Globally Optimal Inlier Set Maximization for Atlanta World Understanding

Area of Science:

• Computer Vision
• Robotics
• 3D Reconstruction

Background:

• Man-made structures are often modeled using the Manhattan world assumption, which assumes orthogonal horizontal directions.
• The Manhattan world assumption is restrictive and cannot represent a wider range of scenes.
• The Atlanta world assumption offers a more flexible model with non-orthogonal horizontal directions.

Purpose of the Study:

• To propose a globally optimal method for estimating Atlanta world directions from surface normals and image lines.
• To develop an efficient branch-and-bound framework for solving the challenging Atlanta direction estimation problem.
• To introduce strategies for efficient bound computation and automatic estimation of the number of horizontal directions.

Main Methods:

• Introduced the Atlanta world assumption, a model with a vertical and non-orthogonal horizontal directions.
• Developed a novel search space and parametrization for the Atlanta world.
• Implemented a branch-and-bound (BnB) framework with rectangular and slice bound computations on the extended Gaussian image (EGI) for efficient optimization.
• Proposed a two-stage method for automatically determining the number of horizontal directions.

Main Results:

• Presented the first globally optimal inlier set maximization method for Atlanta direction estimation.
• Demonstrated efficient bound computation strategies (rectangular and slice bounds) within the BnB framework.
• Successfully validated the approach on synthetic and real-world datasets, confirming its effectiveness.

Conclusions:

• The proposed Atlanta world assumption and associated estimation method provide a more flexible and accurate way to model man-made structures.
• The branch-and-bound approach with efficient bound computations effectively addresses the complexity of the Atlanta world estimation problem.
• The method's validity is confirmed by experimental results, showing its potential for applications in 3D reconstruction and scene understanding.