HOT: Hodge-optimized triangulations
ACM SIGGRAPH 2011 papers
Fast brain matching with spectral correspondence
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Combinatorial Continuous Maximum Flow
SIAM Journal on Imaging Sciences
Interaction based simulation of dynamical system with a dynamical structure (DS)2 in MGS
Proceedings of the 2011 Summer Computer Simulation Conference
LNA: Fast Protein Structural Comparison Using a Laplacian Characterization of Tertiary Structure
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Spectral demons --- image registration via global spectral correspondence
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
On spectral partitioning of co-authorship networks
CISIM'12 Proceedings of the 11th IFIP TC 8 international conference on Computer Information Systems and Industrial Management
Groupwise spectral log-demons framework for atlas construction
MCV'12 Proceedings of the Second international conference on Medical Computer Vision: recognition techniques and applications in medical imaging
On the equilibrium of simplicial masonry structures
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Diffeomorphic spectral matching of cortical surfaces
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
Why starting from differential equations for computational physics?
Journal of Computational Physics
The chain collocation method: A spectrally accurate calculus of forms
Journal of Computational Physics
Spectral Log-Demons: Diffeomorphic Image Registration with Very Large Deformations
International Journal of Computer Vision
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The field of discrete calculus, also known as discrete exterior calculus, focuses on finding a proper set of definitions and differential operators that make it possible to operate the machinery of multivariate calculus on a finite, discrete space. In contrast to traditional goals of finding an accurate discretization of conventional multivariate calculus, discrete calculus establishes a separate, equivalent calculus that operates purely in the discrete space without any reference to an underlying continuous process. This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Although there have been a few intersections in the literature between these disciplines, they have developed largely independently of one another, yet researchers working in any one of these three areas can strongly benefit from the tools and techniques being used in the others. Many example applications from several fields of computational science are provided to demonstrate the usefulness of this framework to a broad range of problems. Readers are assumed to be familiar with the basics of vector calculus, graph theory, and linear algebra. Topics and features: presents a thorough review of discrete calculus, with a focus on key concepts required for successful application; unifies many standard image processing algorithms into a common framework for viewing a wide variety of standard algorithms in filtering, clustering, and manifold learning that may be applied to processing data associated with a graph or network; explains how discrete calculus provides a natural definition of low-frequency on a graph, which then yields filtering and denoising algorithms; discusses how filtering algorithms can give rise to clustering algorithms, which can be used to develop manifold learning and data discovery methods; examines ranking algorithms, as well as algorithms for analyzing the structure of a network. Graduate students and researchers interested in discrete calculus, complex networks, image processing and computer graphics will find this text/reference a clear introduction to the foundations of discrete calculus as well as a useful guide to have readily available for their work. Dr. Leo J. Grady is a Senior Research Scientist with Siemens Corporate Research in Princeton, New Jersey, USA. Dr. Jonathan R. Polimeni is a Research Fellow at the Massachusetts General Hospital in Boston, Massachusetts, USA, and Instructor in Radiology at Harvard Medical School, Boston, Massachusetts, USA.