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Boundary First Flattening

Rohan Sawhney, Keenan Crane
2017 ACM Transactions on Graphics  

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2017 pre-print arXiv:1704.06873v1 fatcat:2b7augpsijd5plqtusgugftm5q

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2018 accepted
arXiv:1704.06873v2 fatcat:73smbccaifdzzjnesgs5wygrwy
Boundary first flattening (BFF) is a linear method for conformal parameterization which is faster than traditional linear methods, yet provides control and quality comparable to sophisticated nonlinear  ...  Since computation demands only a single factorization of the real Laplace matrix, the amortized cost is about 50x less than any previously published technique for boundary-controlled conformal flattening  ...  First, to prescribe exterior anglesκ we simply add linear constraints β jk i = π −κ i at each boundary vertex i.  ... 
doi:10.1145/3132705 fatcat:3rweezit3jgwjpyfo56aqeskyi
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Citation

Rohan Sawhney, Keenan Crane. "Boundary First Flattening." ACM Transactions on Graphics 37.1 (2017) 1-14

Geophysical model of the dynamical flattening of the Earth in agreement with the precession constant

P. Defraigne
1997 Geophysical Journal International  

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https://web.archive.org/web/20180725114405/https://watermark.silverchair.com/130-1-47.pdf?token=AQECAHi208BE49Ooan9kkhW_Ercy7Dm3ZL_9Cf3qfKAc485ysgAAAa8wggGrBgkqhkiG9w0BBwagggGcMIIBmAIBADCCAZEGCSqGSIb3DQEHATAeBglghkgBZQMEAS4wEQQMJ9HkPml2w7yQz8rJAgEQgIIBYvvj877Lla3APd7hKGLp0KhEjHpvhwHyU9mzvhiZ6nZQoZyCqscAzxmZ1ycBDhUi9b76nbHDh7LKcvmKuiJ0i1oP1a80rIhBGXrlkX0e00-Od69SlCXODyEkbG43HoDXljeUrtZQoK2jmo2albiTLJ0WP6jbRcMALU50Nt1aYJoEn_cJNHICFQ42_eq8zG_A-SdVqoyddplOXZhpJJugEXzvpbQcWMCTu4W4SXWwhw_llUdkqLWTxl6psWlp0x5YeUP0M51TGExvpNx9H7XKaIxKaobckOYu6xVL25Vf8pF8uM4w2qmCoXwjXQTlD_NptQXPtP1QGw6leA13svmpct9OnpvwQcDtP8FMn1m6OwTR4NkAQkp35E03HI4zQr7OkqN4CP1yYY2Wp9Z9iaxps6qWbWQ4Avl3ttohqh90Fxv1Du6-PWMtNeNE4XVdyombtO1CGjyWZLuYLrXohBaPAI92kg

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First, we compute mantle circulation associated with the density anomalies derived from a tomography model.  ...  observed by tomography and (2) internal boundary topographies.  ...  We first computed the non-hydrostatic boundary deformations induced by mantle flows associated with lateral density heterogeneities.  ... 
doi:10.1111/j.1365-246x.1997.tb00986.x fatcat:3xdfiu4bwncn3hfjwdo35tcskq
Citation

P. Defraigne. "Geophysical model of the dynamical flattening of the Earth in agreement with the precession constant." Geophysical Journal International 130.1 (1997) 47-56

Reduce the stretch in surface flattening by finding cutting paths to the surface boundary

Charlie C.L. Wang, Yu Wang, Kai Tang, Matthew M.F. Yuen
2004 Computer-Aided Design  

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First, a linear algorithm for computing an approximate boundary geodesic distance map is introduced; the map encapsulates the undirected geodesic distance from every triangular node to the surface boundary  ...  This paper presents a method for finding cutting paths on a 3D triangular mesh surface to reduce the stretch in the flattened surface.  ...  After that, we add the newly generated path into the surface boundary, and go back to the first step to compute the new boundary geodesic distance map.  ... 
doi:10.1016/s0010-4485(03)00024-1 fatcat:zd3jqcwsxvaa3mqnxqayv3al2q
Citation

