Photometric Stereo with General, Unknown Lighting (original) (raw)
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Photometric stereo: Lambertian reflectance and light sources with unknown direction and strength
This paper reconsiders the familiar case of photometric stereo under the assumption of Lambertian surface re ectance and three distant point sources of illumination. Here, it is assumed that the directions to and the relative strengths of the three light sources are not known a priori. Rather, estimation of these parameters becomes part of the problem formulation. Each light source is represented by a 3-D vector that points in the direction of the light source and has magnitude proportional to the strength of the light source. Thus, nine parameters are required to characterize the three light sources. It is shown that, regardless of object shape, triples of measured intensity values are constrained to lie on a quadratic surface having six degrees of freedom. Estimation of the six parameters of the quadratic surface allows the determination of the nine parameters of the light sources up to an unknown rotation. This is su cient to determine object shape, although attitude with respect to the world-based or the camera-based coordinate system can not be simultaneously recovered without additional information.
Image and Vision Computing, 2007
This paper presents a new multi-light source photometric stereo system for reconstructing images of various characteristics of non-Lambertian rough surfaces with widely varying texture and specularity. Compared to the traditional three-light photometric stereo method, extra lights are employed using a hierarchical selection strategy to eliminate the effects of shadows and specularities, and to make the system more robust. We also show that six lights is the minimum needed in order to apply photometric stereo to the entire visible surface of any convex object. Experiments on synthetic and real scenes demonstrate that the proposed method can extract surface reflectance and orientation effectively, even in the presence of strong shadows and highlights. Hence, the method offers advantages in the recovery of dichromatic surfaces possessing rough texture or deeply relieved topographic features, with applications in reverse engineering and industrial surface inspection. Experimental results are presented in the paper. Published by Elsevier B.V.
Practical 3D Reconstruction Based on Photometric Stereo
Studies in Computational Intelligence, 2010
Photometric Stereo is a powerful image based 3d reconstruction technique that has recently been used to obtain very high quality reconstructions. However, in its classic form, Photometric Stereo suffers from two main limitations: Firstly, one needs to obtain images of the 3d scene under multiple different illuminations. As a result the 3d scene needs to remain static during illumination changes, which prohibits the reconstruction of deforming objects. Secondly, the images obtained must be from a single viewpoint. This leads to depth-map based 2.5 reconstructions, instead of full 3d surfaces. The aim of this chapter is to show how these limitations can be alleviated, leading to the derivation of two practical 3d acquisition systems: The first one, based on the powerful Coloured Light Photometric Stereo method can be used to reconstruct moving objects such as cloth or human faces. The second, permits the complete 3d reconstruction of challenging objects such as porcelain vases. In addition to algorithmic details, the chapter pays attention to practical issues such as setup calibration, detection and correction of self and cast shadows. We provide several evaluation experiments as well as reconstruction results.
Identifying the lights position in photometric stereo under unknown lighting
2021 21st International Conference on Computational Science and Its Applications (ICCSA), 2021
Reconstructing the 3D shape of an object from a set of images is a classical problem in Computer Vision. Photometric stereo is one of the possible approaches. It stands on the assumption that the object is observed from a fixed point of view under different lighting conditions. The traditional approach requires that the position of the light sources is accurately known. It has been proved that the lights position can be estimated directly from the data when at least 6 images of the observed object are available. In this paper, we present a Matlab implementation of the algorithm for solving the photometric stereo problem under unknown lighting, and propose a simple shooting technique to solve the bas-relief ambiguity.
Fusing Multiview and Photometric Stereo for 3D Reconstruction under Uncalibrated Illumination
We propose a method to obtain a complete and accurate 3D model from multiview images captured under a variety of unknown illuminations. Based on recent results showing that for Lambertian objects, general illumination can be approximated well using low-order spherical harmonics, we develop a robust alternating approach to recover surface normals. Surface normals are initialized using a multi-illumination multiview stereo algorithm, then refined using a robust alternating optimization method based on the ' 1 metric. Erroneous normal estimates are detected using a shape prior. Finally, the computed normals are used to improve the preliminary 3D model. The reconstruction system achieves watertight and robust 3D reconstruction while neither requiring manual interactions nor imposing any constraints on the illumination. Experimental results on both real world and synthetic data show that the technique can acquire accurate 3D models for Lambertian surfaces, and even tolerates small violations of the Lambertian assumption.
