This paper addresses the problem of photometric stereo for non-Lambertian surfaces. Existing approaches often adopt simplified reflectance models to make the problem more tractable, but this greatly hinders their applications on real-world objects. In this paper, we propose a deep fully convolutional network, called PS-FCN, that takes an arbitrary number of images of a static object captured under different light directions with a fixed camera as input, and predicts a normal map of the object in a fast feed-forward pass. Unlike the recently proposed learning based method, PS-FCN does not require a pre-defined set of light directions during training and testing, and can handle multiple images and light directions in an order-agnostic manner. Although we train PS-FCN on synthetic data, it can generalize well on real datasets. We further show that PS-FCN can be easily extended to handle the problem of uncalibrated photometric stereo.Extensive experiments on public real datasets show that PS-FCN outperforms existing approaches in calibrated photometric stereo, and promising results are achieved in uncalibrated scenario, clearly demonstrating its effectiveness.
Many sophisticated reflectance models have been proposed to approximate the non-Lambertian model, including analytical models like Torrance-Sparrow model @cite_8 , Ward model @cite_34 , Cook-Torrance model @cite_33 , etc. Instead of rejecting specular observations as outliers, sophisticated reflectance model based methods fit an analytical model to all observations. These methods require solving complex optimization problems, and can only handle limited classes of materials. Recently, bivariate BRDF representations @cite_20 @cite_39 were adopted to approximate isotropic BRDF, and a symmetry-based approach @cite_2 was proposed to handle anisotropic reflectance without explicitly estimating a reflectance model.
@cite_33 @cite_8 @cite_39 @cite_2 @cite_34 @cite_20
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Under the Lambertian reflectance model, uncalibrated photometric stereo with unknown light sources is inherently ambiguous. In this paper, we consider the use of a more general reflectance model, namely the Torrance and Sparrow model, in uncalibrated photometric stereo. We demonstrate that this can not only resolve the ambiguity when the light sources are unknown, but can also result in more accurate surface reconstructions and can capture the reflectance properties of a large number of nonLambertian surfaces. Our method uses single light source images with unknown lighting and no knowledge about the parameters of the reflectance model. It can recover the 3D shape of surfaces (up to the binary convex concave ambiguity) together with their reflectance properties. We have successfully tested our algorithm on a variety of nonLambertian surfaces demonstrating the effectiveness of our approach. In the case of human faces, the estimated skin reflectance has been shown to closely resemble the measured skin reflectance reported in the literature. We also demonstrate improved recognition results on 4050 images of 10 faces with variable lighting and viewpoint when the synthetic image-based representations of the faces are generated using the surface reconstructions and reflectance properties recovered while assuming the extended reflectance model. This paper presents a photometric stereo method that is purely pixelwise and handles general isotropic surfaces in a stable manner. Following the recently proposed sum-of-lobes representation of the isotropic reflectance function, we constructed a constrained bivariate regression problem where the regression function is approximated by smooth, bivariate Bernstein polynomials. The unknown normal vector was separated from the unknown reflectance function by considering the inverse representation of the image formation process, and then we could accurately compute the unknown surface normals by solving a simple and efficient quadratic programming problem. Extensive evaluations that showed the state-of-the-art performance using both synthetic and real-world images were performed. This paper presents a technique for acquiring the shape of real-world objects with complex isotropic and anisotropic reflectance. Our method estimates the local normal and tangent vectors at each pixel in a reference view from a sequence of images taken under varying point lighting. We show that for many real-world materials and a restricted set of light positions, the 2D slice of the BRDF obtained by fixing the local view direction is symmetric under reflections of the halfway vector across the normal-tangent and normal-binormal planes. Based on this analysis, we develop an optimization that estimates the local surface frame by identifying these planes of symmetry in the measured BRDF. As with other photometric methods, a key benefit of our approach is that the input is easy to acquire and is less sensitive to calibration errors than stereo or multi-view techniques. Unlike prior work, our approach allows estimating the surface tangent in the case of anisotropic reflectance. We confirm the accuracy and reliability of our approach with analytic and measured data, present several normal and tangent fields acquired with our technique, and demonstrate applications to appearance editing. This paper presents a new photometric stereo method aiming to efficiently estimate BRDF and reconstruct glossy surfaces. Rough specular surfaces exhibit wide specular lobes under different lightnings. They are ubiquitous and usually bring difficulties to both specular pixel removal and surface normal recovery. In our approach, we do not apply unreliable highlight separation and specularity estimation. Instead, an important visual cue, i.e. the cast shadow silhouette of the object, is employed to optimally recover global BRDF parameters. These parameter estimates are then taken into a reflectance model for robustly computing the surface normals and other local parameters using an iterative optimization. Within the unified framework, our method can also be used to reconstruct object surfaces assembled with multiple materials.