Charlie C.L. Wang, Yu Wang, Kai Tang, Matthew M.F. Yuen. "Reduce the stretch in surface flattening by finding cutting paths to the surface boundary." Computer-Aided Design 36.8 (2004) 665-677

Automated image segmentation-assisted flattening of atomic force microscopy images

Yuliang Wang, Tongda Lu, Xiaolai Li, Huimin Wang
2018 Beilstein Journal of Nanotechnology  

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In the first step, the convex and concave features in the foreground were automatically segmented with accurate boundary detection. The extracted foreground features were taken as exclusion masks.  ...  As a result, image flattening is required prior to image analysis.  ...  Results and Discussion In this section, a comparison of different flattening methods was first conducted.  ... 
doi:10.3762/bjnano.9.91 pmid:29719750 pmcid:PMC5905267 fatcat:i62372gsonbjhaapqszcd62aqe
DOAJ
Citation

Yuliang Wang, Tongda Lu, Xiaolai Li, Huimin Wang. "Automated image segmentation-assisted flattening of atomic force microscopy images." Beilstein Journal of Nanotechnology (2018) 975-985

Flattening maps for the visualization of multibranched vessels

Lei Zhu, S. Haker, A. Tannenbaum
2005 IEEE Transactions on Medical Imaging  

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The first approach is a conformal mapping algorithm based on the minimization of two Dirichlet functionals.  ...  In this paper, we present two novel algorithms which produce flattened visualizations of branched physiological surfaces, such as vessels.  ...  In the first step, the boundary values are decided by triangle counts between the root and the other boundaries. This is a very coarse estimation.  ... 
doi:10.1109/tmi.2004.839368 pmid:15707245 pmcid:PMC3640433 fatcat:ch7i4wzhcnepzp3475lcegslgy
Citation

Lei Zhu, S. Haker, A. Tannenbaum. "Flattening maps for the visualization of multibranched vessels." IEEE Transactions on Medical Imaging 24.2 (2005) 191-198

Placental Flattening via Volumetric Parameterization [article]

S. Mazdak Abulnaga, Esra Abaci Turk, Mikhail Bessmeltsev, P. Ellen Grant, Justin Solomon, Polina Golland
2019 arXiv   pre-print

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2019 pre-print
arXiv:1903.05044v1 fatcat:tptqxr2fvbbvzffdoy6s5evzji
2019 pre-print
arXiv:1903.05044v2 fatcat:5ikvuh7qerbp7mmylyz4jlhutu
We achieve sub-voxel accuracy in mapping the boundary of the placenta to the template while successfully controlling distortion throughout the volume.  ...  Our code is freely available at https://github.com/mabulnaga/placenta-flattening .  ...  We first assign to the rim all vertices on the boundary of the two clusters, i.e., those with neighbors in the other cluster.  ... 
arXiv:1903.05044v3 fatcat:bd5vmsblpndtdjkhgnejvstho4
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Citation

S. Mazdak Abulnaga, Esra Abaci Turk, Mikhail Bessmeltsev, P. Ellen Grant, Justin Solomon, Polina Golland. "Placental Flattening via Volumetric Parameterization." arXiv (2019)

Contribution of CRUST2.0 components to the tri-axiality of the Earth and equatorial flattening of the core

Sun Rong, Shen Wenbin
2013 Geodesy and Geodynamics  

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Mter the contribution of density contrast is stripped, the equatorial flattening of the core was found to be 6. 544 x 10-5 , which is still one order of magnitude smaller than the result given by the first  ...  For boundaries of other layers, we used values from the CRUST2. 0 model with a resolution of 2 o.  ...  If the density of the tri-axial ellipsoid is constant, From equation ( 26) we see that e; appears in {3 as second-order terms of flattening, whereas e~ appears as first order of dynamical flattening  ... 
doi:10.3724/sp.j.1246.2013.03053 fatcat:uvxy7syj75hhxct4rjz77ukkmi
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Citation

Sun Rong, Shen Wenbin. "Contribution of CRUST2.0 components to the tri-axiality of the Earth and equatorial flattening of the core." Geodesy and Geodynamics 4.3 (2013) 53-60

