Incomplete 3D motion trajectory segmentation and 2D-to-3D label transfer for dynamic scene analysis

International audience; The knowledge of the static scene parts and the moving objects in a dynamic scene plays a vital role for scene modelling, understanding, and landmark-based robot navigation. The key information for these tasks lies on semantic labels of the scene parts and the motion trajectories of the dynamic objects. In this work, we propose a method that segments the 3D feature trajectories based on their motion behaviours, and assigns them semantic labels using 2D-to-3D label transfer. These feature trajectories are constructed by using the proposed trajectory recovery algorithm which takes the loss of feature tracking into account. We introduce a complete framework for static-m…

An efficient method for fully automatic 3D digitization of unknown objects

Our goal is to develop a complete and automatic scanning strategy with minimum prior information about the object shape. We aim to establish a methodology for the automation of the 3D digitization process. The paper presents a novel approach to determine the Next Best View (NBV) for an efficient reconstruction of highly accurate 3D models. Our method is based on the classification of the acquired surfaces into Well Visible and Barely Visible combined with a best view selection algorithm based on mean shift, which avoids unreachable positions. Our approach is applicable to all kinds of range sensors. To prove the efficiency and the robustness of our method, test objects are first scanned man…

Supershape Recovery from 3D Data Sets

In this paper, we apply supershapes and R-functions to surface recovery from 3D data sets. Individual supershapes are separately recovered from a segmented mesh. R-functions are used to perform Boolean operations between the reconstructed parts to obtain a single implicit equation of the reconstructed object that is used to define a global error reconstruction function. We present surface recovery results ranging from single synthetic data to real complex objects involving the composition of several supershapes and holes.

Universal natural shapes: From unifying shape description to simple methods for shape analysis and boundary value problems

Gielis curves and surfaces can describe a wide range of natural shapes and they have been used in various studies in biology and physics as descriptive tool. This has stimulated the generalization of widely used computational methods. Here we show that proper normalization of the Levenberg-Marquardt algorithm allows for efficient and robust reconstruction of Gielis curves, including self-intersecting and asymmetric curves, without increasing the overall complexity of the algorithm. Then, we show how complex curves of k-type can be constructed and how solutions to the Dirichlet problem for the Laplace equation on these complex domains can be derived using a semi-Fourier method. In all three …

Algorithme d'intersection entre un rayon et un carreau de Bézierpar quasi-interpolant bilinéaire.

International audience

Trois algorithmes intelligents pour la numérisation 3D automatique d'objets inconnus

National audience; Ce papier propose trois approches itératives et intelligentes de planification de vue pour la numérisation 3D d'objets sans connaissance a priori de leurs formes. La première méthode est une approche simple et naïve basée sur la génération d'un ensemble de points de vues par échantillonnage régulier de l'enveloppe englobante des données acquises. La deuxième méthode est basée sur une analyse de l'orientation des différentes parties acquises. La troisième méthode vise à explorer les parties de l'objet qui figurent dans la limite du champ de visibilité et est basée sur un couplage de la visibilité angulaire avec la visibilité réelle par lancer de rayons. Les résultats de nu…

Kolmogorov Superposition Theorem and Wavelet Decomposition for Image Compression

International audience; Kolmogorov Superposition Theorem stands that any multivariate function can be decomposed into two types of monovariate functions that are called inner and external functions: each inner function is associated to one dimension and linearly combined to construct a hash-function that associates every point of a multidimensional space to a value of the real interval $[0,1]$. These intermediate values are then associated by external functions to the corresponding value of the multidimensional function. Thanks to the decomposition into monovariate functions, our goal is to apply this decomposition to images and obtain image compression. We propose a new algorithm to decomp…

