A 3D Face Modelling Approach for Pose-Invariant Face Recognition in a Human-Robot Environment

Face analysis techniques have become a crucial component of human-machine interaction in the fields of assistive and humanoid robotics. However, the variations in head-pose that arise naturally in these environments are still a great challenge. In this paper, we present a real-time capable 3D face modelling framework for 2D in-the-wild images that is applicable for robotics. The fitting of the 3D Morphable Model is based exclusively on automatically detected landmarks. After fitting, the face can be corrected in pose and transformed back to a frontal 2D representation that is more suitable for face recognition. We conduct face recognition experiments with non-frontal images from the MUCT database and uncontrolled, in the wild images from the PaSC database, the most challenging face recognition database to date, showing an improved performance. Finally, we present our SCITOS G5 robot system, which incorporates our framework as a means of image pre-processing for face analysis

Combinatorial models of expanding dynamical systems

We define iterated monodromy groups of more general structures than partial self-covering. This generalization makes it possible to define a natural notion of a combinatorial model of an expanding dynamical system. We prove that a naturally defined "Julia set" of the generalized dynamical systems depends only on the associated iterated monodromy group. We show then that the Julia set of every expanding dynamical system is an inverse limit of simplicial complexes constructed by inductive cut-and-paste rules.Comment: The new version differs substantially from the first one. Many parts are moved to other (mostly future) papers, the main open question of the first version is solve

From 3D Point Clouds to Pose-Normalised Depth Maps

We consider the problem of generating either pairwise-aligned or pose-normalised depth maps from noisy 3D point clouds in a relatively unrestricted poses. Our system is deployed in a 3D face alignment application and consists of the following four stages: (i) data filtering, (ii) nose tip identification and sub-vertex localisation, (iii) computation of the (relative) face orientation, (iv) generation of either a pose aligned or a pose normalised depth map. We generate an implicit radial basis function (RBF) model of the facial surface and this is employed within all four stages of the process. For example, in stage (ii), construction of novel invariant features is based on sampling this RBF over a set of concentric spheres to give a spherically-sampled RBF (SSR) shape histogram. In stage (iii), a second novel descriptor, called an isoradius contour curvature signal, is defined, which allows rotational alignment to be determined using a simple process of 1D correlation. We test our system on both the University of York (UoY) 3D face dataset and the Face Recognition Grand Challenge (FRGC) 3D data. For the more challenging UoY data, our SSR descriptors significantly outperform three variants of spin images, successfully identifying nose vertices at a rate of 99.6%. Nose localisation performance on the higher quality FRGC data, which has only small pose variations, is 99.9%. Our best system successfully normalises the pose of 3D faces at rates of 99.1% (UoY data) and 99.6% (FRGC data)

Equidistribution of iterations of holomorphic correspondences and Hutchinson invariant sets

In this paper we analyze a certain family of holomorphic correspondences on $\hat{\mathbb{C}}\times\hat{\mathbb{C}}$ and prove their equidistribution properties. In particular, for any correspondence in this family we prove that the naturally associated multivalued map $F$ is such that for any $a\in \mathbb{C}$, we have that $(F^n)_*(\delta_a)$ converges to a probability measure $\mu_F$ for which $F_*(\mu_F)=\mu_F d$ where $d$ is the degree of $F$. This result is used to show that the minimal Hutchinson invariant set, introduced in [ABS20a], of a large class of operators and for sufficiently large $n$ exists and is the support of the aforementioned measure. We also prove that in this situation the minimal Hutchinson-invariant set is a Cantor set.Comment: Fixed typos, minor change in exposition of the result