Optimal fitting of strain-controlled flattenable mesh surfaces

Yunbo Zhang, Charlie C. L. Wang, Karthik Ramani
2016 The International Journal of Advanced Manufacturing Technology  

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First, we introduce a new surface modeling method to conduct a sequence of nearly isometric deformations to morph a flattenable mesh surface to a new shape which has a better approximation of the input  ...  Last, to improve the scalability of our optimal surface fitting algorithm, a coarseto-fine fitting framework is exploited so that very dense flattenable mesh surfaces can be modeled and boundaries of the  ...  First, a new surface modeling method is conduct a sequence of nearly isodeformations to morph a flattenable mesh surface to a new shape which has a better approximation of the input surface.  ... 
doi:10.1007/s00170-016-8669-2 fatcat:6mbhlo3d3vfgdamg2x32gfqrvi
Citation

Yunbo Zhang, Charlie C. L. Wang, Karthik Ramani. "Optimal fitting of strain-controlled flattenable mesh surfaces." The International Journal of Advanced Manufacturing Technology 87.9-12 (2016) 2873-2887

A New Approach to Crushing 3-Manifold Triangulations

Benjamin A. Burton
2014 Discrete & Computational Geometry  

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2014 accepted
arXiv:1212.1441v3 fatcat:224cpezetzdvbpai75avwkt5au
2012 pre-print
arXiv:1212.1441v1 fatcat:ssgmkpkprvh7ji2qvcgqmw4jsu
2013 pre-print
arXiv:1212.1441v2 fatcat:o2o34fixrrcsbcmfrayfjjbyru
When the crushing operation was first introduced, the analysis was powerful but extremely complex.  ...  The crushing operation of Jaco and Rubinstein is a powerful technique in algorithmic 3-manifold topology: it enabled the first practical implementations of 3-sphere recognition and prime decomposition  ...  flatten both boundary bigons without problems.  ... 
doi:10.1007/s00454-014-9572-y fatcat:pkwulabrtzfovecbq2zquk5544
Szczepanski Multiple Versions
Citation

Benjamin A. Burton. "A New Approach to Crushing 3-Manifold Triangulations." Discrete & Computational Geometry 52.1 (2014) 116-139

Quasi-Conformally Flat Mapping the Human Cerebellum [chapter]

Monica K. Hurdal, Philip L. Bowers, Ken Stephenson, De Witt L. Sumners, Kelly Rehm, Kirt Schaper, David A. Rottenberg
1999 Lecture Notes in Computer Science  

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) information under flattening.  ...  Our approach attempts to preserve the conformal structure between the original cortical surface in 3-space and the flattened surface.  ...  First, it is completely canonical, meaning that such flattenings are uniquely determined once certain standard normalizations have been chosen.  ... 
doi:10.1007/10704282_31 fatcat:tngmkahqlnhbjbvan4vqbgfvpu
Citation

Monica K. Hurdal, Philip L. Bowers, Ken Stephenson, De Witt L. Sumners, Kelly Rehm, Kirt Schaper, David A. Rottenberg. "Quasi-Conformally Flat Mapping the Human Cerebellum." Lecture Notes in Computer Science (1999) 279-286

Improving Initial Flattening of Convex-Shaped Free-Form Mesh Surface Patches Using a Dynamic Virtual Boundary

Erdem Yavuz, Rıfat Yazıcı, Mustafa Cem Kasapba¸sı, Turgay Tugay Bilgin
2019 Computer systems science and engineering  

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This study proposes an efficient algorithm for improving flattening result of triangular mesh surface patches having a convex shape.  ...  The dynamic virtual boundary approach is utilized to reduce the distortions for the triangles near the boundary caused by the nature of convex combination technique.  ...  hybrid flattening, which is a combination of the first two [9] .  ... 
doi:10.32604/csse.2019.34.339 fatcat:ukcd5zo74fev7iztjkbz5x465q
Citation

