Pose estimation is central to several robotics applications such as registration, hand–eye calibration, and simultaneous localization and mapping (SLAM). Online pose estimation methods typically us...

https://journals.sagepub.com/doi/pdf/10.1177/0278364918778353

Probabilistic pose estimation using a Bingham distribution-based linear filter:

Pose estimation is central to several robotics applications such as registration, hand-eye calibration, SLAM, etc. Online pose estimation methods typically use Gaussian distributions to describe the uncertainty in the pose parameters. Such a description can be inadequate when using parameters such as unit-quaternions that are not unimodally distributed. A Bingham distribution can effectively model the uncertainty in unit-quaternions, as it has antipodal symmetry and is defined on a unit-hypersphere. A combination of Gaussian and Bingham distributions is used to develop a linear filter that accurately estimates the distribution of the pose parameters, in their true space. To the best of our knowledge our approach is the first implementation to use a Bingham distribution for 6 DoF pose estimation. Experiments assert that this approach is robust to initial estimation errors as well as sensor noise. Compared to state of the art methods, our approach takes fewer iterations to converge onto the correct pose estimate. The efficacy of the formulation is illustrated with a number of simulated examples on standard datasets as well as real-world experiments.

http://www.roboticsproceedings.org/rss13/p16.pdf

Bingham Distribution-Based Linear Filter for Online Pose Estimation

In this paper, we present a method for accurately estimating the shape of an object by integrating the surface orientation measured by photometric stereo and the position measured by some range-measuring method. We first show that even if the knowledge of the reflectance/illumination is inaccurate, the first derivatives of the photometrically measured orientation can be accurately estimated at the surface points where they have small values. We propose a probabilistic framework to quantitate the (in)accuracy of the knowledge and connect it to the estimation accuracy of these derivatives. Based on this framework, we consider optimally integrating the surface orientation and position to obtain the object shape with higher accuracy. The integration reduces to an optimization problem, and it is efficiently solved by belief propagation. We present several experimental results showing the effectiveness of the proposed approach.

Optimal integration of photometric and geometric surface measurements using inaccurate reflectance/illumination knowledge

Shape-from-shading (SFS) methods tend to rely on models with few parameters because these parameters need to be hand-tuned. This limits the number of different cues that the SFS problem can exploit. In this paper, we show how machine learning can be applied to an SFS model with a large number of parameters. Our system learns a set of weighting parameters that use the intensity of each pixel in the image to gauge the importance of that pixel in the shape reconstruction process. We show empirically that this leads to a significant increase in the accuracy of the recovered surfaces. Our learning approach is novel in that the parameters are optimized with respect to actual surface output by the system. In the first, offline phase, a hemisphere is rendered using a known illumination direction. The isophotes in the resulting reflectance map are then modelled using Gaussian mixtures to obtain a parametric representation of the isophotes. This Gaussian parameterization is then used in the second phase to learn intensity-based weights using a database of 3D shapes. The weights can also be optimized for a particular input image.

/pdf/training-many-parameter-shape-from-shading-models-using-a-1k18ozya6l.pdf

Training many-parameter shape-from-shading models using a surface database

In this paper we present a new framework for shape-from-shading which relies on a novel regularisation term which preserves surface structure. The resulting algorithm is both robust and accurate. We show that it can recover stable surface estimates from both synthetic and real world images of complex objects, even under extreme illumination.

Structure-Preserving Regularisation Constraints for Shape-from-Shading

The Shape-from-Shading [SfS] problem infers shape from reflected light, collected using a camera at a single point in space only. Reflected light alone does not provide sufficient constraint and extra information is required; typically a smoothness assumption is made. A surface with Lambertian reflectance lit by a single infinitely distant light source is also typical.

We solve this typical SfS problem using belief propagation to marginalise a probabilistic model. The key novel step is in using a directional probability distribution, the Fisher-Bingham distribution. This produces a fast and relatively simple algorithm that does an effective job of both extracting details and being robust to noise. Quantitative comparisons with past algorithms are provided using both synthetic and real data.

/pdf/belief-propagation-with-directional-statistics-for-solving-4fcwwzrcpu.pdf

Tom S. Haines

Papers

Belief Propagation with Directional Statistics for Solving the Shape-from-Shading Problem