CHAPTER 10 Shapeworks Particle-Based Shape Correspondence and Visualization Software

CHAPTER 10 ShapeWorks Particle-Based Shape Correspondence and Visualization Software ,†,‡ ,†,¶ ,§ Joshua Cates∗ ,ShireenElhabian∗ ,RossWhitaker∗ ∗Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, USA †Biomedical Image and Data Analysis Core, University of Utah, Salt Lake City, USA ‡Comprehensive Arrhythmia Research and Management Center, University of Utah, Salt Lake City, USA §School of Computing, University of Utah, Salt Lake City, USA ¶Faculty of Computers and Information, Cairo University, Cairo, Egypt Contents 10.1 Introducing ShapeWorks 258 10.1.1 The Potential and the Challenge 258 10.1.2 Rising to the Challenge 259 10.1.2.1 Particle Systems for a Flexible Shape Representation 259 10.1.2.2 Optimized Correspondences Address the Model Selection Problem 260 10.1.3 ShapeWorks: An Open-Source Implementation of PBM 261 10.2 Particle-Based Modeling 262 10.2.1 Overview 262 10.2.2 Surface Representation 263 10.2.3 Adaptive Distributions on Surface Features 265 10.2.4 Surface Constraint 266 10.2.5 The Kernel Width σ for PDF Estimation 267 10.2.6 Numerical Considerations 267 10.2.7 Correspondence: Entropy Minimization in Shape Space 268 10.2.8 Setting Parameters 270 10.2.9 Illustration of the Properties and Interpretability of the PBM Optimization 271 10.3 PBM Extensions 273 10.3.1 Modeling Shape with Open Surfaces 274 10.3.2 Modeling Shape Complexes 276 10.3.3 Correspondence Based on Functions of Position 277 10.3.4 Correspondence with Regression Against Explanatory Variables 279 10.3.5 Dense PBM Correspondence Models 281 10.4 ShapeWorks Software Implementation and Workflow 284 10.4.1 The ShapeWorks Shape Modeling Workflow 284 10.4.1.1 Segmentation Preprocessing and Alignment 285 10.4.1.2 Initialization and Optimization 286 10.4.1.3 Analysis 287 10.4.2 The PBM Code Library 288 10.4.3 The ShapeWorks Software Tool Suite 289 10.5 ShapeWorks in Biomedical Applications 290 Statistical Shape and Deformation Analysis Copyright © 2017 Elsevier Ltd DOI: 10.1016/B978-0-12-810493-4.00012-2 All rights reserved. 257 258 Statistical Shape and Deformation Analysis 10.6 Conclusions and Future Work 292 References 292 10.1 INTRODUCING SHAPEWORKS 10.1.1 The Potential and the Challenge Arevolutioninshapeanalysisisunderway.Whilemorphometricshavebeenimportant for the study of biology and medicine for 100 years, recent advances in multivari- ate shape representation and statistics [1–8], coupled with the increased availability of computed tomography (CT) and magnetic resonance imaging (MRI), have enabled a whole new generation of morphometric tools. Characterized by the use of modern computational techniques to automatically construct detailed three-dimensional shape representations, these new morphometrics are called Statistical Shape Modeling, and they have the potential to measure anatomy and its variability with an unprecedented level of precision and statistical power. Statistical Shape Modeling (SSM) is beginning to impact a wide spectrum of basic scientific and clinical applications, including the study of mechanisms of disease in neu- robiology [9–11], the design of optimal patient-specific implants and bone substitutes [12–16],reconstructionofanatomicalstructuresfrombothtwo-andthree-dimensional medical images [9,17–27],computer-aidedsurgeriesthroughpre-andpostoperative surgical planning [28–31,20,19],andreconstructivesurgery[32–39].Inaddition,research involving large cohorts of image data, an emerging “big data” problem, is also seeing benefit from population-level SSM to better understand disease etiology, monitor pathology progression, and study treatment [16,40–43]. While SSM is poised to revolutionize morphometry, its widespread adoption by the biological and medical research communities has been hindered by a lack of both effec- tive software implementations and generic approaches that can be applied across a wide variety of anatomies. The relative complexity of SSM algorithms makes it challenging to engineer software implementations that are user friendly. The increased computational requirements of these approaches also make it difficult to deploy SSM algorithms on a standard desktop computer, which is the only hardware widely available in research labs. Thus, to maximize the scientific and clinical impact of SSM, we need approaches that are designed to be both simple to use, from an algorithmic perspective, and that are scalable to commodity computer hardware. Furthermore, approaches that are robust to a variety of anatomies will avoid costly development and validation of multiple custom solutions. General approaches also support a larger user base, which leads to more standardization and acceptance of SSM methodologies within research communities. ShapeWorks 259 10.1.2 