together, these theoretical and computational contributions provide a robust and accessible foundation for advancing multi-phase topology optimisation using unfitted finite element methods. In particular, the methods enable the solution of topology optimisation problems involving multi-phase and multi-physics systems with non-trivial boundary conditions. The open-source software is available at https://github.com/zjwegert/GridapTopOpt.jl.

math.NA↗
arXiv2026

Soliton Profiles in 1D: Enhanced Neural-Network Solvers and Constrained Deep Ritz Methods

We develop and compare enhanced neural-network solvers for one-dimensional ground-state profiles, which are solutions of $$ Q^{\prime\prime}=bQ-γQ^{p},\quad Q>0,\quad p>1, \quad b, γ>0, $$ the stationary profile equation for the nonlinear Schrödinger, generalized Korteweg-de Vries, and nonlinear Klein-Gordon equations. Its explicit sech-type solutions serve as exact reference for error computation and benchmark hyperparameter selection. We improve on the standard Adam-trained physics-informed neural network (PINN) baseline by introducing higher-order optimization via Gauss-Newton/Levenberg-Marquardt and L-BFGS refinements, as well as Fourier-feature PINNs, and constrained Deep Ritz (DR) formulations. In DR approaches we introduce two new neural-network formulations, which implement two classical variational characterizations: a Nehari-constrained Deep Ritz method, in which the height is learned by projecting onto the Nehari/Pokhozhaev manifold, and a Weinstein Deep Ritz method, in which a normalized profile minimizes the Weinstein quotient. The Deep Ritz formulations perform best overall, in particular, the Weinstein variant gives the best error-runtime balance. The neural-network based solvers remain less accurate and efficient than classical Petviashvili iteration in 1D, however, the current study provides a proof of concept: the mesh-free formulation, non-reliance on exact profiles or the related features make them promising in higher dimensions and for more complicated nonlinearities and dispersive operators.

math.NA↗
arXiv2026

Trace Inverse Estimates and Kernel-based Nitsche Galerkin Methods for Elliptic Interface Problems

We establish trace inverse estimates for products of independently generated Sobolev-kernel trial spaces on Lipschitz subdomains and use them to analyze symmetric Nitsche Galerkin methods for elliptic interface problems. The estimates control one-sided gradient traces by subdomain gradients, the interface jump, and an exterior boundary trace. Their conormal form provides the flux control required by the Nitsche formulation without imposing value constraints on the trial spaces, including configurations with an interior inclusion. For quasi-uniform center families with comparable fill distances and a fixed kernel scale, we obtain coercivity and well-posedness for sufficiently large penalty parameters independent of refinement. We prove energy and $L^2$ error bounds of orders $h^{s-1}$ and $h^s$ for piecewise $H^s$ solutions, $2\le s\le m$, where $h$ is the maximum fill distance and $m$ is the kernel Sobolev order. The $L^2$ bound additionally requires piecewise $H^2$ regularity of the homogeneous adjoint interface problem. For scaled kernels $Φ_{m,\varepsilon}$ with $0<\varepsilon\le1$, we also derive a scale-explicit condition-number bound in the kernel-translate basis. The analysis assumes exact geometry and integration. Planar experiments examine convergence and support scaling, whereas a three-dimensional mixed-boundary calculation illustrates the method.

math.NA↗