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Journal of Sensors

Volume 2016, Article ID 3243842, 18 pages

http://dx.doi.org/10.1155/2016/3243842

## A Novel Improved Probability-Guided RANSAC Algorithm for Robot 3D Map Building

^{1}College of Electronic and Control Engineering, Beijing University of Technology, Beijing 100124, China^{2}Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing 100124, China^{3}Engineering Research Center of Digital Community, Ministry of Education, Beijing 100124, China^{4}School of Mechanical and Electrical Engineering, Henan Institute of Science and Technology, Xinxiang 453003, China

Received 4 August 2015; Revised 19 February 2016; Accepted 16 March 2016

Academic Editor: Maan E. El Najjar

Copyright © 2016 Songmin Jia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents a novel improved RANSAC algorithm based on probability and DS evidence theory to deal with the robust pose estimation in robot 3D map building. In this proposed RANSAC algorithm, a parameter model is estimated by using a random sampling test set. Based on this estimated model, all points are tested to evaluate the fitness of current parameter model and their probabilities are updated by using a total probability formula during the iterations. The maximum size of inlier set containing the test point is taken into account to get a more reliable evaluation for test points by using DS evidence theory. Furthermore, the theories of forgetting are utilized to filter out the unstable inliers and improve the stability of the proposed algorithm. In order to boost a high performance, an inverse mapping sampling strategy is adopted based on the updated probabilities of points. Both the simulations and real experimental results demonstrate the feasibility and effectiveness of the proposed algorithm.

#### 1. Introduction

RANSAC algorithm is one of the popular methods for sensor data registration and modeling. In some vision-based SLAM (Simultaneous Localization and Mapping) algorithms, RANSAC algorithm provides an efficient solution for image matching procedure and establishes the data association among different views [1–3]. There are two typical types of algorithm for image matching, the dense way [4, 5] and sparse way [6, 7]. In dense match approach, the whole image is used for parameter estimation [8, 9]. Although this method is quite robust, it may be inaccurate when occlusion regions exist in the matching images. Sometimes, the influence of occlusions is reduced by using a robust weighted cost function. In sparse match step, image features are detected by using SIFT, SURF, or any other feature detection algorithms. The features are matched by using the distance of feature descriptor, and the matching pairs are sometimes ambiguous. To efficiently achieve a correct matching result, some robust algorithms were adopted to remove mismatching pairs, such as M-estimation [10], LMedS (Least Median of Squares) [11], or RANSAC (Random Sample Consensus) [12] algorithm. M-estimation established a new cost function with a robust weight. It worked well in some cases but was vulnerable to the noise. LMedS optimized the model by minimizing the median of errors. When the outlier rate was larger than 50%, M-estimation and LMedS might be no longer applicable. With the advantages of easy implementation and strong robustness, RANSAC algorithm was widely used in model parameter estimation problem. In standard RANSAC algorithm, a hypothesis set was randomly selected to estimate a parameter model. And an inlier set was detected by testing all input data with the estimated parameter model. A maximum size of inlier set was expected to be found within a predetermined iteration. However, the performance of this standard RANSAC was sometimes low. Even worse was the fact that the solution may not be reached when all iterations were finished.

To efficiently improve the performance of standard RANSAC algorithm, some methods have been proposed in recent decades. A hypothesis evaluation function and local optimization procedure were adopted to achieve a more accurate result. MSAC (M-estimation SAC) [10] evaluated the test point set with a bounded loss function to achieve a maximum likelihood consensus set. MLESAC (Maximum Likelihood SAC) [10] evaluated the hypothesis set by using the probability distribution of errors. The inlier error was modeled with an unbiased Gaussian distribution and outlier error used a uniform distribution. The maximum likelihood estimation was solved by minimizing a cost function. MAPSAC (Maximum A Posteriori Estimation SAC) [13] followed a Bayesian approach to solve the RANSAC problem with a robust MAP estimation. LO-RANSAC (Local Optimized RANSAC) [14] adopted an inner model reestimation procedure to improve the accuracy of the RANSAC algorithm.

