Cone Fields and Topological Sampling in Manifolds with Bounded Curvature
Abstract A standard reconstruction problem is how to discover a compact set from a noisy point cloud that approximates it. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the Hausdorff distance between two compact se...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Turner, Katharine [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2013 |
|---|
| Schlagwörter: |
|---|
| Anmerkung: |
© SFoCM 2013 |
|---|
| Übergeordnetes Werk: |
Enthalten in: Foundations of computational mathematics - Springer US, 2001, 13(2013), 6 vom: 23. Okt., Seite 913-933 |
|---|---|
| Übergeordnetes Werk: |
volume:13 ; year:2013 ; number:6 ; day:23 ; month:10 ; pages:913-933 |
| Links: |
|---|
| DOI / URN: |
10.1007/s10208-013-9176-6 |
|---|
| Katalog-ID: |
OLC2057961826 |
|---|
| LEADER | 01000caa a22002652 4500 | ||
|---|---|---|---|
| 001 | OLC2057961826 | ||
| 003 | DE-627 | ||
| 005 | 20230502175656.0 | ||
| 007 | tu | ||
| 008 | 200820s2013 xx ||||| 00| ||eng c | ||
| 024 | 7 | |a 10.1007/s10208-013-9176-6 |2 doi | |
| 035 | |a (DE-627)OLC2057961826 | ||
| 035 | |a (DE-He213)s10208-013-9176-6-p | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | 4 | |a 510 |a 004 |q VZ |
| 082 | 0 | 4 | |a 510 |q VZ |
| 084 | |a 17,1 |2 ssgn | ||
| 084 | |a 31.76$jNumerische Mathematik |2 bkl | ||
| 084 | |a 54.10$jTheoretische Informatik |2 bkl | ||
| 100 | 1 | |a Turner, Katharine |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Cone Fields and Topological Sampling in Manifolds with Bounded Curvature |
| 264 | 1 | |c 2013 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a ohne Hilfsmittel zu benutzen |b n |2 rdamedia | ||
| 338 | |a Band |b nc |2 rdacarrier | ||
| 500 | |a © SFoCM 2013 | ||
| 520 | |a Abstract A standard reconstruction problem is how to discover a compact set from a noisy point cloud that approximates it. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the Hausdorff distance between two compact sets, for when certain offsets of these two sets are homotopic in terms of the absence of μ-critical points in an annular region. We reduce the problem of reconstructing a subset from a point cloud to the existence of a deformation retraction from the offset of the subset to the subset itself. The ambient space can be any Riemannian manifold but we focus on ambient manifolds which have nowhere negative curvature (this includes Euclidean space). We get an improvement on previous bounds for the case where the ambient space is Euclidean whenever μ≤0.945 (μ∈(0,1) by definition). In the process, we prove stability theorems for μ-critical points when the ambient space is a manifold. | ||
| 650 | 4 | |a Distance function | |
| 650 | 4 | |a Surface and manifold reconstruction | |
| 650 | 4 | |a Deformation retraction | |
| 650 | 4 | |a Fibre bundle | |
| 773 | 0 | 8 | |i Enthalten in |t Foundations of computational mathematics |d Springer US, 2001 |g 13(2013), 6 vom: 23. Okt., Seite 913-933 |w (DE-627)330598139 |w (DE-600)2050531-0 |w (DE-576)094479291 |x 1615-3375 |7 nnns |
| 773 | 1 | 8 | |g volume:13 |g year:2013 |g number:6 |g day:23 |g month:10 |g pages:913-933 |
| 856 | 4 | 1 | |u https://doi.org/10.1007/s10208-013-9176-6 |z lizenzpflichtig |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_OLC | ||
| 912 | |a SSG-OLC-MAT | ||
| 912 | |a SSG-OPC-MAT | ||
| 912 | |a GBV_ILN_40 | ||
| 912 | |a GBV_ILN_70 | ||
| 912 | |a GBV_ILN_2002 | ||
| 912 | |a GBV_ILN_2088 | ||
| 912 | |a GBV_ILN_4277 | ||
| 936 | b | k | |a 31.76$jNumerische Mathematik |q VZ |0 106408194 |0 (DE-625)106408194 |
| 936 | b | k | |a 54.10$jTheoretische Informatik |q VZ |0 106418815 |0 (DE-625)106418815 |
| 951 | |a AR | ||
| 952 | |d 13 |j 2013 |e 6 |b 23 |c 10 |h 913-933 | ||
| author_variant |
k t kt |
|---|---|
| matchkey_str |
article:16153375:2013----::oeilsntplgclapignaiodw |
| hierarchy_sort_str |
2013 |
| bklnumber |
31.76$jNumerische Mathematik 54.10$jTheoretische Informatik |
| publishDate |
2013 |
| allfields |
