Smith William A P, Hancock Edwin R
Department of Computer Science, University of York, UK.
IEEE Trans Pattern Anal Mach Intell. 2006 Dec;28(12):1914-30. doi: 10.1109/TPAMI.2006.251.
In this paper, we show how a statistical model of facial shape can be embedded within a shape-from-shading algorithm. We describe how facial shape can be captured using a statistical model of variations in surface normal direction. To construct this model, we make use of the azimuthal equidistant projection to map the distribution of surface normals from the polar representation on a unit sphere to Cartesian points on a local tangent plane. The distribution of surface normal directions is captured using the covariance matrix for the projected point positions. The eigenvectors of the covariance matrix define the modes of shape-variation in the fields of transformed surface normals. We show how this model can be trained using surface normal data acquired from range images and how to fit the model to intensity images of faces using constraints on the surface normal direction provided by Lambert's law. We demonstrate that the combination of a global statistical constraint and local irradiance constraint yields an efficient and accurate approach to facial shape recovery and is capable of recovering fine local surface details. We assess the accuracy of the technique on a variety of images with ground truth and real-world images.
在本文中，我们展示了如何将面部形状的统计模型嵌入到从阴影恢复形状的算法中。我们描述了如何使用表面法线方向变化的统计模型来捕捉面部形状。为了构建这个模型，我们利用方位等距投影将单位球面上极坐标表示的表面法线分布映射到局部切平面上的笛卡尔点。使用投影点位置的协方差矩阵来捕捉表面法线方向的分布。协方差矩阵的特征向量定义了变换后的表面法线场中的形状变化模式。我们展示了如何使用从距离图像获取的表面法线数据来训练这个模型，以及如何利用朗伯定律提供的表面法线方向约束将模型拟合到面部强度图像上。我们证明，全局统计约束和局部辐照度约束的结合产生了一种高效且准确的面部形状恢复方法，并且能够恢复精细的局部表面细节。我们在各种带有真实数据的图像和真实世界图像上评估了该技术的准确性。
