Purposive Sample Consensus: A Paradigm for Model Fitting with Application to Visual Odometry

Abstract

RANSAC (random sample consensus) is a robust algorithm for model fitting and outliers' removal, however, it is neither efficient nor reliable enough to meet the requirement of many applications where time and precision is critical. Various algorithms have been developed to improve its performance for model fitting.A new algorithm named PURSAC (purposive sample consensus) is introduced in this paper, which has three major steps to address the limitations of RANSAC and its variants. Firstly, instead of assuming all the samples have a same probability to be inliers, PURSAC seeks their differences and purposively selects sample sets. Secondly, as sampling noise always exists; the selection is also according to the sensitivity analysis of a model against the noise. The final step is to apply a local optimization for further improving its model fitting performance. Tests show that PURSAC can achieve very high model fitting certainty with a small number of iterations.Two cases are investigated for PURSAC implementation. It is applied to line fitting to explain its principles, and then to feature based visual odometry, which requires efficient, robust and precise model fitting. Experimental results demonstrate that PURSAC improves the accuracy and efficiency of fundamental matrix estimation dramatically, resulting in a precise and fast visual odometry.

Novel adaptive genetic algorithm sample consensus

“…Purposive Sample Consensus (PURSAC) [16] is similar to LO-RANSAC and instead of selecting samples from all of the available data, next sample subset is selected only form the best model inliers. In order to dilute the effect of sampling noise, PUR-SAC uses some different strategies such as selecting subset from data points that have long distance or using all of the inliers to generate a model.…”

“…Bail-out test [13] is another paradigm to terminate the verification early which is similar to R-RANSAC [5]. More specifically, it considers the number of inliers K n within C n which is a subset of all points P follows a hyper-geometric distribution Purposive Sample Consensus (PURSAC) [16] is similar to LO-RANSAC and instead of selecting samples from all of the available data, next sample subset is selected only form the best model inliers. In order to dilute the effect of sampling noise, PUR-SAC uses some different strategies such as selecting a subset of data points that have long distance or using all of the inliers to generate a model.…”

Improving RANSAC for Efficient and Precise Model Fitting with Statistical Analysis

“…The density of the normal distribution ρ is decided by the mean μ and standard deviation σ. The analysis of sampling noise against model hypotheses in PURSAC shows that even if a consensus subset all from the inliers, due to the sampling noise and degenerate configurations, the model hypothesis may be different and far from the optimal one [12]. A semi-purposive subset selection is proposed in PURSAC to reduce the effect of measurement noise for model fitting.…”

“…Many algorithms have been developed as the variants of RANSAC [3][4][5][6][7][8][9][10][11][12][13][14]. MLESAC (maximum likelihood estimation sample consensus) by Torr and Zisserman [8] adopts the same sampling strategy as RANSAC to generate putative solutions, but chooses the solution to maximize the likelihood rather than just the number of inliers.…”

“…Capel developed a statistical bail-out test for RANSAC that permits the scoring process be terminated early and saves computation cost [10]. Wang and Luo introduced PURSAC (purposive) to avoid random searching in RANSAC using discriminative information from a dataset and analysing the noise-model relationship [12]. Uncertainty RANSAC incorporates uncertainty of samples as outliers for reducing the number of iterations [13].…”