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This paper presents an improvement of the J-linkage algorithm for fitting multiple instances of a model to noisy data corrupted by outliers. The binary preference analysis implemented by J-linkage is replaced by a continuous (soft, or fuzzy) generalization that proves to perform better than J-linkage on simulated data, and compares favorably with state of the art methods on public domain real datasets.

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This paper addresses the problem of motion synchronization (or averaging) and describes a simple, closedform solution based on a spectral decomposition, which does not consider rotation and translation separately but works straight in SE(3), the manifold of rigid motions. Besides its theoretical interest, being the first closed form solution in SE (3), experimental results show that it compares favourably with the state of the art both in terms of precision and speed.

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...

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The photorealistic acquisition of 3D objects often requires color information from digital photography to be mapped on the acquired geometry, in order to obtain a textured 3D model. This paper presents a novel fully automatic 2D/3D global registration pipeline consisting of several stages that simultaneously register the input image set on the corresponding 3D object. The first stage exploits Structure From Motion (SFM) on the image set in order to generate a sparse point cloud. During the second stage, this point cloud is aligned to the 3D object using an extension of the 4 Point Congruent Set (4PCS) algorithm for the alignment of range maps. The extension accounts for models with different scales and unknown regions of overlap. In the last processing stage a global refinement algorithm based on mutual information optimizes the color projection of the aligned photos on the 3D object, in order to obtain high quality textures. The proposed registration pipeline is general, capable of dealing with small and big objects of any shape, and robust. We present results from six real cases, evaluating the quality of the final colors mapped onto the 3D object. A comparison with a ground truth dataset is also presented