Andrew J. Stoddart

Reliable Surface Reconstructiuon from Multiple Range Images

This paper addresses the problem of reconstructing an integrated 3D model from multiple 2.5D range images. A novel integration algorithm is presented based on a continuous implicit surface representation. This is the first reconstruction algorithm to use operations in 3D space only. The algorithm is guaranteed to reconstruct the correct topology of surface features larger than the range image sampling resolution. Reconstruction of triangulated models from multi-image data sets is demonstrated for complex objects. Performance characterization of existing range image integration algorithms is addressed in the second part of this paper. This comparison defines the relative computational complexity and geometric limitations of existing integration algorithms.

Registration of multiple point sets

Registering 3D point sets subject to rigid body motion is a common problem in computer vision. The optimal transformation is usually specified to be the minimum of a weighted least squares cost. The case of 2 point sets has been solved by several authors using analytic methods such as SVD. In this paper we present a numerical method for solving the problem when there are more than 2 point sets. Although of general applicability the new method is particularly aimed at the multiview surface registration problem. To date almost all authors have registered only two point sets at a time. This approach discards information and we show in quantitative terms the errors caused.

Genetic algorithms for free-form surface matching

The free-form surface matching problem is important in several practical applications, such as reverse engineering. An accurate, robust and fast solution is, therefore, of great significance. Recently genetic algorithms have attracted great interest for their ability to robustly solve hard optimization problems. In this work we investigate the performance of such an approach for finding the initial guess of the transformation, a translation and a rotation, between the object and the model surface. This is followed by a local gradient descent method, such as iterative closest point, to refine the estimate. Promising results are demonstrated on accurate real data.

Implicit Surface-Based Geometric Fusion

This paper introduces a general purpose algorithm for reliable integration of sets of surface measurements into a single 3D model. The new algorithm constructs a single continuous implicit surface representation which is the zero-set of a scalar field function. An explicit object model is obtained using any implicit surface polygonization algorithm. Object models are reconstructed from both multiple view conventional 2.5D range images and hand-held sensor range data. To our knowledge this is the first geometric fusion algorithm capable of reconstructing 3D object models from noisy hand-held sensor range data.This approach has several important advantages over existing techniques. The implicit surface representation allows reconstruction of unknown objects of arbitrary topology and geometry. A continuous implicit surface representation enables reliable reconstruction of complex geometry. Correct integration of overlapping surface measurements in the presence of noise is achieved using geometric constraints based on measurement uncertainty. The use of measurement uncertainty ensures that the algorithm is robust to significant levels of measurement noise. Previous implicit surface-based approaches use discrete representations resulting in unreliable reconstruction for regions of high curvature or thin surface sections. Direct representation of the implicit surface boundary ensures correct reconstruction of arbitrary topology object surfaces. Fusion of overlapping measurements is performed using operations in 3D space only. This avoids the local 2D projection required for many previous methods which results in limitations on the object surface geometry that is reliably reconstructed. All previous geometric fusion algorithms developed for conventional range sensor data are based on the 2.5D image structure preventing their use for hand-held sensor data. Performance evaluation of the new integration algorithm against existing techniques demonstrates improved reconstruction of complex geometry.

N-View Point Set Registration: A Comparison

Recently 3 algorithms for registration of multiple partially overlapping point sets have been published by Pennec [11], Stoddart & Hilton [12] and Benjemma & Schmitt [1]. The problem is of particular interest in the building of surface models from multiple range images taken from several viewpoints. In this paper we perform a comparison of these three algorithms with respect to cpu time, ease of implementation, accuracy and stability.

Estimating pose uncertainty for surface registration

Accurate registration of surfaces is a common task in computer vision. Several algorithms exist to refine an approximate value for the pose to an accurate value. They are all more or less variants of the iterative closest point (ICP) algorithm of Besl and McKay. Up to now the problem of determining the uncertainty in the pose estimate when registering surfaces has not been solved. In this paper we provide a solution applicable when registering a noisy measured surface to an accurately known surface model. We contend that it is necessary to use the normal-projection ICP of Chen and Medioni to obtain a meaningful uncertainty estimate. Knowledge of the uncertainty provides a quantitative signal for cases of near degenerate surface shape where accurate pose estimation may not be possible. We introduce a new parameter called the registration index to give a simple means of quantifying the pose errors one might expect when registering a particular shape.

On the Foundations of Probabilistic Relaxationwith Product Support

Traditional probabilistic relaxation, as proposed by Rosenfeld, Hummel and Zucker, uses a support function which is a double sum over neighboring nodes and labels. Recently, Pelillo has shown the relevance of the Baum-Eagon theorem to the traditional formulation. Traditional probabilistic relaxation is now well understood in an optimization framework.Kittler and Hancock have suggested a form of probabilistic relaxation with product support, based on an evidence combining formula. In this paper we present a formal basis for Kittler and Hancocks probabilistic relaxation. We show that it too has close links with the Baum-Eagon theorem, and may be understood in an optimization framework. We provide some proofs to show that a stable stationary point must be a local maximum of an objective function.We present a new form of probabilistic relaxation that can be used as an approximate maximizer of the global labeling with maximum posterior probability.

SLIME - A NEW DEFORMABLE SURFACE

Deformable surfaces have many applications in surface reconstruction, tracking and segmentation of range or volumetric data. Many existing deformable surfaces connect control points in a predefined and inflexible way. This means that the surface topology is fixed in advance, and also imposes severe limitations on how a surface can be described. For example a rectangular grid of control points cannot be evenly distributed over a sphere, and singularities occur at the poles. In this paper we introduce a new (G continuous) deformable surface. In contrast to other methods this method can represent a surface of arbitrary topology, and do so in an efficient way. The method is based on a generalization of biquadratic B-splines, and has a comparable computational cost to methods based on traditional tensor product B-splines.

Reconstruction of Smooth Surfaces with Arbitrary Topology Adaptive Splines

We present a novel method for fitting a smooth G 1 continuous spline to point sets. It is based on an iterative conjugate gradient optimisation scheme. Unlike traditional tensor product based splines we can fit arbitrary topology surfaces with locally adaptive meshing. For this reason we call the surface “slime”.

Optimal parameter selection for derivative estimation from range images

Range images may be used for a variety of applications in object recognition, inspection and reverse engineering. In many of these applications it is important to obtain good estimates of the local surface curvature. Good curvature estimates require good derivative estimates, but the estimation of derivatives from sampled data is highly susceptible to noise. In this paper, we introduce a new way of characterizing range data by a single parameter. From this characterization we show how to make an optimal choice of whatever parameters there are in a particular derivative estimation method, and obtain an estimate of the error one might expect. Finally, we show how the analysis may be applied to measuring derivatives on a cylinder.