10.1007/s10208-013-9176-6 doi (DE-627)OLC2057961826 (DE-He213)s10208-013-9176-6-p DE-627 ger DE-627 rakwb eng 510 004 VZ 510 VZ 17,1 ssgn 31.76$jNumerische Mathematik bkl 54.10$jTheoretische Informatik bkl Turner, Katharine verfasserin aut Cone Fields and Topological Sampling in Manifolds with Bounded Curvature 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © SFoCM 2013 Abstract A standard reconstruction problem is how to discover a compact set from a noisy point cloud that approximates it. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the Hausdorff distance between two compact sets, for when certain offsets of these two sets are homotopic in terms of the absence of μ-critical points in an annular region. We reduce the problem of reconstructing a subset from a point cloud to the existence of a deformation retraction from the offset of the subset to the subset itself. The ambient space can be any Riemannian manifold but we focus on ambient manifolds which have nowhere negative curvature (this includes Euclidean space). We get an improvement on previous bounds for the case where the ambient space is Euclidean whenever μ≤0.945 (μ∈(0,1) by definition). In the process, we prove stability theorems for μ-critical points when the ambient space is a manifold. Distance function Surface and manifold reconstruction Deformation retraction Fibre bundle Enthalten in Foundations of computational mathematics Springer US, 2001 13(2013), 6 vom: 23. Okt., Seite 913-933 (DE-627)330598139 (DE-600)2050531-0 (DE-576)094479291 1615-3375 nnns volume:13 year:2013 number:6 day:23 month:10 pages:913-933 https://doi.org/10.1007/s10208-013-9176-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2088 GBV_ILN_4277 31.76$jNumerische Mathematik VZ 106408194 (DE-625)106408194 54.10$jTheoretische Informatik VZ 106418815 (DE-625)106418815 AR 13 2013 6 23 10 913-933 |
| spelling |
10.1007/s10208-013-9176-6 doi (DE-627)OLC2057961826 (DE-He213)s10208-013-9176-6-p DE-627 ger DE-627 rakwb eng 510 004 VZ 510 VZ 17,1 ssgn 31.76$jNumerische Mathematik bkl 54.10$jTheoretische Informatik bkl Turner, Katharine verfasserin aut Cone Fields and Topological Sampling in Manifolds with Bounded Curvature 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © SFoCM 2013 Abstract A standard reconstruction problem is how to discover a compact set from a noisy point cloud that approximates it. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the Hausdorff distance between two compact sets, for when certain offsets of these two sets are homotopic in terms of the absence of μ-critical points in an annular region. We reduce the problem of reconstructing a subset from a point cloud to the existence of a deformation retraction from the offset of the subset to the subset itself. The ambient space can be any Riemannian manifold but we focus on ambient manifolds which have nowhere negative curvature (this includes Euclidean space). We get an improvement on previous bounds for the case where the ambient space is Euclidean whenever μ≤0.945 (μ∈(0,1) by definition). In the process, we prove stability theorems for μ-critical points when the ambient space is a manifold. Distance function Surface and manifold reconstruction Deformation retraction Fibre bundle Enthalten in Foundations of computational mathematics Springer US, 2001 13(2013), 6 vom: 23. Okt., Seite 913-933 (DE-627)330598139 (DE-600)2050531-0 (DE-576)094479291 1615-3375 nnns volume:13 year:2013 number:6 day:23 month:10 pages:913-933 https://doi.org/10.1007/s10208-013-9176-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2088 GBV_ILN_4277 31.76$jNumerische Mathematik VZ 106408194 (DE-625)106408194 54.10$jTheoretische Informatik VZ 106418815 (DE-625)106418815 AR 13 2013 6 23 10 913-933 |
| allfields_unstemmed |
10.1007/s10208-013-9176-6 doi (DE-627)OLC2057961826 (DE-He213)s10208-013-9176-6-p DE-627 ger DE-627 rakwb eng 510 004 VZ 510 VZ 17,1 ssgn 31.76$jNumerische Mathematik bkl 54.10$jTheoretische Informatik bkl Turner, Katharine verfasserin aut Cone Fields and Topological Sampling in Manifolds with Bounded Curvature 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © SFoCM 2013 Abstract A standard reconstruction problem is how to discover a compact set from a noisy point cloud that approximates it. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the Hausdorff distance between two compact sets, for when certain offsets of these two sets are homotopic in terms of the absence of μ-critical points in an annular region. We reduce the problem of reconstructing a subset from a point cloud to the existence of a deformation retraction from the offset of the subset to the subset itself. The ambient space can be any Riemannian manifold but we focus on ambient manifolds which have nowhere negative curvature (this includes Euclidean space). We get an improvement on previous bounds for the case where the ambient space is Euclidean whenever μ≤0.945 (μ∈(0,1) by definition). In the process, we prove stability theorems for μ-critical points when the ambient space is a manifold. Distance function Surface and manifold reconstruction Deformation retraction Fibre bundle Enthalten in Foundations of computational mathematics Springer US, 2001 13(2013), 6 vom: 23. Okt., Seite 913-933 (DE-627)330598139 (DE-600)2050531-0 (DE-576)094479291 1615-3375 nnns volume:13 year:2013 number:6 day:23 month:10 pages:913-933 https://doi.org/10.1007/s10208-013-9176-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2088 GBV_ILN_4277 31.76$jNumerische Mathematik VZ 106408194 (DE-625)106408194 54.10$jTheoretische Informatik VZ 106418815 (DE-625)106418815 AR 13 2013 6 23 10 913-933 |
| allfieldsGer |
10.1007/s10208-013-9176-6 doi (DE-627)OLC2057961826 (DE-He213)s10208-013-9176-6-p DE-627 ger DE-627 rakwb eng 510 004 VZ 510 VZ 17,1 ssgn 31.76$jNumerische Mathematik bkl 54.10$jTheoretische Informatik bkl Turner, Katharine verfasserin aut Cone Fields and Topological Sampling in Manifolds with Bounded Curvature 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © SFoCM 2013 Abstract A standard reconstruction problem is how to discover a compact set from a noisy point cloud that approximates it. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the Hausdorff distance between two compact sets, for when certain offsets of these two sets are homotopic in terms of the absence of μ-critical points in an annular region. We reduce the problem of reconstructing a subset from a point cloud to the existence of a deformation retraction from the offset of the subset to the subset itself. The ambient space can be any Riemannian manifold but we focus on ambient manifolds which have nowhere negative curvature (this includes Euclidean space). We get an improvement on previous bounds for the case where the ambient space is Euclidean whenever μ≤0.945 (μ∈(0,1) by definition). In the process, we prove stability theorems for μ-critical points when the ambient space is a manifold. Distance function Surface and manifold reconstruction Deformation retraction Fibre bundle Enthalten in Foundations of computational mathematics Springer US, 2001 13(2013), 6 vom: 23. Okt., Seite 913-933 (DE-627)330598139 (DE-600)2050531-0 (DE-576)094479291 1615-3375 nnns volume:13 year:2013 number:6 day:23 month:10 pages:913-933 https://doi.org/10.1007/s10208-013-9176-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2088 GBV_ILN_4277 31.76$jNumerische Mathematik VZ 106408194 (DE-625)106408194 54.10$jTheoretische Informatik VZ 106418815 (DE-625)106418815 AR 13 2013 6 23 10 913-933 |
| allfieldsSound |
10.1007/s10208-013-9176-6 doi (DE-627)OLC2057961826 (DE-He213)s10208-013-9176-6-p DE-627 ger DE-627 rakwb eng 510 004 VZ 510 VZ 17,1 ssgn 31.76$jNumerische Mathematik bkl 54.10$jTheoretische Informatik bkl Turner, Katharine verfasserin aut Cone Fields and Topological Sampling in Manifolds with Bounded Curvature 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © SFoCM 2013 Abstract A standard reconstruction problem is how to discover a compact set from a noisy point cloud that approximates it. