Robust Multiple Model Fitting with Preference Analysis and Low-rank Approximation

Abstract

Geometric multi-model fitting aims at extracting parametric models from unstructured data in order to organize and aggregate visual content in suitable higher-level geometric structures. This ubiquitous task can be encountered in many Computer Vision applications, for example in 3D reconstruction, in the processing of 3D point clouds, in face clustering, in body-pose estimation or video motion segmentation, just to name a few.In practice, it is necessary to overcome the "chicken-&-egg dilemma" inherent to this problem: in order to estimate models one needs to first segment the data, but in order to segment the data it is necessary to know the models associated with each data point. The presence of multiple structures hinders robust estimation, which has to cope with both gross outliers and pseudo-outliers. Two somehow orthogonal strategies have been proposed in the literature in order to adress this challenging problem: consensus analysis and preference analysis. Consensus based methods, building on the RANSAC paradigm, instantiate a pool of tentative models and extract the strucutures that have maximal consensus. Preference oriented algorithms [2,3] instead tackle this problem by the data point of view. Residuals between point and putative models are used in order to build a conceptual space in which points are portrayed by their preferences with respect to the instantiated strucures, The multi model fitting problem is then solved by clustering points in this preference space.The method we present reduces the multi-model fitting task to many easier single robust model estimation problems, by combining preference analysis and robust low rank approximation. Three main step can be single out in our appraoch. At first data points are shifted in a conceptual space, where they are framed as a preference matrix Φ as shown in Fig model points preferences, in this way a first protection against outlier is achieved. The preference space is then equipped with a kernel, based on the Tanimoto distance, in this way an affinity matrix K, which measures the agreement between the preferences of points, is derived. The second step is devoted to robustly segment points explointing the information encapsulated in K. This stage can be thought as a sort of "robust spectral clustering". It is well known that spectral clustering produces accurate segmentations in two steps: at first data are projected on the space of the first eigenvectors of the Laplacian matrix and then k-means is applied. The shortcoming of spectral clustering however is that it is not robust to outliers. We propose to follow the same scheme enforcing robustness exploiting the low rank nature of the problem. As pictorially illustrated in Fig. 2, we decompose the affinity matrix asThe matrix S models the sparse preferences expressed by outliers, and is obtained by appling Robust PCA, which replaces the eigen-decomposition Finally, models are extracted inspecting the product of the preference matrix with a thresholded U, mimicking the MSAC strategy. The use of robust...

Multi-H: Efficient recovery of tangent planes in stereo images

“…Table 2 shows the mean and median misclassification errors on all 19 image pairs of the AdelaideRMF dataset. The competitor methods are T-Linkage [11], J-Linkage [24], RPA [10], SA-RCM [20], Greedy-RansaCov [12] and ILP-RansaCov [12]. Multi-H significantly outperforms all published methods.…”

Multiple structure recovery with maximum coverage

“…A consensus matrix P has to be instantiated via random sampling, but we are agnostic here on the specific sampling strategy (e.g. [27,28,17]). At first we concentrate on the case in which all the points are inliers (the case of outliers will be dealt with later on).…”

“…In all these scenarios we compare ILP-RansaCov with JLinkage [8], T-linkage [15] and RPA [17], whose implementation is taken from [40]. In addition, one reference method have been added to the comparison for each specific scenario, namely: MFIGP [38] in the vanishing point experiments, SSC [41] for video motion segmentation and RCMSA [18] for two-views segmentation.…”

“…All the algorithms but SSC and RCMSA were provided with the same pool of putative models, sampled as in [17]. Since none of the competing algorithm had special provisions for the outlier-free case, the Maximum Coverage version of ILP-RansaCov has been used in this experiment, for the sake of fairness.…”

“…Along the same line of J-Linkage, Kernel Fitting (KF) [16], Robust Preference Analysis [17] (RPA) and Random Cluster Model Simulated Annealing (RCMSA) [18] exploits points preferences.…”