Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold
Abstract
Single image pose estimation is a fundamental problem in many vision
and robotics tasks, and existing deep learning approaches suffer by
not completely modeling and handling: i) uncertainty about the
predictions, and ii) symmetric objects with multiple (sometimes
infinite) correct poses. To this end, we introduce a method to
estimate arbitrary, non-parametric distributions on SO(3). Our key
idea is to represent the distributions implicitly, with a neural
network that estimates the probability given the input image and a
candidate pose. Grid sampling or gradient ascent can be used to find
the most likely pose, but it is also possible to evaluate the
probability at any pose, enabling reasoning about symmetries and
uncertainty. This is the most general way of representing
distributions on manifolds, and to showcase the rich expressive power,
we introduce a dataset of challenging symmetric and nearly-symmetric
objects. We require no supervision on pose uncertainty – the model
trains only with a single pose per example. Nonetheless, our implicit
model is highly expressive to handle complex distributions over 3D
poses, while still obtaining accurate pose estimation on standard
non-ambiguous environments, achieving state-of-the-art performance
on Pascal3D+ and ModelNet10-SO(3) benchmarks. Code, data, and
visualizations may be found at implicit-pdf.github.io.
and robotics tasks, and existing deep learning approaches suffer by
not completely modeling and handling: i) uncertainty about the
predictions, and ii) symmetric objects with multiple (sometimes
infinite) correct poses. To this end, we introduce a method to
estimate arbitrary, non-parametric distributions on SO(3). Our key
idea is to represent the distributions implicitly, with a neural
network that estimates the probability given the input image and a
candidate pose. Grid sampling or gradient ascent can be used to find
the most likely pose, but it is also possible to evaluate the
probability at any pose, enabling reasoning about symmetries and
uncertainty. This is the most general way of representing
distributions on manifolds, and to showcase the rich expressive power,
we introduce a dataset of challenging symmetric and nearly-symmetric
objects. We require no supervision on pose uncertainty – the model
trains only with a single pose per example. Nonetheless, our implicit
model is highly expressive to handle complex distributions over 3D
poses, while still obtaining accurate pose estimation on standard
non-ambiguous environments, achieving state-of-the-art performance
on Pascal3D+ and ModelNet10-SO(3) benchmarks. Code, data, and
visualizations may be found at implicit-pdf.github.io.
Research Areas
