In this paper, we propose and analyze several methods to estimate a rigid transformation from a set of 3-D matched points or matched frames, which are important features in geometric algorithms. We also develop tools to predict and verify the accuracy of these estimations. The theoretical contributions are: an intrinsic model of noise for transformations based on composition rather than addition; a unified formalism for the estimation of both the rigid transformation and its covariance matrix for points or frames correspondences, and a statistical validation method to verify the error estimation, which applies even when no “ground truth” is available. We analyze and demonstrate on synthetic data that our scheme is well behaved. The practical contribution of the paper is the validation of our transformation estimation method in the case of 3-D medical images, which shows that an accuracy of the registration far below the size of a voxel can be achieved, and in the case of protein substructure matching, where frame features drastically improve both selectivity and complexity.

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A Framework for Uncertainty and Validation of 3-D RegistrationMethods Based on Points and Frames

In many areas of science, engineering, medicine, and especially in the field of robotics, there is a need to establish a spatial mapping between two or more 3-dimensional (3-D) shape representations of an object. The registration problem is concerned with finding a spatial transformation which best aligns two object representations. Once this mapping is established, a variety of tasks can be performed using the aligned object representations including model-based localization, 3-D object recognition, real-time pose tracking and multi-modality sensor fusion.
The research goals of this dissertation are the design, implementation and validation of fast and accurate methods for performing 3-D shape-based registration. Fast registration is achieved via speed enhancements to an existing registration method (the iterative closest point algorithm). The implemented enhancements increase registration speeds by a factor of nearly two orders of magnitude, and the resulting speeds are much higher than those previously reported in the literature. The ability to perform high-speed registration enables completely new registration applications. For example, this dissertation describes a system for tracking the position and orientation of arbitrarily-shaped objects at speeds of roughly 10 Hz using a high-speed range finder.
The majority of this dissertation focuses on the problem of achieving and ensuring high accuracy shape-based registration. This goal is addressed via two processes: intelligent data selection and online accuracy estimation. Intelligent data selection is based on the observation that all data are not equally beneficial for performing accurate registration. Judicious selection and careful collection of a limited amount of data can result in better registration accuracy than random use of larger amounts of data. In this dissertation, two techniques are proposed for performing intelligent data selection: an optimization process (Constraint Synthesis), and a numerical analysis method which provides a criterion measure for the optimization process (Constraint Analysis). Registration experiments demonstrate that data configurations which are automatically synthesized using these methods can significantly increase registration accuracy.
A fundamental problem in registration is knowing whether an estimated transformation satisfies accuracy requirements at the time of registration. A conventional root-mean-squared error, coupled with the criterion measure from constraint analysis provides the ability to estimate true registration accuracy online. This estimate can be used to guide the online collection of registration data by determining when additional data are required to satisfy accuracy requirements.
While there are many areas to which registration can be applied, the chosen domain for this dissertation is medicine, and most of the results are presented in the context of computer-assisted surgery. Despite the specific nature of the chosen application area, the underlying ideas and methods have application to a broad range of registration problems.

Fast and accurate shape-based registration

A method is developed to analyze the accuracy of the relative head-to-object position and orientation (pose) in augmented reality systems with head-mounted displays. From probabilistic estimates of the errors in optical tracking sensors, the uncertainty in head-to-object pose can be computed in the form of a covariance matrix. The positional uncertainty can be visualized as a 3D ellipsoid. One useful benefit of having an explicit representation of uncertainty is that we can fuse sensor data from a combination of fixed and head-mounted sensors in order to improve the overall registration accuracy. The method was applied to the analysis of an experimental augmented reality system, incorporating an optical see-through head-mounted display, a head-mounted CCD camera, and a fixed optical tracking sensor. The uncertainty of the pose of a movable object with respect to the head-mounted display was analyzed. By using both fixed and head mounted sensors, we produced a pose estimate that is significantly more accurate than that produced by either sensor acting alone.

