# Evolutionary Optimization for Robust Epipolar-Geometry Estimation and Outlier Detection
## 2 Related Works
Although this method accelerates the sampling, it is still sensitive to degeneracy, image noise and uncertainty of the model estimation. This is due to the fact that it reduces the number of potential inliers by thresholding the proposal probabilities that are, themselves, dependent on the robust estimation of normalized residuals. Several studies have attempted to apply evolutionary algorithms instead of the random search [29; 30]. Although promising results were achieved, several limitations were not addressed yet. For instance, their objective functions still require a hard threshold to distinguish outliers from inliers; the two-dimensional spatial configuration of the correspondences is ignored; the uncertainties of the estimated model are not taken into account; and the experiments are limited to small datasets. Genetic Algorithm Sample Consensus (GASAC) is also another technique that is, to the best of the authors' knowledge, the most similar technique to the one proposed in our study. The difference of GASAC from typical RANSAC is that the random sampling is replaced with evolutionary search based on classic genetic algorithms (genetic algorithms are meta-heuristics inspired by biological evolution, which are used for solving optimization problems by relying on evolutionary search operators) [31]. This study shows that the computational cost could be sped up 13-times by applying the evolutionary search instead of the random one. However, according to their report, the technique is applicable to small datasets with less than 50% outliers; the objective function is still based on support cardinality; and it introduces no solution to avoid local optima (such as degeneracy). The second strategy proposed in the literature in order to speed up RANSAC is to reduce the solution space by only verifying the hypotheses with a higher probability of being optimal. These highly probable hypotheses can be selected by a T\({}_{\text{d,d}}\) test [32], a bail-out test [33] or a sequential probability ratio test (SPRT) [34; 35]. In addition, the hypothesis verification can be performed preemptively in a breadth-first manner only for a fixed number of sample sets [36]. These techniques may increase the number of required hypotheses, as good models may wrongly be rejected by not being verified completely. It has been observed that, in the case of degenerate configurations, RANSAC-like algorithms result in a model with a very large support, while it is completely incorrect. This behaviour can be explained by the fact that a high inlier support can be obtained even if the sample set includes some outliers and at least five inliers that belong to a dominant plane or to a very small area of the image. This large support causes the termination of RANSAC before a non-degenerate outlier-free sample set can be picked up [37]. The main strategy to control the degeneracy of solutions is to re-investigate the support of the best tentative model either locally or globally. For instance, the support of the best model can be re-sampled, and the model estimated from those subsamples can be compared to the best one to find out the degenerate models (the Locally Optimized Random Sample Consensus (LO -RANSAC) method by [38]). Another example of such strategies is the Quasi Degenerate Sample Consensus (QDEGSAC) (proposed by [39]), where a hierarchical RANSAC is performed by changing the number of the parameters in the model and verifying it over the entire dataset. The main issue concerning these techniques is that they cause additional operations, as a separate mechanism is added to the original RANSAC; i.e., they do not directly handle degeneracy in the sampling process. Universal RANSAC (USAC) is also a modular fusion of some of the mentioned RANSAC algorithms, including PROSAC sampling, SPRT verification and LO-RANSAC local optimization [40]. In general, its performance is better than any of the single modules integrated into the universal implementation. However, it does not improve any of the modules individually.