We present a new approach to the geometric alignment of a point cloud to a surface and to related registration problems. The standard algorithm is the familiar ICP algorithm. Here we provide an alternative concept which relies on instantaneous kinematics and on the geometry of the squared distance function of a surface. The proposed algorithm exhibits faster convergence than ICP

An important objective in the evaluation of algorithms with sensory inputs is the development of measures characterizing the intrinsic errors in the results. Intrinsic are those errors which are caused by noise in the input data. The particular application which we consider is 3-D reconstruction from stereo. We demonstrate that a radiometric correction of the images could improve signi cantly the accuracy. We propose a con dence interval approach for quantifying the precision. We also illustrate the use of the con dence intervals for the rejection of unreliable 3D points.

This document is the extended version of the work published in [11]. Laser-based range sensors are commonly used on-board autonomous mobile robots for obstacle detection and scene understanding. A popular methodology for analyzing point cloud data from these sensors is to train Bayesian classifiers using locally computed features on labeled data and use them to compute class posteriors on-line at testing time. However, data from range sensors present a unique challenge for feature computation in the form of significant variation in spatial density of points, both across the field-of-view as well as within structures of interest. In particular, this poses the problem of choosing a scale for analysis and a support-region size for computing meaningful features reliably. While scale theory has been rigorously developed for 2-D images, no equivalent exists for unorganized 3-D point data. Choosing a satisfactory fixed scale over the entire dataset makes feature extraction sensitive to the presence of different manifolds in the data and varying data density. We adopt an approach inspired by recent developments in computational geometry [17] and investigate the problem of automatic data-driven scale selection to improve point cloud classification. The approach is validated with results using real data from different sensors in various environments (indoor, urban outdoor and natural outdoor) classified into different terrain types (vegetation, solid surface and linear structure).

Abstract. This paper describes a method for accurate dense reconstruction of a complex scene from a small set of high-resolution unorganized still images taken by a hand-held digital camera. A fully automatic data processing pipeline is proposed. Highly discriminative features are first detected in all images. Correspondences are then found in all image pairs by wide-baseline stereo matching and used in a scene structure and camera reconstruction step that can cope with occlusion and outliers. Image pairs suitable for dense matching are automatically selected, rectified and used in dense binocular matching. The dense point cloud obtained as the union of all pairwise reconstructions is fused by local approximation using oriented geometric primitives. For texturing, every primitive is mapped on the image with the best resolution. The global structure reconstruction in the first step allows us to work with an unorganized set of images and to avoid error accumulation. By using object-centered geometric primitives we are able to preserve the flexibility of the method to describe complex free-form structures, preserve the possibility to build the dense model in an incremental way, and to retain the possibility to refine the cameras and the dense model by bundle adjustment. Results are demonstrated on partial models of a circular church and a Henri de Miller’s sculpture. We observed spatial resolution in the range of centimeters on objects of about 20 m in size. 1

We present our long-term effort focused on building a 3-D model acquisition system for teleimmersion applications. In our project we stress fast processing and high fidelity of the result: it is not just geometric accuracy of the recovered geometric model but also radiometric correctness of the recovered surface texture. We suggest that single-type geometric model is not sufficient for modeling large and complex scenes. In this paper, a hierarchy of representations suitable for 3-D structure models recoverable from visual data is presented and the related problems of data acquisition and fusion, outlier identification, and models reconstruction are discussed. 1 Introduction The goal of teleimmersion is to provide people at remote places with realistic experiences that they are all sharing virtual and `real' objects, including their partners present `in the same room.' This is done by creating a virtual world for each participant, one that is a dynamically updated representation of th...

We show in this paper that the bottom-up approach to 3D surface model reconstruction is feasible and may be used in applications requiring precision and accuracy. We focus on acquiring 3D models of natural objects for medical applications, augmented reality, and telepresence. The reconstruction consists of several successive steps in which more complex models are inferred from simpler models. The low-level model we use is a set of unorganized points in 3-space obtained from polynocular stereo. The intermediate-level model consists of local geometric primitives which we call fish-scales. Fish-scales are reconstructed from the unorganized point model by local PCA. The high-level model is a discrete pseudo-surface. It is reconstructed by linking together close and orientation-compatible fish-scales. The ungrouped isolated points and the unlinked fish-scales remain unexplained by the higher-level models. The approach is demonstrated on textured 3D geometric model reconstruction of a human ...

Our work is concerned with obtaining high-fidelity 3D surface models from passive polynocular stereo. In this report we formulate our effort towards refining a reconstructed geometric surface model. In order to avoid computational complexity of simultaneous polynocular stereo matching, depth and orientation recovery, partial model fusion, and consistent model reconstruction, we break the task down to simpler modules that work efficiently although introducing artifacts due to unrealistic a priori assumptions (surface-image plane planparalelity, etc.) These modules solve one problem at a time. The parameters of reconstructed semi-local disk-like geometric primitives (so called fish-scales) are refined in a verification step that closes the loop by returning back to the original images. We hope that this approach will lead us to an efficient high-fidelity surface model recovery algorithm from polynocular stereo. 1 Introduction 1.1 Motivation Imagine one wants a robot capable of grasping...

........................................................................................... x CHAPTER 1 INTRODUCTION ...............................................................................1 1.1 WHAT IS IMAGE-BASED RENDERING AND MODELING...........................................1 1.2 ISSUES.................................................................................................................4 1.3 OBJECTIVE AND APPROACH .................................................................................6 1.4 OUTLINE AND NOTATIONS ...................................................................................8 CHAPTER 2 ELEMENTS OF PROJECTIVE GEOMETRY ...............................10 2.1 PROJECTIVE SPACE............................................................................................10 2.1.1 Definitions .................................................................................................10 2.1.2 Canonical affine space embedding and the plane-at-...

A new technique for computing the differential invariants of a surface from 3D sample points and normals. It is based on a new conformal geometric approach to computing shape invariants directly from the Gauss map. In the current implementation we compute the mean curvature, the Gauss curvature, and the principal curvature axes at 3D points reconstructed by area-based stereo. The differential invariants are computed directly from the points and the normals without prior recovery of a 3D surface model and an approximate surface parameterization. The technique is stable computationally.

Our work is concerned with obtaining high-delity 3-D surface models from passive polynocular stereo. In this paper we extend our previous work towards rening a reconstructed geometric surface model. In order to avoid computational complexity of simultaneous polynocular stereo matching, depth and orientation recovery, partial model fusion, and consistent surface reconstruction, we break the task down to simpler modules that work eciently albeit introducing artifacts due to unrealistic a priori assumptions (surface plan-parallelity, etc.) These modules solve one problem at a time. The parameters of reconstructed semi-local disk-like geometric primitives (so called sh-scales) are rened in a verication step that closes the loop by recurring back to the original images. We hope that this approach will lead us to an ecient high-delity surface model recovery algorithm from polynocular stereo. 1 Introduction This work is motivated by the need for passive 3-D surface reconstruction. Alth...