Analysis of head pose accuracy in augmented reality

Optic flow motion analysis represents an important family of visual information processing techniques in computer vision. Segmenting an optic flow field into coherent motion groups and estimating each underlying motion is a very challenging task when the optic flow field is projected from a scene of several independently moving objects. The problem is further complicated if the optic flow data are noisy and partially incorrect. In this paper, the authors present a novel framework for determining such optic flow fields by combining the conventional robust estimation with a modified genetic algorithm. The baseline model used in the development is a linear optic flow motion algorithm due to its computational simplicity. The statistical properties of the generalized linear regression (GLR) model are thoroughly explored and the sensitivity of the motion estimates toward data noise is quantitatively established. Conventional robust estimators are then incorporated into the linear regression model to suppress a small percentage of gross data errors or outliers. However, segmenting an optic flow field consisting of a large portion of incorrect data or multiple motion groups requires a very high robustness that is unattainable by the conventional robust estimators. To solve this problem, the authors propose a genetic partitioning algorithm that elegantly combines the robust estimation with the genetic algorithm by a bridging genetic operator called self-adaptation.

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Optic flow field segmentation and motion estimation using a robust genetic partitioning algorithm

Les primitives geometriques usuelles en traitement d'image tridimensionnel (points, points orientes, reperes) forment une variete qui n'est generalement pas un espace vectoriel, sur lequel agit un groupe de transformation qui modelise les differentes prises de vue possibles de l'image. Leur mesure est, de plus, intrinsequement incertaine a cause de l'accumulation des erreurs et des imprecisions au cours de la chaine de traitement. Le but de ce travail est de generaliser a ces primitives les notions de statistiques usuelles ainsi que les algorithmes de reconnaissance et de recalage utilisant normalement les points. La premiere partie de la these est consacree au developpement d'outils mathematiques pour aborder ces problemes. Nous montrons tout d'abord que l'on ne peut pas considerer ces primitives comme de simples vecteurs, puis, sur des bases de geometrie riemannienne, nous developpons une notion de moyenne coherente, puis de matrice de covariance. Nous generalisons alors d'autres operations statistiques, telles que la distance de mahalanobis et le test du chi 2. Enfin, nous montrons comment cette theorie peut etre appliquee et implantee en machine dans une structure orientee objet generique. Dans la seconde partie de la these, nous developpons les calculs relatifs a ce formalisme pour les rotations et les transformations rigides agissant sur differents types de reperes. Apres analyse des algorithmes classiques sur les points, nous developpons des algorithmes de recalage generiques bases sur les primitives, et nous proposons en particulier des methodes pour estimer l'incertitude sur le recalage obtenu. Nous exposons parallelement une methode de validation statistique pour confirmer la precision de cette analyse, qui montre qu'un recalage d'une precision bien inferieure a la taille du voxel peut etre obtenue dans le cas des images medicales 3d. Un deuxieme volet de l'analyse statistique concerne la robustesse des algorithmes de reconnaissance. Le champ applicatif que nous considerons va du recalage d'images medicales tridimensionnelles a la reconnaissance de sous-structures (3d) dans les proteines et souligne la validite de l'approche generique orientee primitive que nous avons choisie pour le traitement haut niveau de donnees geometriques.

L'incertitude dans les problèmes de reconnaissance et de recalage -- Applications en imagerie médicale et biologie moléculaire

The correspondence focuses on the robust 3-D-3-D pose estimation, especially, multiple pose estimation. The robust 3-D-3-D multiple pose estimation problem is formulated as a series of general regressions which involve a successively size-decreasing data set, with each regression relating to one particular pose of interest. Since the first few regressions may carry a severely contaminated Gaussian error noise model, the MF-estimator (Zhuang et al., 1992) is used to solve each regression for each pose of interest. Extensive computer experiments with both real imagery and simulated data are conducted and results are promising. Three distinctive features of the MF-estimator are theoretically discussed and experimentally demonstrated: It is highly robust in the sense that it is not much affected by a possible large portion of outliers or incorrect matches as long as the minimum number of inliers necessary to give a unique solution are provided; It is made virtually independent of initial guesses; It is computationally reasonable and admits an efficient parallel implementation. >

Yan Huang

Papers

Robust 3-D-3-D pose estimation