From a single RGB image of an unknown face, taken under unknown conditions, we estimate a physically plausible lighting model. First, the 3D geometry and texture of the face are estimated by fitting a 3D Morphable Model to the 2D input. With this estimated 3D model and a Virtual Light Stage (VLS), we generate a gallery of images of the face with all the same conditions, but different lighting. We consider non-lambertian reflectance and non-convex geometry to handle more realistic illumination effects in complex lighting conditions. Our hierarchical Bayesian approach automatically suppresses inconsistencies between the model and the input. It estimates the RGB values for the light sources of a VLS to reconstruct the input face with the estimated 3D face model. We discuss the relevance of the hierarchical approach to this minimally constrained inverse rendering problem and show how the hyperparameters can be controlled to improve the results of the algorithm for complex effects, such as cast shadows. Our algorithm is a contribution to single image face modeling and analysis, provides information about the imaging condition and facilitates realistic reconstruction of the input image, relighting, lighting transfer and lighting design.

中文翻译：

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具有虚拟灯光舞台的人像的多层贝叶斯逆照明

根据在未知条件下拍摄的未知面孔的单个RGB图像，我们可以估算出物理上合理的照明模型。首先，通过将3D变形模型拟合到2D输入来估算面部的3D几何形状和纹理。使用此估算的3D模型和虚拟灯光平台（VLS），我们生成了在所有相同条件下但光照不同的情况下面部图像的库。我们考虑非朗伯反射率和非凸几何形状，以在复杂的照明条件下处理更逼真的照明效果。我们的分层贝叶斯方法会自动消除模型与输入之间的不一致性。它估计VLS光源的RGB值，以使用估计的3D人脸模型重建输入人脸。我们讨论了分层方法与此最小约束逆渲染问题的相关性，并展示了如何控制超参数以改善算法对复杂效果（如投射阴影）的结果。我们的算法对单张图像人脸建模和分析做出了贡献，提供了有关成像条件的信息，并有助于对输入图像进行逼真的重建，重新照明，照明传递和照明设计。