Werner Stuetzle

Surface reconstruction from unorganized points

This thesis describes a general method for automatic reconstruction of accurate, concise, piecewise smooth surfaces from unorganized 3D points. Instances of surface reconstruction arise in numerous scientific and engineering applications, including reverse-engineering--the automatic generation of CAD models from physical objects. nPrevious surface reconstruction methods have typically required additional knowledge, such as structure in the data, known surface genus, or orientation information. In contrast, the method outlined in this thesis requires only the 3D coordinates of the data points. From the data, the method is able to automatically infer the topological type of the surface, its geometry, and the presence and location of features such as boundaries, creases, and corners. nThe reconstruction method has three major phases: (1) initial surface estimation, (2) mesh optimization, and (3) piecewise smooth surface optimization. A key ingredient in phase 3, and another principal contribution of this thesis, is the introduction of a new class of piecewise smooth representations based on subdivision. The effectiveness of the three-phase reconstruction method is demonstrated on a number of examples using both simulated and real data. nPhases 2 and 3 of the surface reconstruction method can also be used to approximate existing surface models. By casting surface approximation as a global optimization problem with an energy function that directly measures deviation of the approximation from the original surface, models are obtained that exhibit excellent accuracy to conciseness trade-offs. Examples of piecewise linear and piecewise smooth approximations are generated for various surfaces, including meshes, NURBS surfaces, CSG models, and implicit surfaces.

Projection pursuit regression

Abstract A new method for nonparametric multiple regression is presented. The procedure models the regression surface as a sum of general smooth functions of linear combinations of the predictor variables in an iterative manner. It is more general than standard stepwise and stagewise regression procedures, does not require the definition of a metric in the predictor space, and lends itself to graphical interpretation.

Multiresolution analysis of arbitrary meshes

In computer graphics and geometric modeling, shapes are often represented by triangular meshes. With the advent of laser scanning systems, meshes of extreme complexity are rapidly becoming commonplace. Such meshes are notoriously expensive to store, transmit, render, and are awkward to edit. Multiresolution analysis offers a simple, unified, and theoretically sound approach to dealing with these problems. Lounsbery et al. have recently developed a technique for creating multiresolution representations for a restricted class of meshes with subdivision connectivity. Unfortunately, meshes encountered in practice typically do not meet this requirement. In this paper we present a method for overcoming the subdivision connectivity restriction, meaning that completely arbitrary meshes can now be converted to multiresolution form. The method is based on the approximation of an arbitrary initial mesh M by a mesh MJ that has subdivision connectivity and is guaranteed to be within a specified tolerance. The key ingredient of our algorithm is the construction of a parametrization of M over a simple domain. We expect this parametrization to be of use in other contexts, such as texture mapping or the approximation of complex meshes by NURBS patches. CR

Piecewise smooth surface reconstruction

We present a general method for automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data. The method can be used in a variety of applications such as reverse engineering—the automatic generation of CAD models from physical objects. Novel aspects of the method are its ability to model surfaces of arbitrary topological type and to recover sharp features such as creases and corners. The method has proven to be effective, as demonstrated by a number of examples using both simulated and real data. A key ingredient in the method, and a principal contribution of this paper, is the introduction of a new class of piecewise smooth surface representations based on subdivision. These surfaces have a number of properties that make them ideal for use in surface reconstruction: they are simple to implement, they can model sharp features concisely, and they can be fit to scattered range data using an unconstrained optimization procedure.

Surface light fields for 3D photography

A surface light field is a function that assigns a color to each ray originating on a surface. Surface light fields are well suited to constructing virtual images of shiny objects under complex lighting conditions. This paper presents a framework for construction, compression, interactive rendering, and rudimentary editing of surface light fields of real objects. Generalization of vector quantization and principal component analysis are used to construct a compressed representation of an objects surface light field from photographs and range scans. A new rendering algorithm achieves interactive rendering of images from the compressed representation, incorporating view-dependent geometric level-of-detail control. The surface light field representation can also be directly edited to yield plausible surface light fields for small changes in surface geometry and reflectance properties.

Projection pursuit density estimation

Abstract The projection pursuit methodology is applied to the multivariate density estimation problem. The resulting nonparametric procedure is often less biased than the kernel and near-neighbor methods. In addition, graphical information is produced that can be used to help gain geometric insight into the multivariate data distribution.

Analysis of the adolescent growth spurt using smoothing spline functions

Height growth velocity curves between 4.5 and 17.75 years were estimated, using smoothing spline functions, for 112 boys and 110 girls from the Zurich Longitudinal Study (1955--1976). Parameters characterizing the growth process, such as peak height velocity and age at peak height velocity, were calculated directly from the estimated curves. The variability of parameters describing the adolescent growth spurt is large, both between and within sexes. Peak height, defined as increase of height velocity during the growth spurt, and age at peak height velocity both characterize the sex difference in growth in a highly significant manner. Peak height of at least 4 cm/year is found in 70% of the boys, but in only 11% of the girls. The age at peak height velocity averages 12.2 years in girls and 13.9 years in boys and has a wide range of 5.7 years and 3.8 years respectively. The sex difference in adult height of 12.6 cm is composed of the following 4 factors: +1.6 cm caused by more prepubertal growth in boys, +6.4 cm by the boys delay in spurt, +6.0 cm by the more extensive spurt in boys and -1.4 cm by more post-spurt growth in girls. Correlations between parameters indicate that the adult height depends neither on the duration of growth, nor on the duration and height of the peak. Minimal pre-spurt height velocity and peak height velocity, but not peak height, are age- and height-dependent. Partial correlations given adult height reveal two compensating mechanisms between growth in the prepubertal and in the pubertal period. Small prepubertal height and low height velocity with respect to adult height are followed by a late adolescent spurt and vice versa. Small height at the onset of the spurt with respect to adult height is followed by a longer lasting, but not higher spurt and vice versa.

Interactive multiresolution surface viewing

Multiresolution analysis has been proposed as a basic tool supporting compression, progressive transmission, and level-of-detail control of complex meshes in a unified and theoretically sound way. We extend previous work on multiresolution analysis of meshes in two ways. First, we show how to perform multiresolution analysis of colored meshes by separately analyzing shape and color. Second, we describe efficient algorithms and data structures that allow us to incrementally construct lower resolution approximations to colored meshes from the geometry and color wavelet coefficients at interactive rates. We have integrated these algorithms in a prototype mesh viewer that supports progressive transmission, dynamic display at a constant frame rate independent of machine characteristics and load, and interactive choice of tradeoff between the amount of detail in geometry and color. The viewer operates as a helper application to Netscape, and can therefore be used to rapidly browse and display complex geometric models stored on the World Wide Web. CR

Robust meshes from multiple range maps

This paper presents a method for modeling the surface of an object from a sequence of range maps. Our method is based on a volumetric approach that produces a compact surface without boundary. It provides robustness through the use of interval analysis techniques and computational efficiency through hierarchical processing using octrees.

Multidimensional Additive Spline Approximation

We describe an adaptive procedure that approximates a function of many variables by a sum of (univariate) spline functions