Erdem Yavuz, Rıfat Yazıcı, Mustafa Cem Kasapba¸sı, Turgay Tugay Bilgin. "Improving Initial Flattening of Convex-Shaped Free-Form Mesh Surface Patches Using a Dynamic Virtual Boundary." Computer systems science and engineering (2019) 339-355

Density-Equalizing Maps for Simply Connected Open Surfaces

Gary P. T. Choi, Chris H. Rycroft
2018 SIAM Journal of Imaging Sciences  

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In this paper, we are concerned with the problem of creating flattening maps of simply connected open surfaces in \BbbR 3 .  ...  By varying the initial density distribution, a large variety of flattening maps with different properties can be achieved.  ...  first flattening [38] .  ... 
doi:10.1137/17m1124796 fatcat:ihvgreuztrguvl74f66kav5uny
Citation

Gary P. T. Choi, Chris H. Rycroft. "Density-Equalizing Maps for Simply Connected Open Surfaces." SIAM Journal of Imaging Sciences 11.2 (2018) 1134-1178

Freeform surface flattening based on fitting a woven mesh model

Charlie C.L. Wang, Kai Tang, Benjamin M.L. Yeung
2005 Computer-Aided Design  

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We will first review some related work in surface flattening. The woven mesh model is then introduced.  ...  The freeform 3D surface considered in this paper is represented as a two-manifold polygonal mesh with a boundary, which is topologically equivalent to a disk.  ...  Their algorithm first obtains an approximate planar shape by flattening the triangles on the surface, cracks are generated while triangles are flattened one by one; and then, they reorient cracks and overlap  ... 
doi:10.1016/j.cad.2004.09.009 fatcat:xbykvohwnjezphh3l3tcph3ena
Citation

Charlie C.L. Wang, Kai Tang, Benjamin M.L. Yeung. "Freeform surface flattening based on fitting a woven mesh model." Computer-Aided Design 37.8 (2005) 799-814

Real-Time Automatic Segmentation of Optical Coherence Tomography Volume Data of the Macular Region

Jing Tian, Boglárka Varga, Gábor Márk Somfai, Wen-Hsiang Lee, William E. Smiddy, Delia Cabrera DeBuc, Daniel L Rubin
2015 PLoS ONE  

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The proposed method is implemented using the shortestpath based graph search, which detects the retinal boundaries by searching the shortest-path between two end nodes using Dijkstra's algorithm.  ...  Additional techniques, such as inter-frame flattening, inter-frame search region refinement, masking and biasing were introduced to exploit the spatial dependency between adjacent frames for the reduction  ...  Particularly, in order to detect each boundary, flattening is first performed to reduce the curvature of the target boundary.  ... 
doi:10.1371/journal.pone.0133908 pmid:26258430 pmcid:PMC4530974 fatcat:yxyymscuyvdf5khui2l2hux6na
DOAJ
Citation

Jing Tian, Boglárka Varga, Gábor Márk Somfai, Wen-Hsiang Lee, William E. Smiddy, Delia Cabrera DeBuc, Daniel L Rubin. "Real-Time Automatic Segmentation of Optical Coherence Tomography Volume Data of the Macular Region." PLoS ONE 10.8 (2015) e0133908

Conformal flattening maps for the visualization of vessels

Lei Zhu, Steven Haker, Allen R. Tannenbaum, Seong K. Mun
2002 Medical Imaging 2002: Visualization, Image-Guided Procedures, and Display  

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In this note, we employ a conformal mapping technique for flattening branching tubular structures for visualization of MRA and CT volumetric vessel imagery.  ...  Our method is based on a discretization of the Laplace-Beltrami operator to flatten a surface onto a planar polygonal region in an angle-preserving manner.  ...  First, using the segmentation method in Ref. 3 and Ref. 7, we found the surface of a section of vessel.  ... 
doi:10.1117/12.466985 dblp:conf/miigp/ZhuHT02 fatcat:76w2keflmveprgzpyk4goiarfq
Citation

Lei Zhu, Steven Haker, Allen R. Tannenbaum, Seong K. Mun. "Conformal flattening maps for the visualization of vessels." Medical Imaging 2002: Visualization, Image-Guided Procedures, and Display (2002)

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