A Principled Approach for Coarse-to-Fine MAP Inference

Abstract

In this work we reconsider labeling problems with (virtually) continuous state spaces, which are of relevance in low level computer vision. In order to cope with such huge state spaces multi-scale methods have been proposed to approximately solve such labeling tasks. Although performing well in many cases, these methods do usually not come with any guarantees on the returned solution. A general and principled approach to solve labeling problems is based on the well-known linear programming relaxation, which appears to be prohibitive for large state spaces at the first glance. We demonstrate that a coarse-to-fine exploration strategy in the label space is able to optimize the LP relaxation for non-trivial problem instances with reasonable run-times and moderate memory requirements.

Full Flow: Optical Flow Estimation By Global Optimization over Regular Grids

“…In contrast, we operate on dense grids with large twodimensional label spaces. A number of works considered a simplified MRF formulation that decomposes the horizontal and vertical components of the flow [34,27,47]. In contrast, we demonstrate the feasibility of operating on much larger models with two-dimensional label spaces.…”

Maximum persistency via iterative relaxed inference with graphical models

“…(61) Expression (60b) is a message passing for f , but the minimum is only over Yu and the result is needed only for j ∈ Yv. This message can be computed in time O(|Yu|+|Yv|) using the same algorithms [15,28,3] (see also non-uniform min-convolution in [52] [19] run for one iteration with predefined label order, denoted by MQPBO, and run 10 iterations in 10 random label orders, denoted by MQPBO-10.…”

“…(61) Expression (60b) is a message passing for f , but the minimum is only over Yu and the result is needed only for j ∈ Yv. This message can be computed in time O(|Yu|+|Yv|) using the same algorithms [15,28,3] (see also non-uniform min-convolution in [52]). Evaluating (61) takes additional O(|Yv|) time and minimum in (58) takes O(|Yu|) time assuming that components of a(i) are equal for j / ∈ Yv (because it is already true for ḡ and ϕ).…”

Random field optimization using local label hierarchy

“…The study in [Zach 2014] proposed a coarse-to-fine approach based on primaldual min-sum belief propagation. Their dead-end elimination detects states that are unfavorable due to having extremely large unary potentials and other possible causes that render them not to be part of any optimal solution.…”