Rational supershapes for surface reconstruction

Simple representation of complex 3D data sets is a fundamental problem in computer vision. From a quality control perspective, it is crucial to use efficient and simple techniques do define a reference model for further recognition or comparison tasks. In this paper, we focus on reverse engineering 3D data sets by recovering rational supershapes to build an implicit function to represent mechanical parts. We derive existing techniques for superquadrics recovery to the supershapes and we adapt the concepts introduced for the ratioquadrics to introduce the rational supershapes. The main advantage of rational supershapes over standard supershapes is that the radius is now expressed as a ration…

Scale invariant line matching on the sphere

International audience; This paper proposes a novel approach of line matching across images captured by different types of cameras, from perspective to omnidirectional ones. Based on the spherical mapping, this method utilizes spherical SIFT point features to boost line matching and searches line correspondences using an affine invariant measure of similarity. It permits to unify the commonest cameras and to process heterogeneous images with the least distortion of visual information.

From Nowhere to Everywhere

International audience; This paper presents a synthetic view of a variety of projects built upon an Erasmuss Mundus Master Course. It highlights double degree programs, European credits transfer, joint PhDs, research collaborations as well as few other related European projects going from Thematic Networks to another Erasmus Mundus Course.

Reconstruction 3D de scènes dynamiques par segmentation au sens du mouvement

National audience; L'objectif de ce travail est de reconstruire les parties sta-tiques et dynamiques d'une scène 3D à l'aide d'un robot mobile équipé d'un capteur 3D. Cette reconstruction né-cessite la classification des points 3D acquis au cours du temps en point fixe et point mobile indépendamment du dé-placement du robot. Notre méthode de segmentation utilise directement les données 3D et étudie les mouvements des objets dans la scène sans hypothèse préalable. Nous déve-loppons un algorithme complet reconstruisant les parties fixes de la scène à chaque acquisition à l'aide d'un RAN-SAC qui ne requiert que 3 points pour recaler les nuages de points. La méthode a été expérimentée sur de la…

Static and Dynamic Objects Analysis as a 3D Vector Field

International audience; In the context of scene modelling, understanding, and landmark-based robot navigation, the knowledge of static scene parts and moving objects with their motion behaviours plays a vital role. We present a complete framework to detect and extract the moving objects to reconstruct a high quality static map. For a moving 3D camera setup, we propose a novel 3D Flow Field Analysis approach which accurately detects the moving objects using only 3D point cloud information. Further, we introduce a Sparse Flow Clustering approach to effectively and robustly group the motion flow vectors. Experiments show that the proposed Flow Field Analysis algorithm and Sparse Flow Clusterin…

Enhancement and assessment of WKS variance parameter for intelligent 3D shape recognition and matching based on MPSO

This paper presents an improved wave kernel signature (WKS) using the modified particle swarm optimization (MPSO)-based intelligent recognition and matching on 3D shapes. We select the first feature vector from WKS, which represents the 3D shape over the first energy scale. The choice of this vector is to reinforce robustness against non-rigid 3D shapes. Furthermore, an optimized WKS-based method for extracting key-points from objects is introduced. Due to its discriminative power, the associated optimized WKS values with each point remain extremely stable, which allows for efficient salient features extraction. To assert our method regarding its robustness against topological deformations,…

PROCEDE DE NUMERISATION TRIDIMENSIONNELLE AUTOMATIQUE

G1-Blend between a Differentiable Superquadric of Revolution and a Plane or a Sphere Using Dupin Cyclides

In this article, we present a method to perform G1-continuous blends between a differentiable superquadric of revolution and a plane or a sphere using Dupin cyclides. These blends are patches delimited by four lines of curvature. They allow to avoid parameterization problems that may occur when parametric surfaces are used. Rational quadratic Bezier curves are used to approximate the principal circles of the Dupin cyclide blends and thus a complex 3D problem is now reduced to a simpler 2D problem. We present the necessary conditions to be satisfied to create the blending patches and illustrate our approach by a number of superellipsoid/plane and superellipsoid/sphere blending examples.

