[{"type":"journal_article","publist_id":"2139","issue":"4","abstract":[{"text":"We combine topological and geometric methods to construct a multiresolution representation for a function over a two-dimensional domain. In a preprocessing stage, we create the Morse-Smale complex of the function and progressively simplify its topology by cancelling pairs of critical points. Based on a simple notion of dependency among these cancellations, we construct a hierarchical data structure supporting traversal and reconstruction operations similarly to traditional geometry-based representations. We use this data structure to extract topologically valid approximations that satisfy error bounds provided at runtime.","lang":"eng"}],"extern":1,"year":"2004","_id":"3984","intvolume":" 10","publisher":"IEEE","status":"public","title":"A topological hierarchy for functions on triangulated surfaces","publication_status":"published","author":[{"first_name":"Peer","last_name":"Bremer","full_name":"Bremer, Peer-Timo"},{"full_name":"Herbert Edelsbrunner","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Hamann, Bernd","last_name":"Hamann","first_name":"Bernd"},{"full_name":"Pascucci, Valerio","first_name":"Valerio","last_name":"Pascucci"}],"volume":10,"date_updated":"2021-01-12T07:53:39Z","date_created":"2018-12-11T12:06:16Z","day":"01","month":"07","citation":{"chicago":"Bremer, Peer, Herbert Edelsbrunner, Bernd Hamann, and Valerio Pascucci. “A Topological Hierarchy for Functions on Triangulated Surfaces.” IEEE Transactions on Visualization and Computer Graphics. IEEE, 2004. https://doi.org/10.1109/TVCG.2004.3.","short":"P. Bremer, H. Edelsbrunner, B. Hamann, V. Pascucci, IEEE Transactions on Visualization and Computer Graphics 10 (2004) 385–396.","mla":"Bremer, Peer, et al. “A Topological Hierarchy for Functions on Triangulated Surfaces.” IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 4, IEEE, 2004, pp. 385–96, doi:10.1109/TVCG.2004.3.","ieee":"P. Bremer, H. Edelsbrunner, B. Hamann, and V. Pascucci, “A topological hierarchy for functions on triangulated surfaces,” IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 4. IEEE, pp. 385–396, 2004.","apa":"Bremer, P., Edelsbrunner, H., Hamann, B., & Pascucci, V. (2004). A topological hierarchy for functions on triangulated surfaces. IEEE Transactions on Visualization and Computer Graphics. IEEE. https://doi.org/10.1109/TVCG.2004.3","ista":"Bremer P, Edelsbrunner H, Hamann B, Pascucci V. 2004. A topological hierarchy for functions on triangulated surfaces. IEEE Transactions on Visualization and Computer Graphics. 10(4), 385–396.","ama":"Bremer P, Edelsbrunner H, Hamann B, Pascucci V. A topological hierarchy for functions on triangulated surfaces. IEEE Transactions on Visualization and Computer Graphics. 2004;10(4):385-396. doi:10.1109/TVCG.2004.3"},"publication":"IEEE Transactions on Visualization and Computer Graphics","page":"385 - 396","quality_controlled":0,"date_published":"2004-07-01T00:00:00Z","doi":"10.1109/TVCG.2004.3"},{"type":"journal_article","publist_id":"2142","issue":"5","abstract":[{"lang":"eng","text":"We consider scientific data sets that describe density functions over three-dimensional geometric domains. Such data sets are often large and coarsened representations are needed for visualization and analysis. Assuming a tetrahedral mesh representation, we construct such representations with a simplification algorithm that combines three goals: the approximation of the function, the preservation of the mesh topology, and the improvement of the mesh quality. The third goal is achieved with a novel extension of the well-known quadric error metric. We perform a number of computational experiments to understand the effect of mesh quality improvement on the density map approximation. In addition, we study the effect of geometric simplification on the topological features of the function by monitoring its critical points."}],"extern":1,"year":"2004","_id":"3987","publisher":"IEEE","intvolume":" 10","status":"public","title":"Simplification of three-dimensional density maps","publication_status":"published","author":[{"full_name":"Natarajan, Vijay","first_name":"Vijay","last_name":"Natarajan"},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Herbert Edelsbrunner"}],"volume":10,"date_created":"2018-12-11T12:06:17Z","date_updated":"2021-01-12T07:53:40Z","month":"07","day":"12","citation":{"short":"V. Natarajan, H. Edelsbrunner, IEEE Transactions on Visualization and Computer Graphics 10 (2004) 587–597.","mla":"Natarajan, Vijay, and Herbert Edelsbrunner. “Simplification of Three-Dimensional Density Maps.” IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 5, IEEE, 2004, pp. 587–97, doi:10.1109/TVCG.2004.32.","chicago":"Natarajan, Vijay, and Herbert Edelsbrunner. “Simplification of Three-Dimensional Density Maps.” IEEE Transactions on Visualization and Computer Graphics. IEEE, 2004. https://doi.org/10.1109/TVCG.2004.32.","ama":"Natarajan V, Edelsbrunner H. Simplification of three-dimensional density maps. IEEE Transactions on Visualization and Computer Graphics. 