Partial Procedural Geometric Model Fitting for Point Clouds

TL;DR

This paper introduces a novel partial geometric similarity metric enabling the fitting of arbitrary models to incomplete point cloud data, using a procedural model space and MCMC optimization for improved accuracy and speed.

Contribution

It proposes a new similarity metric and a partial procedural geometric model fitting method capable of handling incomplete point clouds, with a coarse-to-fine rejection strategy for acceleration.

Findings

The method effectively fits non-complete point clouds to arbitrary models.

It outperforms existing metrics in fitting incomplete data.

The approach accelerates fitting by several times through early rejection.

Abstract

Geometric model fitting is a fundamental task in computer graphics and computer vision. However, most geometric model fitting methods are unable to fit an arbitrary geometric model (e.g. a surface with holes) to incomplete data, due to that the similarity metrics used in these methods are unable to measure the rigid partial similarity between arbitrary models. This paper hence proposes a novel rigid geometric similarity metric, which is able to measure both the full similarity and the partial similarity between arbitrary geometric models. The proposed metric enables us to perform partial procedural geometric model fitting (PPGMF). The task of PPGMF is to search a procedural geometric model space for the model rigidly similar to a query of non-complete point set. Models in the procedural model space are generated according to a set of parametric modeling rules. A typical query is a point cloud. PPGMF is very useful as it can be used to fit arbitrary geometric models to non-complete (incomplete, over-complete or hybrid-complete) point cloud data. For example, most laser scanning data is non-complete due to occlusion. Our PPGMF method uses Markov chain Monte Carlo technique to optimize the proposed similarity metric over the model space. To accelerate the optimization process, the method also employs a novel coarse-to-fine model dividing strategy to reject dissimilar models in advance. Our method has been demonstrated on a variety of geometric models and non-complete data. Experimental results show that the PPGMF method based on the proposed metric is able to fit non-complete data, while the method based on other metrics is unable. It is also shown that our method can be accelerated by several times via early rejection.