Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold

Kieran A Murphy, Carlos Esteves, Varun Jampani, Srikumar Ramalingam, Ameesh Makadia
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:7882-7893, 2021.

Abstract

In the deep learning era, the vast majority of methods to predict pose from a single image are trained to classify or regress to a single given ground truth pose per image. Such methods have two main shortcomings, i) they cannot represent uncertainty about the predictions, and ii) they cannot handle symmetric objects, where multiple (potentially infinite) poses may be correct. Only recently these shortcomings have been addressed, but current approaches as limited in that they cannot express the full rich space of distributions on the rotation manifold. 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 density, given the input image and a candidate pose. At inference time, grid sampling or gradient ascent can be used to find the most likely pose, but it is also possible to evaluate the density at any pose, enabling reasoning about symmetries and uncertainty. This is the most general way of representing distributions on manifolds, and to demonstrate its expressive power we introduce a new dataset containing symmetric and nearly-symmetric objects. Our method also shows advantages on the popular object pose estimation benchmarks ModelNet10-SO(3) and T-LESS. Code, data, and visualizations may be found at implicit-pdf.github.io.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-murphy21a, title = {Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold}, author = {Murphy, Kieran A and Esteves, Carlos and Jampani, Varun and Ramalingam, Srikumar and Makadia, Ameesh}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {7882--7893}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/murphy21a/murphy21a.pdf}, url = {https://proceedings.mlr.press/v139/murphy21a.html}, abstract = {In the deep learning era, the vast majority of methods to predict pose from a single image are trained to classify or regress to a single given ground truth pose per image. Such methods have two main shortcomings, i) they cannot represent uncertainty about the predictions, and ii) they cannot handle symmetric objects, where multiple (potentially infinite) poses may be correct. Only recently these shortcomings have been addressed, but current approaches as limited in that they cannot express the full rich space of distributions on the rotation manifold. 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 density, given the input image and a candidate pose. At inference time, grid sampling or gradient ascent can be used to find the most likely pose, but it is also possible to evaluate the density at any pose, enabling reasoning about symmetries and uncertainty. This is the most general way of representing distributions on manifolds, and to demonstrate its expressive power we introduce a new dataset containing symmetric and nearly-symmetric objects. Our method also shows advantages on the popular object pose estimation benchmarks ModelNet10-SO(3) and T-LESS. Code, data, and visualizations may be found at implicit-pdf.github.io.} }
Endnote
%0 Conference Paper %T Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold %A Kieran A Murphy %A Carlos Esteves %A Varun Jampani %A Srikumar Ramalingam %A Ameesh Makadia %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-murphy21a %I PMLR %P 7882--7893 %U https://proceedings.mlr.press/v139/murphy21a.html %V 139 %X In the deep learning era, the vast majority of methods to predict pose from a single image are trained to classify or regress to a single given ground truth pose per image. Such methods have two main shortcomings, i) they cannot represent uncertainty about the predictions, and ii) they cannot handle symmetric objects, where multiple (potentially infinite) poses may be correct. Only recently these shortcomings have been addressed, but current approaches as limited in that they cannot express the full rich space of distributions on the rotation manifold. 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 density, given the input image and a candidate pose. At inference time, grid sampling or gradient ascent can be used to find the most likely pose, but it is also possible to evaluate the density at any pose, enabling reasoning about symmetries and uncertainty. This is the most general way of representing distributions on manifolds, and to demonstrate its expressive power we introduce a new dataset containing symmetric and nearly-symmetric objects. Our method also shows advantages on the popular object pose estimation benchmarks ModelNet10-SO(3) and T-LESS. Code, data, and visualizations may be found at implicit-pdf.github.io.
APA
Murphy, K.A., Esteves, C., Jampani, V., Ramalingam, S. & Makadia, A.. (2021). Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:7882-7893 Available from https://proceedings.mlr.press/v139/murphy21a.html.

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