Joint Prediction of Depths, Normals and Surface Curvature from RGB Images using CNNs

Understanding the 3D structure of a scene is of vital importance, when it comes to developing fully autonomous robots. To this end, we present a novel deep learning based framework that estimates depth, surface normals and surface curvature by only using a single RGB image. To the best of our knowledge this is the first work to estimate surface curvature from colour using a machine learning approach. Additionally, we demonstrate that by tuning the network to infer well designed features, such as surface curvature, we can achieve improved performance at estimating depth and normals.This indicates that network guidance is still a useful aspect of designing and training a neural network. We run extensive experiments where the network is trained to infer different tasks while the model capacity is kept constant resulting in different feature maps based on the tasks at hand. We outperform the previous state-of-the-art benchmarks which jointly estimate depths and surface normals while predicting surface curvature in parallel

Spherical Regression: Learning Viewpoints, Surface Normals and 3D Rotations on n-Spheres

Many computer vision challenges require continuous outputs, but tend to be solved by discrete classification. The reason is classification's natural containment within a probability $n$-simplex, as defined by the popular softmax activation function. Regular regression lacks such a closed geometry, leading to unstable training and convergence to suboptimal local minima. Starting from this insight we revisit regression in convolutional neural networks. We observe many continuous output problems in computer vision are naturally contained in closed geometrical manifolds, like the Euler angles in viewpoint estimation or the normals in surface normal estimation. A natural framework for posing such continuous output problems are $n$-spheres, which are naturally closed geometric manifolds defined in the $\mathbb{R}^{(n+1)}$ space. By introducing a spherical exponential mapping on $n$-spheres at the regression output, we obtain well-behaved gradients, leading to stable training. We show how our spherical regression can be utilized for several computer vision challenges, specifically viewpoint estimation, surface normal estimation and 3D rotation estimation. For all these problems our experiments demonstrate the benefit of spherical regression. All paper resources are available at https://github.com/leoshine/Spherical_Regression.Comment: CVPR 2019 camera read

Recovering facial shape using a statistical model of surface normal direction

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