Structure-from-motion in Spherical Video using the von Mises-Fisher Distribution

In this paper, we present a complete pipeline for computing structure-from-motion from the sequences of spherical images. We revisit problems from multiview geometry in the context of spherical images. In particular, we propose methods suited to spherical camera geometry for the spherical-n-point problem (estimating camera pose for a spherical image) and calibrated spherical reconstruction (estimating the position of a 3-D point from multiple spherical images). We introduce a new probabilistic interpretation of spherical structure-from-motion which uses the von Mises-Fisher distribution to model noise in spherical feature point positions. This model provides an alternate objective function that we use in bundle adjustment. We evaluate our methods quantitatively and qualitatively on both synthetic and real world data and show that our methods developed for spherical images outperform straightforward adaptations of methods developed for perspective images. As an application of our method, we use the structure-from-motion output to stabilise the viewing direction in fully spherical video

Linear Depth Estimation from an Uncalibrated, Monocular Polarisation Image

We present a method for estimating surface height directly from a single polarisation image simply by solving a large, sparse system of linear equations. To do so, we show how to express polarisation constraints as equations that are linear in the unknown depth. The ambiguity in the surface normal azimuth angle is resolved globally when the optimal surface height is reconstructed. Our method is applicable to objects with uniform albedo exhibiting diffuse and specular reflectance. We extend it to an uncalibrated scenario by demonstrating that the illumination (point source or first/second order spherical harmonics) can be estimated from the polarisation image, up to a binary convex/concave ambiguity. We believe that our method is the first monocular, passive shape-from-x technique that enables well-posed depth estimation with only a single, uncalibrated illumination condition. We present results on glossy objects, including in uncontrolled, outdoor illumination

A Data-augmented 3D Morphable Model of the Ear

Morphable models are useful shape priors for biometric recognition tasks. Here we present an iterative process of refinement for a 3D Morphable Model (3DMM) of the human ear that employs data augmentation. The process employs the following stages 1) landmark-based 3DMM fitting; 2) 3D template deformation to overcome noisy over-fitting; 3) 3D mesh editing, to improve the fit to manual 2D landmarks. These processes are wrapped in an iterative procedure that is able to bootstrap a weak, approximate model into a significantly better model. Evaluations using several performance metrics verify the improvement of our model using the proposed algorithm. We use this new 3DMM model-booting algorithm to generate a refined 3D morphable model of the human ear, and we make this new model and our augmented training dataset public

What Does 2D Geometric Information Really Tell Us About 3D Face Shape?

A face image contains geometric cues in the form of configurational information and contours that can be used to estimate 3D face shape. While it is clear that 3D reconstruction from 2D points is highly ambiguous if no further constraints are enforced, one might expect that the face-space constraint solves this problem. We show that this is not the case and that geometric information is an ambiguous cue. There are two sources for this ambiguity. The first is that, within the space of 3D face shapes, there are flexibility modes that remain when some parts of the face are fixed. The second occurs only under perspective projection and is a result of perspective transformation as camera distance varies. Two different faces, when viewed at different distances, can give rise to the same 2D geometry. To demonstrate these ambiguities, we develop new algorithms for fitting a 3D morphable model to 2D landmarks or contours under either orthographic or perspective projection and show how to compute flexibility modes for both cases. We show that both fitting problems can be posed as a separable nonlinear least squares problem and solved efficiently. We demonstrate both quantitatively and qualitatively that the ambiguity is present in reconstructions from geometric information alone but also in reconstructions from a state-of-the-art CNN-based method

Inverse Rendering of Faces with a 3D Morphable Model

In this paper, we present a complete framework to inverse render faces with a 3D Morphable Model (3DMM). By decomposing the image formation process into geometric and photometric parts, we are able to state the problem as a multilinear system which can be solved accurately and efficiently. As we treat each contribution as independent, the objective function is convex in the parameters and a global solution is guaranteed. We start by recovering 3D shape using a novel algorithm which incorporates generalization error of the model obtained from empirical measurements. We then describe two methods to recover facial texture, diffuse lighting, specular reflectance, and camera properties from a single image. The methods make increasingly weak assumptions and can be solved in a linear fashion. We evaluate our findings on a publicly available database, where we are able to outperform an existing state-of-the-art algorithm. We demonstrate the usability of the recovered parameters in a recognition experiment conducted on the CMU-PIE database