Pose Estimation in Conformal Geometric Algebra

2D-3D pose estimation means to estimate the relative position and orientation of a 3D object with respect to a reference camera system. This work has its main focus on the theoretical foundations of the 2D-3D pose estimation problem: We discuss the involved mathematical spaces and their interaction within higher order entities. To cope with the pose problem (how to compare 2D projective image features with 3D Euclidean object features), the principle we propose is to reconstruct image features (e.g. points or lines) to one dimensional higher entities (e.g. 3D projection rays or 3D reconstructed planes) and express constraints in the 3D space. It turns out that the stratification hierarchy \cite{faugerasstrat} introduced by Faugeras is involved in the scenario. But since the stratification hierarchy by Faugeras is based on pure point concepts a new algebraic embedding is required when dealing with higher order entities. The conformal geometric algebra (CGA) \cite{hli1} is well suited to solve this problem, since it subsumes the involved mathematical spaces. Operators are defined to switch entities between the algebras of the conformal space and its Euclidean and projective subspace. This leads to another interpretation of the stratification hierarchy, which is not restricted to be based solely on point concepts. This work summarizes the theoretical foundations needed to deal with the pose problem. Therefore it contains mainly basics of Euclidean, projective and conformal geometry. Since especially conformal geometry is not well known in computer science, we recapitulate the mathematical concepts in some detail. We believe that this geometric model is useful also for many other computer vision tasks and has been ignored so far. Applications of these foundations are presented in part II. Part II: Part II uses the foundations of part I to define constraint equations for 2D-3D pose estimation of different corresponding entities. Most articles on pose estimation concentrate on specific types of correspondences, mostly between point, and only rarely line correspondences. The first aim of this part is to extend pose estimation scenarios to correspondences of an extended set of geometric entities. In this context we are interested to relate the following (2D) image and (3D) model types: 2D point/3D point, 2D line/3D point, 2D line/3D line, 2D conic/3D circle, 2D circle/3D sphere. Furthermore, to handle articulated objects, we describe kinematic chains in this context in a similar manner. We ensure that all constraint equations end up in a distance measure in the Euclidean space, which is well posed in the context of noisy data. We also discuss the numerical estimation of the pose. We propose to use linearized twist transformations which result in well conditioned and fast solvable systems of equations. The key idea is not to search for the representation of the Lie group, describing the rigid body motion, but for the representation of their generating Lie algebra. This leads to real-time capable algorithms

Pose Estimation of Free-form Objects: Theory and Experiments

In this report we present geometric foundations and an algorithmic approach to deal with the 2D-3D pose estimation problem for free-form surface models. This work is an extension to earlier studies presented in [29]. The discussion of 1D contour models in [29] is extended to 2D free-form surface models. We use a parametric representation of surfaces and apply Fourier transformations to gain low-pass descriptions of objects. We present an algorithm for pose estimation, which uses the silhouette of the object as pictorial information and recovers the 3D pose of the object even for changing aspects of the object during image sequences. We further present extensions to couple surface and contour information on objects and show the potential of our chosen approach for complex objects and scenes

Unsupervised Reconstruction of 3D Human Pose Interactions From 2D Poses Alone

Current unsupervised 2D-3D human pose estimation (HPE) methods do not work in multi-person scenarios due to perspective ambiguity in monocular images. Therefore, we present one of the first studies investigating the feasibility of unsupervised multi-person 2D-3D HPE from just 2D poses alone, focusing on reconstructing human interactions. To address the issue of perspective ambiguity, we expand upon prior work by predicting the cameras' elevation angle relative to the subjects' pelvis. This allows us to rotate the predicted poses to be level with the ground plane, while obtaining an estimate for the vertical offset in 3D between individuals. Our method involves independently lifting each subject's 2D pose to 3D, before combining them in a shared 3D coordinate system. The poses are then rotated and offset by the predicted elevation angle before being scaled. This by itself enables us to retrieve an accurate 3D reconstruction of their poses. We present our results on the CHI3D dataset, introducing its use for unsupervised 2D-3D pose estimation with three new quantitative metrics, and establishing a benchmark for future research

EgoHumans: An Egocentric 3D Multi-Human Benchmark

We present EgoHumans, a new multi-view multi-human video benchmark to advance the state-of-the-art of egocentric human 3D pose estimation and tracking. Existing egocentric benchmarks either capture single subject or indoor-only scenarios, which limit the generalization of computer vision algorithms for real-world applications. We propose a novel 3D capture setup to construct a comprehensive egocentric multi-human benchmark in the wild with annotations to support diverse tasks such as human detection, tracking, 2D/3D pose estimation, and mesh recovery. We leverage consumer-grade wearable camera-equipped glasses for the egocentric view, which enables us to capture dynamic activities like playing tennis, fencing, volleyball, etc. Furthermore, our multi-view setup generates accurate 3D ground truth even under severe or complete occlusion. The dataset consists of more than 125k egocentric images, spanning diverse scenes with a particular focus on challenging and unchoreographed multi-human activities and fast-moving egocentric views. We rigorously evaluate existing state-of-the-art methods and highlight their limitations in the egocentric scenario, specifically on multi-human tracking. To address such limitations, we propose EgoFormer, a novel approach with a multi-stream transformer architecture and explicit 3D spatial reasoning to estimate and track the human pose. EgoFormer significantly outperforms prior art by 13.6% IDF1 on the EgoHumans dataset.Comment: Accepted to ICCV 2023 (Oral

Pose Estimation 3D Free-form Contours

In this report we discuss the 2D-3D pose estimation problem of 3D free-form contours. In our scenario we observe objects of any 3D shape in an image of a calibrated camera. Pose estimation means to estimate the relative position and orientation (containing a rotation $R$ and translation $T$) of the 3D object to the reference camera system. The fusion of modeling free-form contours within the pose estimation problem is achieved by using the conformal geometric algebra. The conformal geometric algebra is a geometric algebra which models entities as stereographic projected entities in an homogeneous model. This leads to a linear description of kinematics on the one hand and projective geometry on the other hand. To model free-form contours in the conformal framework we use twists to model cycloidal curves as twist-depending functions and interpret $n$-times nested cycloidal curves as functions generated by 3D Fourier descriptors. This means, we use the twist concept to apply a spectral domain representation of 3D contours within the pose estimation problem. We will show that twist representations of objects can numerically efficient and easily be applied to the pose estimation problem. The pose problem itself is formalized as implicit problem and we gain constraint equations, which have to be fulfilled with respect to the unknown rigid body motion. Several experiments visualize the robustness and real-time performance of our algorithms