Matlab codes for shape from shading.zip

# Codes_Shape_from_shading Matlab codes for shape-from-shading. Several variants are implemented: - ADMM-based variational shape from shading with general camera (orthographic or perspective) and lighting (spherical harmonics), see [1] - Lax-Friedriechs solving of the eikonal case (orthographic camera, frontal directional lighting), cf. Equation (8) in [2] - Semi-Lagrangian solver for the eikonal case (orthographic camera, frontal directional lighting), see [3] - Semi-Lagrangian solver for the perspective eikonal case (perspective camera, frontal directional lighting), see [4] ## Introduction These codes can be used to solve the shape-from-shading (SfS) problem (estimate shape, given a single image). Main features: - possibility to add a shape prior in order to guide the solution (useful for instance in RGB-D sensing) - minimal surface regularization to smooth out the residual noise - handles second-order spherical harmonics lighting - handles orthographic or perspective camera - handles grey or RGB images Note: the classic eikonal SfS can also be achieved as a special case. ## Demos The following two demo files accompanying [1] are provided: - `demo_1_lena_eikonal.m` : classic SfS (greylevel image, orthographic camera, frontal lighting) applied to the standard Lena image - `demo_2_vase_SH2.m` : refinement of the depth map obtained with a RGB-D sensor. Source of the dataset: https://github.com/pengsongyou/SRmeetsPS The three other demo files illustrate alternative PDE-based methods based semi-Lagrangian schemes, when lighting is frontal and directional, see [2,3,4] for details. ## Contents The main fuctions for ref [1] are in the Toolbox/ folder: - `generic_sfs.m`: main SfS code - `theta_fun.m`: cost function with respect to the surface gradient values - `estimate_lighting.m`: can be used to estimate spherical harmonics lighting, given an image and a shape estimate - `make_gradient.m`: finite differences stencils on a non-rectangular grid - `export_obj2.m`: to produce a .obj file readable with meshlab ## Dependencies - minFunc: need first be compiled: go to Toolbox/minFunc and run mexAll.m script (source: https://www.cs.ubc.ca/~schmidtm/Software/minFunc.html) - CMG (recommended for faster results): http://www.cs.cmu.edu/~jkoutis/cmg.html ## References [1] "A Variational Approach to Shape-from-shading Under Natural Illumination", Y. Quéau et al., EMMCVPR 2017 [2] "A comprehensive introduction to photometric 3D-reconstruction", J.-D. Durou et al., 2020 [3] "An algorithm for the global solution of the Shape-fromShading model", M. Falcone and M. Sagona, ICIAP 1997 [4] "Some remarks on perspective shape-from-shading models", E. Cristiani et al., SSVM 2007