Moreover, some heuristic mechanism sampling strategies and partial evaluation procedures were adopted to speed up the convergence of the algorithm. It seemed that a good sample strategy will reduce the time cost which was spent in finding the solution. A hypothesis set was selected based on the probabilities of test points in the Guided MLESAC [15]. In PROSAC (Progressive SAC) [16], the matching score was used as a prior knowledge for sorting the test data. A hypothesis set was selected among the data which was in the top-ranked matching score. It was also progressively tested on the less ranked data. In some extreme cases, the whole data would be tried in this algorithm. According to the assumption that an inlier tends to be closer to the inliers, NAPSAC (N Adjacent Points SAC) [17] sampled the data within a defined radius around a selected point. Based on the preliminary test of the hypothesis, Chum and Matas proposed R-RANSAC (Randomized RANSAC) [18] and R-RANSAC SPPR (Sequential Probability Ratio Test) [19]. These two methods performed a preliminary test based on and SPPR test after evaluating test points in every iteration. And a full test procedure was performed only when a hypothesis set passed the preliminary test. The preliminary test procedure effectively removed the obvious mistakes of hypothesis sets and improved the efficiency of RANSAC algorithm. Optimal RANSAC [20] adopted an inlier sample procedure to achieve a more accurate model estimation. When the size of the current inlier set was larger than a threshold, an inlier sample procedure would be performed to achieve a more reliable solution in the inlier set.

Furthermore, some intelligent algorithms such as Genetic Algorithm (GA) and multilayered feed-forward neural networks (NFNN) were also proposed in RANSAC algorithm. Rodehorst proposed a novel RANSAC algorithm based on GA [21]. In GASAC, the parents were generated by a standard RANSAC algorithm with a robust cost evaluation. Then, the best solution was achieved by using crossover and mutation operators on parents in GA procedure. Moumen presented a rather comprehensive study of robust supervised training of MFNN in a RANSAC framework from the standpoint of both accuracy and time [22]. In the iteration of RANSAC, the parameter model was estimated by using a small MFNN which was minimizing the mean squared error (MSE) with a standard back propagation algorithm. All inlier points were used to reestimate a new parameter model by training a new MFNN. And a new hypothesis set was achieved by using this new MFNN model. The convergence solution was achieved until the inlier set did not change any more.

In this paper, we propose a novel improved probability-guided RANSAC (IPGSAC) algorithm for mobile robot 3D map building. Under the framework of standard RANSAC algorithm, two types of probabilities are evaluated for test points by using a total probability formula and the statistics of maximum size of inlier set. To achieve a more robust evaluation of test points, DS evidence theory [23] is adopted to synthesize the multisource evaluation of test points. Moreover, the theories of forgetting are employed to filter out the unstable inliers. Based on the probability of test points, an inverse mapping sampling strategy is utilized to improve the convergence rate of the proposed algorithm. Finally, this proposed IPGSAC algorithm is applied for the mobile robot 3D map building. All the experimental results show the feasibility and effectiveness of the proposed algorithm.

The rest of this paper is organized as follows: in Section 2, we summarize IPGSAC before explaining each in detail. The components of our robot map building procedure are detailed in Section 3. Our simulation and real experimental results are described in Section 4. Finally, we give our conclusions and future work in Section 5.

#### 2. IPGSAC Algorithm

##### 2.1. Methodology Overview

The proposed IPGSAC algorithm is illustrated in Figure 1. At the beginning of IPGSAC algorithm, the probabilities of test points are initialized with a hybrid distribution. Based on those probabilities, points are selected for model estimation by employing an inverse mapping sampling strategy. The inlier and outlier sets are distinguished with a tolerance threshold . When the residual error of point is larger than , the is identified as an outlier point. Then, two types of probabilities are evaluated for test points by using a total probability formula and the statistics of maximum size of inlier set. According to the average observations of inlier points, the theories of forgetting are employed to reduce the redundancy of unstable inliers. To achieve a more reliable evaluation, the probability evaluations are synthesized by using DS evidence theory. When the maximum iteration limit is arrived at or the stopping criterion is reached, the main loop of IPGSAC will be finished. Finally, we reestimate the model parameter by using all inliers to achieve a more reliable inlier set with 3~5 iterations. In the standard RANSAC, the minimum number of iterations ensures that a correct hypothesis set is achieved with a determined confidence level at least once and it can be estimated bywhere is the confidence level, indicates the inlier rate, and indicates the minimum number of test points for model estimation. In the proposed IPGSAC algorithm, the maximum number of iterations is limited by (1) with the confidence level 98%.