On the Use of Fuzzy Metrics for Robust Model Estimation: a RANSAC-based Approach

Application domains, such as robotics and computer vision (actually, any sensor data processing field), often require from robust model estimation techniques because of the imprecise nature of sensor data. In this regard, this paper describes a robust model estimator which is actually a modified version of RANSAC that takes inspiration from the notion of fuzzy metric, as a suitable tool for measuring similarities in the presence of the uncertainty inherent to noisy data. More precisely, it makes use of a fuzzy metric within the main RANSAC loop to encode as a similarity the compatibility of each sample to the current hypothesis/model. Further, once a number of hypotheses have been explored and the winning model has been selected, we make use of the same fuzzy metric to obtain a refined version of the model. In this work, we consider two fuzzy metrics that permit us to express the distance between the sample and the model under consideration as a kind of degree of similarity measured relative to a parameter. By way of illustration of the performance of the approach, we report on the accuracy achieved by the proposed estimator and other RANSAC variants for a benchmark comprising two kinds of perception problems typically encountered in vision applications, and a large number of datasets with varying proportion of outliers and different levels of noise. The proposed estimator is shown able to outperform the classical counterparts considered.