1. Fast and accurate surface normal integration on non-rectangular domains
- Author
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Ali Sharifi Boroujerdi, Yvain Quéau, Martin Bähr, Michael Breuß, Jean-Denis Durou, Brandenburg University of Technology [Cottbus – Senftenberg] (BTU), Technische Universität Munchen - Université Technique de Munich [Munich, Allemagne] (TUM), Real Expression Artificial Life (IRIT-REVA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - INPT (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Brandenburgische Technische Universität Cottbus-Senftenberg - BTU (GERMANY), Institut de Recherche en Informatique de Toulouse - IRIT (Toulouse, France), and Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
- Subjects
FOS: Computer and information sciences ,Mathematical optimization ,Photometric stereo ,Computer Vision and Pattern Recognition (cs.CV) ,Computer Science - Computer Vision and Pattern Recognition ,Fast marching method ,68U10 ,Preconditioning ,02 engineering and technology ,Conjugate gradient method ,lcsh:QA75.5-76.95 ,Computational science ,[INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI] ,Poisson integration ,Traitement des images ,[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing ,Artificial Intelligence ,Robustness (computer science) ,preconditioning ,FOS: Mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Conjugate residual method ,Traitement du signal et de l'image ,3D reconstruction ,Synthèse d'image et réalité virtuelle ,fast marching method ,Mathematics ,Computer Science - Numerical Analysis ,[INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV] ,020207 software engineering ,Numerical Analysis (math.NA) ,Krylov subspace ,Vision par ordinateur et reconnaissance de formes ,Solver ,Intelligence artificielle ,Computer Graphics and Computer-Aided Design ,[INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR] ,Surface normal integration ,[INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] ,conjugate gradient method ,Krylov subspace methods ,020201 artificial intelligence & image processing ,Computer Vision and Pattern Recognition ,lcsh:Electronic computers. Computer science ,surface normal integration - Abstract
The integration of surface normals for the purpose of computing the shape of a surface in 3D space is a classic problem in computer vision. However, even nowadays it is still a challenging task to devise a method that combines the flexibility to work on non-trivial computational domains with high accuracy, robustness and computational efficiency. By uniting a classic approach for surface normal integration with modern computational techniques we construct a solver that fulfils these requirements. Building upon the Poisson integration model we propose to use an iterative Krylov subspace solver as a core step in tackling the task. While such a method can be very efficient, it may only show its full potential when combined with a suitable numerical preconditioning and a problem-specific initialisation. We perform a thorough numerical study in order to identify an appropriate preconditioner for our purpose. To address the issue of a suitable initialisation we propose to compute this initial state via a recently developed fast marching integrator. Detailed numerical experiments illuminate the benefits of this novel combination. In addition, we show on real-world photometric stereo datasets that the developed numerical framework is flexible enough to tackle modern computer vision applications.
- Published
- 2017