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the Hausdorff distance between two compact sets, for when certain offsets of these two sets are homotopic in terms of the absence of μ-critical points in an annular region. We reduce the problem of reconstructing a subset from a point cloud to the existence of a deformation retraction from the offset of the subset to the subset itself. The ambient space can be any Riemannian manifold but we focus on ambient manifolds which have nowhere negative curvature (this includes Euclidean space). We get an improvement on previous bounds for the case where the ambient space is Euclidean whenever μ≤0.945 (μ∈(0,1) by definition). In the process, we prove stability theorems for μ-critical points when the ambient space is a manifold. Distance function Surface and manifold reconstruction Deformation retraction Fibre bundle Enthalten in Foundations of computational mathematics Springer US, 2001 13(2013), 6 vom: 23. Okt., Seite 913-933 (DE-627)330598139 (DE-600)2050531-0 (DE-576)094479291 1615-3375 nnns volume:13 year:2013 number:6 day:23 month:10 pages:913-933 https://doi.org/10.1007/s10208-013-9176-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2088 GBV_ILN_4277 31.76$jNumerische Mathematik VZ 106408194 (DE-625)106408194 54.10$jTheoretische Informatik VZ 106418815 (DE-625)106418815 AR 13 2013 6 23 10 913-933 |
| language |
English |
| source |
Enthalten in Foundations of computational mathematics 13(2013), 6 vom: 23. Okt., Seite 913-933 volume:13 year:2013 number:6 day:23 month:10 pages:913-933 |
| sourceStr |
Enthalten in Foundations of computational mathematics 13(2013), 6 vom: 23. Okt., Seite 913-933 volume:13 year:2013 number:6 day:23 month:10 pages:913-933 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| topic_facet |
Distance function Surface and manifold reconstruction Deformation retraction Fibre bundle |
| dewey-raw |
510 |
| isfreeaccess_bool |
false |
| container_title |
Foundations of computational mathematics |
| authorswithroles_txt_mv |
Turner, Katharine @@aut@@ |
| publishDateDaySort_date |
2013-10-23T00:00:00Z |
| hierarchy_top_id |
330598139 |
| dewey-sort |
3510 |
| id |
OLC2057961826 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2057961826</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230502175656.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2013 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10208-013-9176-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2057961826</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10208-013-9176-6-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="a">004</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.76$jNumerische Mathematik</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">54.10$jTheoretische Informatik</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Turner, Katharine</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Cone Fields and Topological Sampling in Manifolds with Bounded Curvature</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2013</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© SFoCM 2013</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract A standard reconstruction problem is how to discover a compact set from a noisy point cloud that approximates it. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the Hausdorff distance between two compact sets, for when certain offsets of these two sets are homotopic in terms of the absence of μ-critical points in an annular region. We reduce the problem of reconstructing a subset from a point cloud to the existence of a deformation retraction from the offset of the subset to the subset itself. The ambient space can be any Riemannian manifold but we focus on ambient manifolds which have nowhere negative curvature (this includes Euclidean space). We get an improvement on previous bounds for the case where the ambient space is Euclidean whenever μ≤0.945 (μ∈(0,1) by definition). In the process, we prove stability theorems for μ-critical points when the ambient space is a manifold.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Distance function</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Surface and manifold reconstruction</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Deformation retraction</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fibre bundle</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Foundations of computational mathematics</subfield><subfield code="d">Springer US, 2001</subfield><subfield code="g">13(2013), 6 vom: 23. Okt., Seite 913-933</subfield><subfield code="w">(DE-627)330598139</subfield><subfield code="w">(DE-600)2050531-0</subfield><subfield code="w">(DE-576)094479291</subfield><subfield code="x">1615-3375</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:13</subfield><subfield