Counter-Hypothetical Particle Filters for Single Object Pose Tracking

TL;DR

Inspired by the notions of plausibility and implausibility from Evidential Reasoning, the addition of the Counter-Hypothetical likelihood function assigns a level of doubt to each particle in the particle filter to estimate the level of failure within the filter.

Abstract

Particle filtering is a common technique for six degrees of freedom (6D) pose estimation due to its ability to tractably represent belief over object pose. However, the particle filter is prone to particle deprivation due to the high-dimensional nature of 6D pose. When particle deprivation occurs, it can cause mode collapse of the underlying belief distribution during importance sampling. If the region surrounding the true state suffers from mode collapse, recovering its belief is challenging since the area is no longer represented in the probability mass formed by the particles. Previous methods mitigate this problem by randomizing and resetting particles in the belief distribution, but determining the frequency of reinvigoration has relied on hand-tuning abstract heuristics. In this paper, we estimate the necessary reinvigoration rate at each time step by introducing a Counter-Hypothetical likelihood function, which is used alongside the standard likelihood. Inspired by the notions of plausibility and implausibility from Evidential Reasoning, the addition of our Counter-Hypothetical likelihood function assigns a level of doubt to each particle. The competing cumulative values of confidence and doubt across the particle set are used to estimate the level of failure within the filter, in order to determine the portion of particles to be reinvigorated. We demonstrate the effectiveness of our method on the rigid body object 6D pose tracking task.

Figures (6)

• Figure 1: To estimate when the particle filter is failing, we measure the doubt associated with each sample through a Counter-Hypothetical likelihood function. We quantify both the evidence against a given estimate (gray), as well as in support of it (yellow). We estimate these quantities independently of one another, because they are not zero-sum due to ambiguity in the observation (blue). The relative magnitudes of these weightings fluctuate based on the quality of both the observations and estimates, as illustrated by a mug that is (A) unambiguously unlikely (B) plausible yet ambiguous due to the occluded handle (C) unambiguously likely (D) highly ambiguous.
• Figure 2: An illustration of the proposed modification to the traditional resampling step of the particle filter, visualized as was presented in the Condensation Algorithm work isard1998condensation In the traditional particle filter (left), each iteration begins with a set of weighted particles (top). The samples are drawn with replacement, and then the action model and diffusion are applied to create the prediction distribution (blue). Each sample is then passed through the likelihood function (yellow) to receive a weighting. This posterior distribution then becomes the prior for the next iteration. In our proposed modification (right), each iteration begins with a set of weighted particles (top), as well as a weighting for the Counter-Hypothetical (black). In the resampling stage, only five of the eight particles are created by sampling off the prior distribution (blue), and the Counter-Hypothetical weighting causes three samples to be randomly sampled from the candidate distribution (pink). All of these samples are passed through the Counter-Hypothetical likelihood to be assigned a Counter-Hypothetical weighting (gray). These raw weightings are summed to create a new, singular Counter-Hypothetical weighting representing the doubt across the set. All samples are also passed through the traditional likelihood function (yellow). The posterior distribution and Counter-Hypothetical weighting then become the inputs for the next iteration.
• Figure 3: Relationship of the quantities in Evidential Reasoning shafer1976mathematical. This paradigm inspires our Counter-Hypothetical likelihood function visualized in Figure \ref{['fig:overview']}
• Figure 4: Area Under the Curve scores for all methods for object 6D pose tracking on the YCB Video Dataset. ADD scores and the symmetric version (ADD-S) are presented. Our presented method, CH-PF, outperforms other methods focused on alleviating particle deprivation in instances of occlusion, when the information from the likelihood function is the most noisy (RGB data).
• Figure 5: Selected qualitative results for the Counter-Hypothetical Particle Filter. The cracker box is significantly occluded by other objects in the scene. In early iterations (left), the cracker box belief is not converged and the estimate has high error. The reinvigoration rate, calculated from the belief, is high. In later iterations (middle), the belief converges to the ground truth state, and the reinvigoration rate drops. Once the belief has converged (right), the reinvigoration rate is low. This figure is best viewed in color.