PARTICLE SWARM OPTIMIZATION BASED APPROACH TO ESTIMATE EPIPOLAR GEOMETRY FOR REMOTELY SENSED STEREO IMAGES

The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-5, 2018 ISPRS TC V Mid-term Symposium “Geospatial Technology – Pixel to People”, 20–23 November 2018, Dehradun, India PARTICLE SWARM OPTIMIZATION BASED APPROACH TO ESTIMATE EPIPOLAR GEOMETRY FOR REMOTELY SENSED STEREO IMAGES Manimala Mahato 1,*, Shirishkumar Gedam 1 1 Centre of Studies in Resources Engineering, Indian Institute of Technology Bombay, India – (manimala.mahato, shirish)@iitb.ac.in Commission V, WG V/5 KEY WORDS: Fundamental Matrix, Particle Swarm Optimization, Epipolar Geometry, Remote Sensing, Random Sample Consensus, Stereo Vision ABSTRACT: A novel particle swarm optimization based approach for the estimation of epipolar geometry for remotely sensed images is proposed and implemented in this work. In stereo vision, epipolar geometry is described using 3 x 3 fundamental matrix and is used as a validation tool to assess the accuracy of the stereo correspondences. The validation is performed by enforcing the geometrical constraint of stereo images on the two perspective projections of a point in the scene for finding inliers. In the proposed method, the steps of particle swarm optimization such as the initialization of the position and velocity of the particles, the objective function to compute the best position found by the swarm as well as by each particle experienced so far, the updating rule of velocity for the improvement of the position of each particle, is designed and implemented to estimate the fundamental matrix. To demonstrate the effectiveness of the proposed approach, the results are obtained on a pair of remotely sensed stereo image. A comparison of the result obtained using the proposed algorithm with RANSAC algorithm is carried out. The comparison shows that, the proposed method is effective to estimate robust fundamental matrix by giving improved number of inliers than RANSAC. 1. INTRODUCTION One of the most challenging problems in the area of computer vision and computer graphics is to find the geometrical constraint available between the two images of a stereo image pair irrespective of the specific objects in the scene. In stereo, the images capture different view of the same scene and are related by the epipolar constraint which is expressed mathematically by 3 X 3 fundamental matrix. The estimation of epipolar geometry from the stereo images has received a large attention and has become a core research area in the last two decades due to its enormous applications such as reconstruction, stereo analysis, camera self-calibration, motion segmentation, etc. The accurate fundamental matrix is computed using the parameters of the stereo camera. However, the complexity in estimation of fundamental matrix increases in case of remotely sensed images as the camera parameters are unknown. In this case, the most effective way of estimating the epipolar geometry is through the analysis of the stereo correspondence points (Longuet-Higgins 1981), (Xu and Zhang 1996). The computation of stereo correspondence points is extremely challenging due to the presence of noise, occlusion, and discontinuity, geometric and radiometric distortion in the stereo image pair. In case of remotely sensed images, the scenario becomes more complicated. The accuracy of the epipolar geometry of stereo image pair depends on the accuracy and density of the stereo correspondence points. Stereo correspondences are obtained using feature matching algorithm (Joglekar, Gedam, and Krishna Mohan 2014) which are divided into four steps: i) The detection of interest points in the left image and right image of the stereo image pair; ii) A feature descriptor is assigned by analyzing the neighbourhood pixels; iii) The matching of the conjugate feature points from left image to right image; iv) Pruning of correspondence points using * consistency property such as left-right consistency. Feature matching algorithms estimates accurate but sparse correspondence points. Some well known robust methods for fundamental matrix estimation are M-estimator, Least Median of Square regression LMedS, Random Sample Consensus (RANSAC) (Fischler and Bolles 1981) etc. In the literature, the estimation of fundamental matrix is optimized based on random sampling of stereo correspondence points. This is the basis of almost all highly robust estimators. These methods have in-built mechanism to reduce the influence of outliers. However, in case of remotely sensed images, the correspondence points may be inevitably corrupted by noise and outliers, such as false matches and badly located points due to occlusion, geometric and radiometric distortions. Moreover, if the correspondence points do not belong to different depth planes, the estimated fundamental matrix with the use of such correspondence points may not be able to represent the accurate epipolar geometry of the stereo image pair. However, RANSAC works poorly when outlier proportion is higher than half of the total number of stereo correspondence points used in the process of optimization. Hence, there is a need of a robust algorithm to estimate the fundamental matrix for which the performance of the algorithm should not be affected significantly due to outliers and noise. The aim of the proposed method is to use particle swarm optimization (PSO) algorithm to compute the epipolar geometry of the stereo image pair by solving the above mentioned issues. PSO is based on the behaviour of bird flocking for searching food. In this work, the estimation of fundamental matrix, is considered as an optimization problem and is solved using particle swarm optimization strategy by evolving the swarm through iterations. Corresponding Author This contribution has been peer-reviewed. https://doi.org/10.5194/isprs-archives-XLII-5-85-2018 | © Authors 2018. CC BY 4.0 License. 85 The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-5, 2018 ISPRS TC V Mid-term Symposium “Geospatial Technology – Pixel to People”, 20–23 November 2018, Dehradun, India PSO algorithm was invented by Eberhart and Kennedy (Eberhart and Kennedy 1995) as part of a sociocognitive study while investigating the notion of collective intelligence in the graceful motion of swarm of birds. There are several reasons due to which particle swarm optimization (PSO) is one of the most popular swarm intelligence techniques for continuous optimization problems (Gong et al. 2014). PSO converges very fast toward optimal solution, and is simple and efficient. PSO has less number of tuning parameters which makes it easy to implement. PSO algorithm simulates the intelligence and the ability of flocks of birds, schools of fish and herds of animals to adapt to their environment by finding the rich sources of food and avoiding the predators using the “information sharing” mechanism. The set of randomly generated solutions which is represented (...truncated)