[Paper Review] Progressive-X+: Clustering in the Consensus Space.

Dániel Baráth, Denys Rozumnyi+3 more|arXiv (Cornell University)|Mar 25, 2021

Data Management and Algorithms62 references4 citations

TL;DR

Progressive-X+ is a real-time, iterative algorithm for detecting an unknown number of geometric models—such as homographies—by progressively identifying dominant model instances through RANSAC-like sampling and clustering in the consensus space. It achieves state-of-the-art accuracy by using a quality-driven consolidation process and a spatially coherent sampler that exploits neighborhood connectivity in data, enabling robust performance in multi-model vision tasks.

ABSTRACT

We propose Progressive-X+, a new algorithm for finding an unknown number of geometric models, e.g., homographies. The problem is formalized as finding dominant model instances progressively without forming crisp point-to-model assignments. Dominant instances are found via RANSAC-like sampling and a consolidation process driven by a model quality function considering previously proposed instances. New ones are found by clustering in the consensus space. This new formulation leads to a simple iterative algorithm with state-of-the-art accuracy while running in real-time on a number of vision problems. Also, we propose a sampler reflecting the fact that real-world data tend to form spatially coherent structures. The sampler returns connected components in a progressively growing neighborhood-graph. We present a number of applications where the use of multiple geometric models improves accuracy. These include using multiple homographies to estimate relative poses for global SfM; pose estimation from generalized homographies; and trajectory estimation of fast-moving objects.

Motivation & Objective

• To address the challenge of detecting an unknown number of geometric models in computer vision without requiring prior knowledge of model count.
• To improve accuracy and efficiency in multi-model estimation tasks such as pose estimation and trajectory tracking.
• To develop a sampling strategy that reflects spatial coherence in real-world data, enhancing model detection reliability.
• To enable real-time processing of complex vision problems involving multiple geometric structures.
• To provide a unified framework applicable to diverse applications like global SfM, generalized homography estimation, and fast-moving object tracking.

Proposed method

• Progressive-X+ uses RANSAC-like sampling to iteratively propose candidate models in the consensus space.
• A model quality function evaluates and consolidates previously detected instances, guiding the discovery of new dominant models.
• New model instances are identified through clustering in the consensus space, avoiding crisp point-to-model assignments.
• A novel spatially coherent sampler generates connected components in a growing neighborhood graph, reflecting real-world data structure.
• The algorithm operates iteratively, progressively refining model detection without requiring model count as input.
• The method is designed to be lightweight and efficient, enabling real-time performance across multiple vision applications.

Experimental results

Research questions

• RQ1 How can geometric model detection be performed efficiently and accurately when the number of models is unknown?
• RQ2 Can spatial coherence in real-world data be leveraged to improve the robustness of model sampling in multi-model estimation?
• RQ3 To what extent does clustering in the consensus space outperform traditional point-to-model assignment in multi-model fitting?
• RQ4 Can a quality-driven consolidation process enhance the detection of dominant models without prior model count?
• RQ5 How does Progressive-X+ perform in real-time on complex vision tasks involving multiple geometric models?

Key findings

• Progressive-X+ achieves state-of-the-art accuracy in multi-model geometric fitting tasks, outperforming existing methods in benchmark evaluations.
• The algorithm runs in real-time, making it suitable for online and interactive vision applications.
• The spatially coherent sampler improves model detection by favoring connected, plausible structures in data, enhancing robustness.
• Clustering in the consensus space enables effective discovery of new models without requiring crisp point-to-model assignments.
• The method successfully improves relative pose estimation in global SfM by modeling multiple homographies.
• It enables accurate trajectory estimation for fast-moving objects by modeling multiple motion structures.