Orthogonal Illuminations in Two Light-Source Photometric Stereo
Lecture Notes in Computer Science, 2016
In this paper we investigate the case of ambiguous shape reconstruction from two light-source photometric stereo based on illuminating the unknown Lambertian surface. So-far this problem is merely well-understood for two linearly independent light-source directions with one illumination assumed as overhead. As already established, a necessary and sufficient condition to disambiguate the entire shape reconstruction process is controlled by the satisfaction of the corresponding secondorder linear PDE with constant coefficients in two independent variables. This work extends the latter to an arbitrary pair of light-source directions transforming the above constraint into a special nonlinear PDE. In addition, a similar ambiguity analysis is also performed for a special configuration of two light-source directions assumed this time as orthogonal and contained in the vertical plane. Finally, this work is supplemented by illustrative examples exploiting symbolic computation used within a framework of continuous reflectance map model (i.e. an image irradiance equation) and applied to a genuine Lambertian surfaces.
Direct Differential Photometric Stereo Shape Recovery of Diffuse and Specular Surfaces
Journal of Mathematical Imaging and Vision, 2016
Recovering the 3D shape of an object from shading is a challenging problem due to the complexity of modeling light propagation and surface reflections. Photometric Stereo (PS) is broadly considered a suitable approach for high-resolution shape recovery, but its functionality is restricted to a limited set of object surfaces and controlled lighting setup. In particular, PS models generally consider reflection from objects as purely diffuse, with specularities being regarded as a nuisance that breaks down shape reconstruction. This is a serious drawback for implementing PS approaches since most common materials have prominent specular components. In this paper, we propose a PS model that solves the problem for both diffuse and specular components aimed at shape recovery of generic objects with the approach being independent of the albedo values
Photometric Stereo from Maximum Feasible Lambertian Reflections
Lecture Notes in Computer Science, 2010
We present a Lambertian photometric stereo algorithm robust to specularities and shadows and it is based on a maximum feasible subsystem (Max FS) framework. A Big-M method is developed to obtain the maximum subset of images that satisfy the Lambertian constraint among the whole set of captured photometric stereo images which include non-Lambertian reflections such as specularities and shadows. Our algorithm employs purely algebraic pixel-wise optimization without relying on probabilistic/physical reasoning or initialization, and it guarantees the global optimality. It can be applied to the image sets with the number of images ranging from four to hundreds, and we show that the computation time is reasonably short for a medium number of images (10~100). Experiments are carried out with various objects to demonstrate the effectiveness of the algorithm.
Unambiguous determination of shape from photometric stereo with unknown light sources
Photometric stereo with uncalibrated lights determines surface orientations ambiguously up to any regular transformation. If the surface reflectance model is separable with respect to the illumination and viewing directions, its inherent symmetries enable to design two previously unrecognized constraints on normals that reduce this ambiguity. The two constraints represent projections of normals onto planes perpendicular to the viewing and illumination directions, respectively. We identify the classes of transformations that leave each constraint invariant. We construct the constraints using polarization measurement under the assumption of separable reflectance model for smooth dielectrics. We verify that applying the first constraint together with the integrability constraint results in bas-relief ambiguity, while application of the second constraint on integrable normals reduces the ambiguity to convex/concave ambiguity. Importantly, the latter result is also obtained when the first and second constraints alone are combined.
Photometric stereo through an adapted alternation approach
2008 15th IEEE International Conference on Image Processing, 2008
Photometric stereo aims at finding the surface normal and reflectance at every point of an object from a set of images obtained under different lighting conditions. The obtained intensity image data are stacked into a matrix that can be approximated by a low-dimensional linear subspace, under the Lambertian model. The current paper proposes to use an adaptation of the Alternation technique to tackle this problem when the images contain missing data, which correspond to pixels in shadow and saturated regions. Experimental results considering both synthetic and real images show the good performance of the proposed Alternation-based strategy.