This paper aims to build the static-map of a dynamic scene using a mobile robot equipped with 3D sensors. The sought static-map consists of only the static scene parts, which has a vital role in scene understanding and landmark based navigation. Building static-map requires the categorization of moving and static objects. In this work, we propose a Sparse Subspace Clustering-based Motion Segmentation method that categories the static scene parts and the multiple moving objects using their 3D motion trajectories. Our motion segmentation method uses the raw trajectory data, allowing the objects to move in direct 3D space, without any projection model assumption or whatsoever. We also propose a complete pipeline for static-map building which estimates the inter-frame motion parameters by exploiting the minimal 3-point Random Sample Consensus algorithm on the feature correspondences only from the static scene parts. The proposed method has been especially designed and tested for large scene in real outdoor environments. On one hand, our 3D Motion Segmentation approach outperforms its 2D based counterparts, for extensive experiments on KITTI dataset. On the other hand, separately reconstructed static-maps and moving objects for various dynamic scenes are very satisfactory.

Because of the distortions produced by the insertion of a mirror, catadioptric images can not be processed similarly to classical perspective images. Now, although the equivalence between such images and spherical images is well known, the use of spherical harmonic analysis often leads to image processing methods which are more difficult to implement. In this paper, we propose to define catadioptric image processing from the geodesic metric on the unitary sphere. We show that this definition allows to adapt very simply classical image processing methods. We focus more particularly on image gradient estimation, interest point detection, and matching. More generally, the proposed approach extends traditional image processing techniques based on Euclidean metric to central catadioptric images. We show in this paper the efficiency of the approach through different experimental results and quantitative evaluations.

We present a new and efficient algorithm to accurately polygonize an implicit surface generated by multiple Boolean operations with globally deformed primitives. Our algorithm is special in the sense that it can be applied to objects with both an implicit and a parametric representation, such as superquadrics, supershapes, and Dupin cyclides. The input is a Constructive Solid Geometry tree (CSG tree) that contains the Boolean operations, the parameters of the primitives, and the global deformations. At each node of the CSG tree, the implicit formulations of the subtrees are used to quickly determine the parts to be transmitted to the parent node, while the primitives' parametric definition are used to refine an intermediary mesh around the intersection curves. The output is both an implicit equation and a mesh representing its solution. For the resulting object, an implicit equation with guaranteed differential properties is obtained by simple combinations of the primitives' implicit equations using R-functions. Depending on the chosen R-function, this equation is continuous and can be differentiable everywhere. The primitives' parametric representations are used to directly polygonize the resulting surface by generating vertices that belong exactly to the zero-set of the resulting implicit equation. The proposed approach has many potential applications, ranging from mechanical engineering to shape recognition and data compression. Examples of complex objects are presented and commented on to show the potential of our approach for shape modeling.

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