11 research outputs found
A Smooth Representation of Belief over SO(3) for Deep Rotation Learning with Uncertainty
Accurate rotation estimation is at the heart of robot perception tasks such
as visual odometry and object pose estimation. Deep neural networks have
provided a new way to perform these tasks, and the choice of rotation
representation is an important part of network design. In this work, we present
a novel symmetric matrix representation of the 3D rotation group, SO(3), with
two important properties that make it particularly suitable for learned models:
(1) it satisfies a smoothness property that improves convergence and
generalization when regressing large rotation targets, and (2) it encodes a
symmetric Bingham belief over the space of unit quaternions, permitting the
training of uncertainty-aware models. We empirically validate the benefits of
our formulation by training deep neural rotation regressors on two data
modalities. First, we use synthetic point-cloud data to show that our
representation leads to superior predictive accuracy over existing
representations for arbitrary rotation targets. Second, we use image data
collected onboard ground and aerial vehicles to demonstrate that our
representation is amenable to an effective out-of-distribution (OOD) rejection
technique that significantly improves the robustness of rotation estimates to
unseen environmental effects and corrupted input images, without requiring the
use of an explicit likelihood loss, stochastic sampling, or an auxiliary
classifier. This capability is key for safety-critical applications where
detecting novel inputs can prevent catastrophic failure of learned models.Comment: In Proceedings of Robotics: Science and Systems (RSS'20), Corvallis ,
Oregon, USA, Jul. 12-16, 202
Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection
Semidefinite Programming (SDP) and Sums-of-Squares (SOS) relaxations have led
to certifiably optimal non-minimal solvers for several robotics and computer
vision problems. However, most non-minimal solvers rely on least-squares
formulations, and, as a result, are brittle against outliers. While a standard
approach to regain robustness against outliers is to use robust cost functions,
the latter typically introduce other non-convexities, preventing the use of
existing non-minimal solvers. In this paper, we enable the simultaneous use of
non-minimal solvers and robust estimation by providing a general-purpose
approach for robust global estimation, which can be applied to any problem
where a non-minimal solver is available for the outlier-free case. To this end,
we leverage the Black-Rangarajan duality between robust estimation and outlier
processes (which has been traditionally applied to early vision problems), and
show that graduated non-convexity (GNC) can be used in conjunction with
non-minimal solvers to compute robust solutions, without requiring an initial
guess. Although GNC's global optimality cannot be guaranteed, we demonstrate
the empirical robustness of the resulting robust non-minimal solvers in
applications, including point cloud and mesh registration, pose graph
optimization, and image-based object pose estimation (also called shape
alignment). Our solvers are robust to 70-80% of outliers, outperform RANSAC,
are more accurate than specialized local solvers, and faster than specialized
global solvers. We also propose the first certifiably optimal non-minimal
solver for shape alignment using SOS relaxation.Comment: 10 pages, 5 figures, published at IEEE Robotics and Automation
Letters (RA-L), 2020, Best Paper Award in Robot Vision at ICRA 202
In Perfect Shape: Certifiably Optimal 3D Shape Reconstruction from 2D Landmarks
We study the problem of 3D shape reconstruction from 2D landmarks extracted
in a single image. We adopt the 3D deformable shape model and formulate the
reconstruction as a joint optimization of the camera pose and the linear shape
parameters. Our first contribution is to apply Lasserre's hierarchy of convex
Sums-of-Squares (SOS) relaxations to solve the shape reconstruction problem and
show that the SOS relaxation of minimum order 2 empirically solves the original
non-convex problem exactly. Our second contribution is to exploit the structure
of the polynomial in the objective function and find a reduced set of basis
monomials for the SOS relaxation that significantly decreases the size of the
resulting semidefinite program (SDP) without compromising its accuracy. These
two contributions, to the best of our knowledge, lead to the first certifiably
optimal solver for 3D shape reconstruction, that we name Shape*. Our third
contribution is to add an outlier rejection layer to Shape* using a truncated
least squares (TLS) robust cost function and leveraging graduated non-convexity
to solve TLS without initialization. The result is a robust reconstruction
algorithm, named Shape#, that tolerates a large amount of outlier measurements.
We evaluate the performance of Shape* and Shape# in both simulated and real
experiments, showing that Shape* outperforms local optimization and previous
convex relaxation techniques, while Shape# achieves state-of-the-art
performance and is robust against 70% outliers in the FG3DCar dataset.Comment: Camera-ready, CVPR 2020. 18 pages, 5 figures, 1 tabl
Optimal Pose and Shape Estimation for Category-level 3D Object Perception
We consider a category-level perception problem, where one is given 3D sensor
data picturing an object of a given category (e.g. a car), and has to
reconstruct the pose and shape of the object despite intra-class variability
(i.e. different car models have different shapes). We consider an active shape
model, where -- for an object category -- we are given a library of potential
CAD models describing objects in that category, and we adopt a standard
formulation where pose and shape estimation are formulated as a non-convex
optimization. Our first contribution is to provide the first certifiably
optimal solver for pose and shape estimation. In particular, we show that
rotation estimation can be decoupled from the estimation of the object
translation and shape, and we demonstrate that (i) the optimal object rotation
can be computed via a tight (small-size) semidefinite relaxation, and (ii) the
translation and shape parameters can be computed in closed-form given the
rotation. Our second contribution is to add an outlier rejection layer to our
solver, hence making it robust to a large number of misdetections. Towards this
goal, we wrap our optimal solver in a robust estimation scheme based on
graduated non-convexity. To further enhance robustness to outliers, we also
develop the first graph-theoretic formulation to prune outliers in
category-level perception, which removes outliers via convex hull and maximum
clique computations; the resulting approach is robust to 70%-90% outliers. Our
third contribution is an extensive experimental evaluation. Besides providing
an ablation study on a simulated dataset and on the PASCAL3D+ dataset, we
combine our solver with a deep-learned keypoint detector, and show that the
resulting approach improves over the state of the art in vehicle pose
estimation in the ApolloScape datasets
A Quaternion-Based Certifiably Optimal Solution to the Wahba Problem With Outliers
© 2019 IEEE. The Wahba problem, also known as rotation search, seeks to find the best rotation to align two sets of vector observations given putative correspondences, and is a fundamental routine in many computer vision and robotics applications. This work proposes the first polynomial-time certifiably optimal approach for solving the Wahba problem when a large number of vector observations are outliers. Our first contribution is to formulate the Wahba problem using a Truncated Least Squares (TLS) cost that is insensitive to a large fraction of spurious correspondences. The second contribution is to rewrite the problem using unit quaternions and show that the TLS cost can be framed as a Quadratically-Constrained Quadratic Program (QCQP). Since the resulting optimization is still highly non-convex and hard to solve globally, our third contribution is to develop a convex Semidefinite Programming (SDP) relaxation. We show that while a naive relaxation performs poorly in general, our relaxation is tight even in the presence of large noise and outliers. We validate the proposed algorithm, named QUASAR (QUAternion-based Semidefinite relAxation for Robust alignment), in both synthetic and real datasets showing that the algorithm outperforms RANSAC, robust local optimization techniques, global outlier-removal procedures, and Branch-and-Bound methods. QUASAR is able to compute certifiably optimal solutions (i.e. the relaxation is exact) even in the case when 95% of the correspondences are outliers