Differential Invariants as the Base of Triangulated Surface Registration

  title={Differential Invariants as the Base of Triangulated Surface Registration},
  author={Pavel Krsek and Tom{\'a}s Pajdla and V{\'a}clav Hlav{\'a}{\vc}},
  journal={Comput. Vis. Image Underst.},
The paper addresses the problem of 3D model reconstruction from overlapping triangulated range images. A technique for automatic matching of curved freeform surfaces exploiting curvilinear differential structures of the surfaces is presented. We propose a hybrid registration algorithm that combines advantages of working with small amounts of interest points (to attain computational speed), estimates the Euclidean transform matching both surfaces, and uses all available points and the iterative… 

Figures and Tables from this paper

Efficient partial-surface registration for 3D objects
An algorithm for the least squares matching of overlapping 3D surfaces is presented. It estimates the transformation parameters between two or more fully 3D surfaces, using the Generalized
Least squares 3 D surface matching
An algorithm for the least squares matching of overlapping 3D surfaces is presented. It estimates the transformation parameters between two or more fully 3D surfaces, using the Generalized
Least squares 3D surface and curve matching
3 D Shape Registration
Registration is the problem of bringing together two or more 3D shapes, either of the same object or of two different but similar objects. This chapter first introduces the classical Iterative
3D Shape Registration
This chapter first introduces the classical Iterative Closest Point (ICP) algorithm, which represents the gold standard registration method, and the most popular variants are described to improve the basic implementation in several ways.
Automatic Correspondence for 3d Modeling: an Extensive Review
An extensive review of existing "automatic" correspondence techniques shows that none of these techniques fully meets these criteria and that there is still a need for the development of practical automatic correspondence algorithms.
Globally convergent range image registration by graph kernel algorithm
This work defines a graph in which each vertex represents a putative match of two points, each edge represents binary consistency decision between two matches, and each edge orientation represents match quality from worse to better putativeMatch.
3D Shape Registration with Estimating Illumination and Photometric Properties of a Convex Object
This work proposes a novel method for a convex Lamber- tian object which enables us to perform 3D registration and, at the same time, to estimate radiometric properties of the object.


A Method for Registration of 3-D Shapes
A general-purpose, representation-independent method for the accurate and computationally efficient registration of 3-D shapes including free-form curves and surfaces based on the iterative closest point (ICP) algorithm.
Matching of 3-D curves using semi-differential invariants
  • T. Pajdla, L. Gool
  • Computer Science
    Proceedings of IEEE International Conference on Computer Vision
  • 1995
It is shown that by combining /spl epsiv/-reciprocal correspondence with the robust least median of squares motion estimation, the registration of partially occluded curves can be accomplished.
New feature points based on geometric invariants for 3D image registration
  • J. Thirion
  • Mathematics
    International Journal of Computer Vision
  • 2004
A new type of feature points of 3D surfaces, based on geometric invariants, are introduced, and it is shown that the relative positions of those 3D points are invariant according to 3D rigid transforms (rotation and translation).
Building 3-D models from unregistered range images
The authors describe an approach to building a three-dimensional model from a set of range images based on building discrete meshes representing the surfaces observed in each of the range images, to map Each of the meshes to a spherical image, and to compute the transformations between the views by matching the spherical images.
Algorithms for Computing Curvatures from Range Data
This article presents a comparison of several methods for local estimation of normal direction, principal curvatures and principal directions, given a range image as input. Here we take a range image
Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography
New results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form that provide the basis for an automatic system that can solve the Location Determination Problem under difficult viewing.
Free-Form Surface Matching using Mean Field Theory
A new method for free-form surface matching is presented, based on Mean Field Theory, which provides an initial guess of the transformation, which may subsequently be reened by the Iterated Closest Point method.
Laser Plane Range Finder; The Implementation at the CVL
This report describes the implementation of a 3-D scanner-Laser Plane Range Finder. The sensor builds on the triangulation and active illumination using laser light plane. It delivers 3-D coordinates
Estimation of differential parameters on triangulated surface, in Proceedings of the Czech Pattern Recognition workshop’97, pp
  • 151–155, Czech Pattern Recognition Society, Prague, Czech Republic,
  • 1997