The Kolmogorov Spline Network for Image Processing

In 1900, Hilbert stated that high order equations cannot be solved by sums and compositions of bivariate functions. In 1957, Kolmogorov proved this hypothesis wrong and presented his superposition theorem (KST) that allowed for writing every multivariate functions as sums and compositions of univariate functions. Sprecher has proposed in (Sprecher, 1996) and (Sprecher, 1997) an algorithm for exact univariate function reconstruction. Sprecher explicitly describes construction methods for univariate functions and introduces fundamental notions for the theorem comprehension (such as tilage). Köppen has presented applications of this algorithm to image processing in (Köppen, 2002) and (Köppen &…

New Representations for Multidimensional Functions Based on Kolmogorov Superposition Theorem. Applications on Image Processing

Mastering the sorting of the data in signal (nD) can lead to multiple applications like new compression, transmission, watermarking, encryption methods and even new processing methods for image. Some authors in the past decades have proposed to use these approaches for image compression, indexing, median filtering, mathematical morphology, encryption. A mathematical rigorous way for doing such a study has been introduced by Andrei Nikolaievitch Kolmogorov (1903-1987) in 1957 and recent results have provided constructive ways and practical algorithms for implementing the Kolmogorov theorem. We propose in this paper to present those algorithms and some preliminary results obtained by our team…

A new Adaptive and Progressive Image Transmission Approach using Function Superpositions

International audience; We present a novel approach to adaptive and progressive image transmission, based on the decomposition of an image into compositions and superpositions of monovariate functions. The monovariate functions are iteratively constructed and transmitted, one after the other, to progressively reconstruct the original image: the progressive transmission is performed directly in the 1D space of the monovariate functions and independently of any statistical properties of the image. Each monovariate function contains only a fraction of the pixels of the image. Each new transmitted monovariate function adds data to the previously transmitted monovariate functions. After each tra…

Promotion et Développement d'un Master Erasmus Mundus - L'Exemple du VIBOT

Cet article decrit l’offre de formation a l’internationale proposee au Centre Universitaire Condorcet du Creusot (Universite de Bourgogne) dans le domaine de la vision par ordinateur et de la robotique. Il presente l’organisation particuliere de ces formations et les actions de support mises en place pour en assurer la perennite.

A more distinctive representation for 3D shape descriptors using principal component analysis

Many researchers have used the Heat Kernel Signature (or HKS) for characterizing points on non-rigid three-dimensional shapes and Classical Multidimensional Scaling (Classical MDS) method in object classification which we quote, in particular, the example of Jian Sun et al. (2009) [1]. However, in this paper, the main focuses on classification that we propose a concise and provably factorial method by invoking Principal Component Analysis (PCA) as a classifier to improve the scheme of 3D shape classification. To avoid losing or disordering information after extracting features from the mesh, PCA is used instead of the Classical MDS to discriminate-as much as possible-feature points for each…

Central catadioptric image processing with geodesic metric

International audience; Because of the distortions produced by the insertion of a mirror, catadioptric images cannot 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, th…

Boolean operations with implicit and parametric representation of primitives using R-functions

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 …

View planning algorithms for fully automatic 3D acquisition of unknown objects

International audience; This paper addresses the view planning problem for the digitization of 3D objects without prior knowledge on their shape and presents a novel method called Orientation, Angle and Covering (OAC). The proposed method is based on a combination of two concepts: the Mass Vector Chains (MVC) and the Measurability Matrix. The MVC allows to define the global orientation of the scanned part. All of the view points are sorted using an orientation criterion to define a first set of candidates for the Next Best View (NBV). The Measurability Matrix allows to determine the coverage rate for each candidate. The covering criterion leads to reduce the number of view points of the fir…

A Geometric Algorithm for Ray/Bezier Surfaces Intersectionusing Quasi-interpolating Control Net

