Model-free Consensus Maximization for Non-Rigid Shapes

TL;DR

This paper introduces a model-free consensus maximization approach formulated as an Integer Program and solved with Branch and Bound, effectively removing outliers in non-rigid shape matching and 3D image correspondence even at high outlier ratios.

Contribution

It presents a novel model-free consensus maximization method formulated as an Integer Program and solved optimally, improving outlier removal in non-rigid shape and image matching tasks.

Findings

Outperforms state-of-the-art in non-rigid shape outlier removal

Effective with outlier ratios up to 80%

Achieves comparable or better results in 3D template-image matching

Abstract

Many computer vision methods use consensus maximization to relate measurements containing outliers with the correct transformation model. In the context of rigid shapes, this is typically done using Random Sampling and Consensus (RANSAC) by estimating an analytical model that agrees with the largest number of measurements (inliers). However, small parameter models may not be always available. In this paper, we formulate the model-free consensus maximization as an Integer Program in a graph using `rules' on measurements. We then provide a method to solve it optimally using the Branch and Bound (BnB) paradigm. We focus its application on non-rigid shapes, where we apply the method to remove outlier 3D correspondences and achieve performance superior to the state of the art. Our method works with outlier ratio as high as 80\%. We further derive a similar formulation for 3D template to image matching, achieving similar or better performance compared to the state of the art.