John Alan McDonald

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. Previous 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. The 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. Phases 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.

Mesh optimization

We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh M0, produce a mesh M, of the same topological type as M0 , that fits the data well and has a small number of vertices. Our approach is to minimize an energy function that explicitly models the competing desires of conciseness of representation and fidelity to the data. We show that mesh optimization can be effectively used in at least two applications: surface reconstruction from unorganized points, and mesh simplification (the reduction of the number of vertices in an initially dense mesh of triangles). 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.

Cardiac-Specific Induction of the Transcriptional Coactivator Peroxisome Proliferator-Activated Receptor γ Coactivator-1α Promotes Mitochondrial Biogenesis and Reversible Cardiomyopathy in a Developmental Stage-Dependent Manner

Abstract— Recent evidence has identified the peroxisome proliferator-activated receptor &ggr; coactivator-1&agr; (PGC-1&agr;) as a regulator of cardiac energy metabolism and mitochondrial biogenesis. We describe the development of a transgenic system that permits inducible, cardiac-specific overexpression of PGC-1&agr;. Expression of the PGC-1&agr; transgene in this system (tet-on PGC-1&agr;) is cardiac-specific in the presence of doxycycline (dox) and is not leaky in the absence of dox. Overexpression of PGC-1&agr; in tet-on PGC-1&agr; mice during the neonatal stages leads to a dramatic increase in cardiac mitochondrial number and size coincident with upregulation of gene markers associated with mitochondrial biogenesis. In contrast, overexpression of PGC-1&agr; in the hearts of adult mice leads to a modest increase in mitochondrial number, derangements of mitochondrial ultrastructure, and development of cardiomyopathy. The cardiomyopathy in adult tet-on PGC-1&agr; mice is characterized by an increase in ventricular mass and chamber dilatation. Surprisingly, removal of dox and cessation of PGC-1&agr; overexpression in adult mice results in complete reversal of cardiac dysfunction within 4 weeks. These results indicate that PGC-1&agr; drives mitochondrial biogenesis in a developmental stage-dependent manner permissive during the neonatal period. This unique murine model should prove useful for the study of the molecular regulatory programs governing mitochondrial biogenesis and characterization of the relationship between mitochondrial dysfunction and cardiomyopathy and as a general model of inducible, reversible cardiomyopathy.

Interactive data visualization using focusing and linking

Two basic principles for interactive visualization of high-dimensional data-focusing and linking-are discussed. Focusing techniques may involve selecting subsets, dimension reduction, or some more general manipulation of the layout information on the page or screen. A consequent of focusing is that each view only conveys partial information about the data and needs to be linked so that the information contained in individual views can be integrated into a coherent image of the data as a whole. Examples are given of how graphical data analysis methods based on focusing and linking are used in applications including linguistics, geographic information systems, time series analysis, and the analysis of multi-channel images arising in radiology and remote sensing.<<ETX>>

System for quantitative three-dimensional echocardiography of the left ventricle based on a magnetic-field position and orientation sensing system

Accurate measurement of left-ventricular (LV) volume and function are important to monitor disease progression and assess prognosis in patients with heart disease. Existing methods of three-dimensional (3-D) imaging of the heart using ultrasound have shown the potential of this modality, but each suffers from inherent restrictions which limit its applicability to the full range of clinical situations. The authors have developed a technique for image acquisition using a magnetic-field system to track the 3-D echocardiographic imaging planes and 3-D image analysis software including the piecewise smooth subdivision method for surface reconstruction. The technique offers several advantages over existing methods of 3-D echocardiography. The results of validation using in vitro LVs show that the technique allows accurate measurement of LV volume and anatomically accurate 3-D reconstruction of LV shape and is, therefore, suitable for analysis of regional as well as global function.

Smoothing with split linear fits

We introduce a family of smoothing algorithms that can produce discontinuous output. Unlike most commonly used smoothers, that tend to blur discontinuities in the data, this smoother can be used for smoothing with edge detection. We cite examples of other approaches to (two-dimensional) smoothing with edge detection in image processing, and apply our one-dimensional smoother to sea surface temperature data where the discontinuities arise from changes in ocean currents.

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.

Three-dimensional echocardiographic measurement of left and right ventricular mass and volume: in vitro validation.

Introduction: Three-dimensional (3D) echocardiography has been shown to offer highly accurate measurements of left ventricular (LV) volume and mass. The present study evaluated the accuracy of 3D surface reconstruction by the piecewise smooth subdivision method in measuring volume and mass not only in the LV but also in the more complexly shaped right ventricle (RV). Methods: 3D echo scans were obtained of in vitro LVs (n = 15) and RVs (n = 10). From digitized images, ventricular borders were traced and used in surface reconstructions. Mass and volume determined from the reconstructions were compared to true volume and mass determined prior to imaging. Additionally casts of two RVs were made and laser-scanned. Distances between the laser-identified points on the RV surface and the corresponding 3D echo reconstructions were measured. Results: 3D LV volume agreed well with the true volume (y = 0.99x + 1.73, r = 0.99, SEE = 3.35 ml, p < 0.0001), as did 3D LV mass (y = 0.99x − 4.71, r = 0.99, SEE = 9.85 g, p < 0.0001). 3D RV volume overestimated true volume (y = 1.11x + 1.77, r = 0.99, SEE = 3.36 ml, p < 0.001) by 6.23 ± 3.70 ml (p < 0.0001). 3D mass agreed well with RV mass (y = 0.78x + 17.32, r2 = 0.93, SEE = 3.54 g, p < 0.0001). 3D echo reconstructions matched the laser-scanned RV closely with residual distances of 1.1 ± 0.9 and 1.4 ± 1.2 mm, respectively. Conclusions: 3D echo using freehand scanning combined with surface reconstruction by the piecewise smooth subdivision surface method enables accurate determination of LV mass and volume, of RV mass and volume, and of the RVs complex shape.

Painting multiple views of complex objects

This paper reviews and illustrates a direct manipulation approach to visualization of complex objects called painting multiple views. We describe a programming model for direct manipulation in general and for painting in particular, based on simple constraints between entities in an the underlying scientific database and the components of displays used to examine the data. With this model, the original notion of “brushing scatterplots” is easily extended.