International audience

Kolmogorov superposition theorem for image compression

International audience; The authors present a novel approach for image compression based on an unconventional representation of images. The proposed approach is different from most of the existing techniques in the literature because the compression is not directly performed on the image pixels, but is rather applied to an equivalent monovariate representation of the wavelet-transformed image. More precisely, the authors have considered an adaptation of Kolmogorov superposition theorem proposed by Igelnik and known as the Kolmogorov spline network (KSN), in which the image is approximated by sums and compositions of specific monovariate functions. Using this representation, the authors trad…

Kolmogorov Superposition Theorem and Its Application to Multivariate Function Decompositions and Image Representation

International audience; In this paper, we present the problem of multivariate function decompositions into sums and compositions of monovariate functions. We recall that such a decomposition exists in the Kolmogorov's superposition theorem, and we present two of the most recent constructive algorithms of these monovariate functions. We first present the algorithm proposed by Sprecher, then the algorithm proposed by Igelnik, and we present several results of decomposition for gray level images. Our goal is to adapt and apply the superposition theorem to image processing, i.e. to decompose an image into simpler functions using Kolmogorov superpositions. We synthetise our observations, before …

Dynamic 3D Scene Reconstruction and Enhancement

International audience; In this paper, we present a 3D reconstruction and enhancement approach for high quality dynamic city scene reconstructions. We first detect and segment the moving objects using 3D Motion Segmenta-tion approach by exploiting the feature trajectories' behaviours. Getting the segmentations of both the dynamic scene parts and the static scene parts, we propose an efficient point cloud registration approach which takes the advantages of 3-point RANSAC and Iterative Closest Points algorithms to produce precise point cloud alignment. Furthermore, we proposed a point cloud smoothing and texture mapping framework to enhance the results of reconstructions for both the static a…

Progressive transmission of secured images with authentication using decompositions into monovariate functions

International audience; We propose a progressive transmission approach of an image authenticated using an overlapping subimage that can be removed to restore the original image. Our approach is different from most visible water- marking approaches that allow one to later remove the watermark, because the mark is not directly introduced in the two-dimensional image space. Instead, it is rather applied to an equivalent monovariate representation of the image. Precisely, the approach is based on our progressive transmission approach that relies on a modified Kolmogorov spline network, and therefore inherits its advantages: resilience to packet losses during transmis- sion and support of hetero…

Road Signs Detection and Reconstruction using Gielis Curves

International audience; Road signs are among the most important navigation tools in transportation systems. The identification of road signs in images is usually based on first detecting road signs location using color and shape information. In this paper, we introduce such a two-stage detection method. Road signs are located in images based on color segmentation, and their corresponding shape is retrieved using a unified shape representation based on Gielis curves. The contribution of our approach is the shape reconstruction method which permits to detect any common road sign shape, i.e. circle, triangle, rectangle and octagon, by a single algorithm without any training phase. Experimental…

A Geometric Algorithm for Ray/Bézier Surfaces Intersection Using Quasi-Interpolating Control Net

In this paper, we present a new geometric algorithm to compute the intersection between a ray and a rectangular Bezier patch. The novelty of our approach resides in the use of bounds of the difference between a Bezier patch and its quasi-interpolating control net. The quasi-interpolating polygon of a Bezier surface of arbitrary degree approximates the limit surface within a precision that is function of the second order difference of the control points, which allows for very simple projections and 2D intersection tests to determine sub-patches containing a potential intersection. Our algorithm is simple, because it only determines a 2D parametric interval containing the solution, and effici…

View Planning Approach for Automatic 3D Digitization of Unknown Objects

International audience; This paper addresses the view planning problem for the digitization of 3D objects without prior knowledge on their shape and presents a novel surface approach for the Next Best View (NBV) computation. The proposed method uses the concept of Mass Vector Chains (MVC) to define the global orientation of the scanned part. All of the viewpoints satisfying an orientation constraint are clustered using the Mean Shift technique to construct a first set of candidates for the NBV. Then, a weight is assigned to each mode according to the elementary orientations of its different descriptors. The NBV is chosen among the modes with the highest weights and which comply with the rob…