Rising to the Challenge It is in response to the preceding challenges that we introduce ShapeWorks. Shape- Works is an open source software implementation of a surface correspondence approach to SSM called Particle Based Modeling (PBM). PBM is designed to be simple to use, robust, and applicable to general anatomy. Simplicity and generalizability are achieved through the use of a particle system representation of shape, instead of relying on specific shape parameterizations. Correspondence points are modeling as interacting sets of particles that redistribute themselves under an energy optimization. The optimization finds correspondence configurations that minimize the entropy of the model, which is a metric of information content. Thus, the optimization learns the shape parameters that are the most efficient descriptors of the geometry of the anatomy, which increases the robustness and statistical power of the model. This energy minimization is then balanced by a parameter-free regularization strategy that maximizes entropy of correspondence positions, in order to ensure good shape representations through efficient surface sampling. 10.1.2.1 Particle Systems for a Flexible Shape Representation The choice of a specific shape representation defines, and may also limit, the class of shapes that can be modeled. To be applicable to the full range of shape analysis problems in biomedicine, a modeling methodology must be capable of representing different topological classes of shape. A correspondence-based model that relies on spherical parameterizations of shape, for example, can only represent manifold surfaces with spherical topologies [44,10].Bycontrast,manyimportantstructuresinthebody,such as the heart, for example, consist of multiple interconnected chambers, with shared boundaries and open surfaces. The boundaries of other structures may be somewhat arbitrarily defined by specific landmarks or regions of interest. Many problems in or- thopedics, for example, are concerned only with variability in specific areas of bone or the interaction of bone and cartilage surfaces at joints. In short, human anatomy can be very complex, and the simplifying assumptions of parametric models may even lead to erroneous or misleading results. Another important consideration is that medical or biological shapes are typically derived from the interfaces between organs or tissue types and usually defined implicitly in the form of segmented volumes, rather than explicit parameterizations, triangulations, or surface point samples. Such representations therefore require additional preprocessing steps that may limit the fidelity of the model and introduce error, especially as hypotheses regarding shape become more complex. Instead of a parametric shape representation, PBM uses the idea of the particle system surface representation first proposed by Witkin and Heckbert, who introduced the idea of modeling a point set as a system of interacting particles that are constrained to lie on an implicit surface. Particles interact with one another with mutually repelling forces, such as electrostatic charge, so that they find distributions that optimally cover, 260 Statistical Shape and Deformation Analysis Figure 10.1 Femur shape representation using increasing numbers of particles. and therefore describe, the surface geometry [45].Meyeretal.proposednumerically robust extensions to this approach, including a new class of radial-basis energy functions and methods for curvature-adaptive surface sampling [46].PBMadaptsthenumeri- cal approaches of Meyer et al. for correspondence models by using a set of interacting particle systems, one for each shape in the sample, to produce optimal sets of surface correspondences. Adopting a point-based surface representation avoids many of the lim- itations and complexities inherent in parametric representations, such as the limitation to specific topologies and processing steps necessary to construct parameterizations. An- other advantage is that, unlike representations that rely on surface meshes, particles do not have fixed neighbors and are free to move past one another to form different neigh- borhood configurations during the optimization process. This property means that the result is less constrained by the initialization and can potentially produce a less biased, more fully optimized model. Fig. 10.1 illustrates the concept of a particle system representation of an implicit surface on a femur bone shape. The panels from left to right show an increasing number of particles placed on the surface and the resulting surface reconstruction from the particles. The surface reconstruction is done using the method for unorganized sets of points given by Hoppe et al. [47]. The number of particles doubles in each panel (256, 512, and 1024).

Load more