2004;10(5):587-597. doi:10.1109/TVCG.2004.32","apa":"Natarajan, V., & Edelsbrunner, H. (2004). Simplification of three-dimensional density maps. IEEE Transactions on Visualization and Computer Graphics. IEEE. https://doi.org/10.1109/TVCG.2004.32","ieee":"V. Natarajan and H. Edelsbrunner, “Simplification of three-dimensional density maps,” IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 5. IEEE, pp. 587–597, 2004.","ista":"Natarajan V, Edelsbrunner H. 2004. Simplification of three-dimensional density maps. IEEE Transactions on Visualization and Computer Graphics. 10(5), 587–597."},"publication":"IEEE Transactions on Visualization and Computer Graphics","page":"587 - 597","quality_controlled":0,"date_published":"2004-07-12T00:00:00Z","doi":"10.1109/TVCG.2004.32"},{"day":"01","month":"07","doi":"10.1007/s00454-004-1122-6","date_published":"2004-07-01T00:00:00Z","page":"231 - 244","quality_controlled":0,"citation":{"chicago":"Cole Mclaughlin, Kree, Herbert Edelsbrunner, John Harer, Vijay Natarajan, and Valerio Pascucci. “Loops in Reeb Graphs of 2-Manifolds.” Discrete & Computational Geometry. Springer, 2004. https://doi.org/10.1007/s00454-004-1122-6.","short":"K. Cole Mclaughlin, H. Edelsbrunner, J. Harer, V. Natarajan, V. Pascucci, Discrete & Computational Geometry 32 (2004) 231–244.","mla":"Cole Mclaughlin, Kree, et al. “Loops in Reeb Graphs of 2-Manifolds.” Discrete & Computational Geometry, vol. 32, no. 2, Springer, 2004, pp. 231–44, doi:10.1007/s00454-004-1122-6.","ieee":"K. Cole Mclaughlin, H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci, “Loops in Reeb graphs of 2-manifolds,” Discrete & Computational Geometry, vol. 32, no. 2. Springer, pp. 231–244, 2004.","apa":"Cole Mclaughlin, K., Edelsbrunner, H., Harer, J., Natarajan, V., & Pascucci, V. (2004). Loops in Reeb graphs of 2-manifolds. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-004-1122-6","ista":"Cole Mclaughlin K, Edelsbrunner H, Harer J, Natarajan V, Pascucci V. 2004. Loops in Reeb graphs of 2-manifolds. Discrete & Computational Geometry. 32(2), 231–244.","ama":"Cole Mclaughlin K, Edelsbrunner H, Harer J, Natarajan V, Pascucci V. Loops in Reeb graphs of 2-manifolds. Discrete & Computational Geometry. 2004;32(2):231-244. doi:10.1007/s00454-004-1122-6"},"publication":"Discrete & Computational Geometry","extern":1,"publist_id":"2140","issue":"2","abstract":[{"text":"Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(n log n), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.","lang":"eng"}],"type":"journal_article","volume":32,"date_created":"2018-12-11T12:06:16Z","date_updated":"2021-01-12T07:53:39Z","author":[{"full_name":"Cole-McLaughlin, Kree","first_name":"Kree","last_name":"Cole Mclaughlin"},{"full_name":"Herbert Edelsbrunner","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"John","last_name":"Harer","full_name":"Harer, John"},{"first_name":"Vijay","last_name":"Natarajan","full_name":"Natarajan, Vijay"},{"full_name":"Pascucci, Valerio","first_name":"Valerio","last_name":"Pascucci"}],"intvolume":" 32","publisher":"Springer","status":"public","publication_status":"published","title":"Loops in Reeb graphs of 2-manifolds","year":"2004","_id":"3985","acknowledgement":"Partially supported by NSF under Grants EIA-99-72879 and CCR-00-86013."},{"date_published":"2004-10-01T00:00:00Z","doi":"10.1109/VISUAL.2004.68","conference":{"name":"VIS: IEEE Visualization"},"citation":{"mla":"Edelsbrunner, Herbert, et al. Local and Global Comparison of Continuous Functions. IEEE, 2004, pp. 275–80, doi:10.1109/VISUAL.2004.68.","short":"H. Edelsbrunner, J. Harer, V. Natarajan, V. Pascucci, in:, IEEE, 2004, pp. 275–280.","chicago":"Edelsbrunner, Herbert, John Harer, Vijay Natarajan, and Valerio Pascucci. “Local and Global Comparison of Continuous Functions,” 275–80. IEEE, 2004. https://doi.org/10.1109/VISUAL.2004.68.","ama":"Edelsbrunner H, Harer J, Natarajan V, Pascucci V. Local and global comparison of continuous functions. In: IEEE; 2004:275-280. doi:10.1109/VISUAL.2004.68","ista":"Edelsbrunner H, Harer J, Natarajan V, Pascucci V. 2004. Local and global comparison of continuous functions. VIS: IEEE Visualization, 275–280.","apa":"Edelsbrunner, H., Harer, J., Natarajan, V., & Pascucci, V. (2004). Local and global comparison of continuous functions (pp. 275–280). Presented at the VIS: IEEE Visualization, IEEE. https://doi.org/10.1109/VISUAL.2004.68","ieee":"H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci, “Local and global comparison of continuous functions,” presented at the VIS: IEEE Visualization, 2004, pp. 275–280."