Abstract
In several machine vision problems, a relevant issue is the estimation of homographies between two different perspectives that hold an extensive set of abnormal data. A method to find such estimation is the random sampling consensus (RANSAC); in this, the goal is to maximize the number of matching points given a permissible error (Pe), according to a candidate model. However, those objectives are in conflict: a low Pe value increases the accuracy of the model but degrades its generalization ability that refers to the number of matching points that tolerate noisy data, whereas a high Pe value improves the noise tolerance of the model but adversely drives the process to false detections. This work considers the estimation process as a multiobjective optimization problem that seeks to maximize the number of matching points whereas Pe is simultaneously minimized. In order to solve the multiobjective formulation, two different evolutionary algorithms have been explored: the Nondominated Sorting Genetic Algorithm II (NSGA-II) and the Nondominated Sorting Differential Evolution (NSDE). Results considering acknowledged quality measures among original and transformed images over a well-known image benchmark show superior performance of the proposal than Random Sample Consensus algorithm.
Highlights
A homography is a transformation that maps points of interest by considering movements as translation, rotation, skewing, scaling, and projection among image planes, all of them contained into a single, invertible matrix
In order to overcome the typical Random Sample Consensus (RANSAC) problems, we propose to visualize the RANSAC operation as a multiobjective problem solved by an evolutionary algorithm
The results exhibit the performance of Nondominated Sorting Genetic Algorithm II (NSGA-II) and Nondominated Sorting Differential Evolution (NSDE) solving the estimation problem as a multiobjective optimization task in comparison to RANSAC
Summary
A homography is a transformation that maps points of interest by considering movements as translation, rotation, skewing, scaling, and projection among image planes, all of them contained into a single, invertible matrix. Some other variants to the original RANSAC are the projectionpursuit method, the Two-Step Scale Estimator, and the CCRANSAC [15, 21, 22], all of them focused on maximizing the number of inliers by making more searches into the data and making the complete process more expensive, computationally speaking In such sense, an algorithm that tries to reduce the computational cost is the one proposed in [17], where the maximization of the inliers is achieved by using a metaheuristic technique, called Harmony Search. In order to overcome the typical RANSAC problems, we propose to visualize the RANSAC operation as a multiobjective problem solved by an evolutionary algorithm Under such point of view, at each iteration, new candidate solutions are built by using evolutionary operators taking into account the quality of the previously generated models, rather than purely random, reducing significantly the number of iterations.
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