},"page":"275 - 280","quality_controlled":0,"month":"10","day":"01","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Herbert Edelsbrunner"},{"last_name":"Harer","first_name":"John","full_name":"Harer, John"},{"last_name":"Natarajan","first_name":"Vijay","full_name":"Natarajan, Vijay"},{"last_name":"Pascucci","first_name":"Valerio","full_name":"Pascucci, Valerio"}],"date_updated":"2021-01-12T07:53:41Z","date_created":"2018-12-11T12:06:18Z","_id":"3989","year":"2004","publisher":"IEEE","status":"public","publication_status":"published","title":"Local and global comparison of continuous functions","publist_id":"2137","abstract":[{"lang":"eng","text":"We introduce local and global comparison measures for a collection of k less than or equal to d real-valued smooth functions on a common d-dimensional Riemannian manifold. For k = d = 2 we relate the measures to the set of critical points of one function restricted to the level sets of the other. The definition of the measures extends to piecewise linear functions for which they ace easy to compute. The computation of the measures forms the centerpiece of a software tool which we use to study scientific datasets."}],"extern":1,"type":"conference"},{"extern":"1","publist_id":"1948","issue":"11","abstract":[{"text":"During vertebrate gastrulation, a relatively limited number of blastodermal cells undergoes a stereotypical set of cellular movements that leads to formation of the three germ layers: ectoderm, mesoderm and endoderm. Gastrulation, therefore, provides a unique developmental system in which to study cell movements in vivo in a fairly simple cellular context. Recent advances have been made in elucidating the cellular and molecular mechanisms that underlie cell movements during zebrafish gastrulation. These findings can be compared with observations made in other model systems to identify potential general mechanisms of cell migration during development.","lang":"eng"}],"type":"journal_article","oa_version":"None","volume":14,"date_created":"2018-12-11T12:07:23Z","date_updated":"2021-01-12T07:55:02Z","author":[{"full_name":"Montero, Juan","last_name":"Montero","first_name":"Juan"},{"full_name":"Heisenberg, Carl-Philipp J","id":"39427864-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0912-4566","first_name":"Carl-Philipp J","last_name":"Heisenberg"}],"intvolume":" 14","publisher":"Cell Press","status":"public","title":"Gastrulation dynamics: cells move into focus","publication_status":"published","_id":"4172","year":"2004","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","day":"01","month":"11","language":[{"iso":"eng"}],"date_published":"2004-11-01T00:00:00Z","doi":"10.1016/j.tcb.2004.09.008","page":"620 - 627","citation":{"ista":"Montero J, Heisenberg C-PJ. 2004. Gastrulation dynamics: cells move into focus. Trends in Cell Biology. 14(11), 620–627.","ieee":"J. Montero and C.-P. J. Heisenberg, “Gastrulation dynamics: cells move into focus,” Trends in Cell Biology, vol. 14, no. 11. Cell Press, pp. 620–627, 2004.","apa":"Montero, J., & Heisenberg, C.-P. J. (2004). Gastrulation dynamics: cells move into focus. Trends in Cell Biology. Cell Press. https://doi.org/10.1016/j.tcb.2004.09.008","ama":"Montero J, Heisenberg C-PJ. Gastrulation dynamics: cells move into focus. Trends in Cell Biology. 2004;14(11):620-627. doi:10.1016/j.tcb.2004.09.008","chicago":"Montero, Juan, and Carl-Philipp J Heisenberg. “Gastrulation Dynamics: Cells Move into Focus.” Trends in Cell Biology. Cell Press, 2004. https://doi.org/10.1016/j.tcb.2004.09.008.","mla":"Montero, Juan, and Carl-Philipp J. Heisenberg. “Gastrulation Dynamics: Cells Move into Focus.” Trends in Cell Biology, vol. 14, no. 11, Cell Press, 2004, pp. 620–27, doi:10.1016/j.tcb.2004.09.008.","short":"J. Montero, C.-P.J. Heisenberg, Trends in Cell Biology 14 (2004) 620–627."},"publication":"Trends in Cell Biology"}]