code="g">year:2013</subfield><subfield code="g">number:6</subfield><subfield code="g">day:23</subfield><subfield code="g">month:10</subfield><subfield code="g">pages:913-933</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s10208-013-9176-6</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2002</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4277</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">31.76$jNumerische Mathematik</subfield><subfield code="q">VZ</subfield><subfield code="0">106408194</subfield><subfield code="0">(DE-625)106408194</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">54.10$jTheoretische Informatik</subfield><subfield code="q">VZ</subfield><subfield code="0">106418815</subfield><subfield code="0">(DE-625)106418815</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">13</subfield><subfield code="j">2013</subfield><subfield code="e">6</subfield><subfield code="b">23</subfield><subfield code="c">10</subfield><subfield code="h">913-933</subfield></datafield></record></collection>
|
| author |
Turner, Katharine |
| spellingShingle |
Turner, Katharine ddc 510 ssgn 17,1 bkl 31.76$jNumerische Mathematik bkl 54.10$jTheoretische Informatik misc Distance function misc Surface and manifold reconstruction misc Deformation retraction misc Fibre bundle Cone Fields and Topological Sampling in Manifolds with Bounded Curvature |
| authorStr |
Turner, Katharine |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)330598139 |
| format |
Article |
| dewey-ones |
510 - Mathematics 004 - Data processing & computer science |
| delete_txt_mv |
keep |
| author_role |
aut |
| collection |
OLC |
| remote_str |
false |
| illustrated |
Not Illustrated |
| issn |
1615-3375 |
| topic_title |
510 004 VZ 510 VZ 17,1 ssgn 31.76$jNumerische Mathematik bkl 54.10$jTheoretische Informatik bkl Cone Fields and Topological Sampling in Manifolds with Bounded Curvature Distance function Surface and manifold reconstruction Deformation retraction Fibre bundle |
| topic |
ddc 510 ssgn 17,1 bkl 31.76$jNumerische Mathematik bkl 54.10$jTheoretische Informatik misc Distance function misc Surface and manifold reconstruction misc Deformation retraction misc Fibre bundle |
| topic_unstemmed |
ddc 510 ssgn 17,1 bkl 31.76$jNumerische Mathematik bkl 54.10$jTheoretische Informatik misc Distance function misc Surface and manifold reconstruction misc Deformation retraction misc Fibre bundle |
| topic_browse |
ddc 510 ssgn 17,1 bkl 31.76$jNumerische Mathematik bkl 54.10$jTheoretische Informatik misc Distance function misc Surface and manifold reconstruction misc Deformation retraction misc Fibre bundle |
| format_facet |
Aufsätze Gedruckte Aufsätze |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
nc |
| hierarchy_parent_title |
Foundations of computational mathematics |
| hierarchy_parent_id |
330598139 |
| dewey-tens |
510 - Mathematics 000 - Computer science, knowledge & systems |
| hierarchy_top_title |
Foundations of computational mathematics |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)330598139 (DE-600)2050531-0 (DE-576)094479291 |
| title |
Cone Fields and Topological Sampling in Manifolds with Bounded Curvature |
| ctrlnum |
(DE-627)OLC2057961826 (DE-He213)s10208-013-9176-6-p |
| title_full |
Cone Fields and Topological Sampling in Manifolds with Bounded Curvature |
| author_sort |
Turner, Katharine |
| journal |
Foundations of computational mathematics |
| journalStr |
Foundations of computational mathematics |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
500 - Science 000 - Computer science, information & general works |
| recordtype |
marc |
| publishDateSort |
2013 |
| contenttype_str_mv |
txt |
| container_start_page |
913 |
| author_browse |
Turner, Katharine |
| container_volume |
13 |
| class |
510 004 VZ 510 VZ 17,1 ssgn 31.76$jNumerische Mathematik bkl 54.10$jTheoretische Informatik bkl |
| format_se |
Aufsätze |
| author-letter |
Turner, Katharine |
| doi_str_mv |
10.1007/s10208-013-9176-6 |
| normlink |
106408194 106418815 |
| normlink_prefix_str_mv |
106408194 (DE-625)106408194 106418815 (DE-625)106418815 |
| dewey-full |
510 004 |
| title_sort |
cone fields and topological sampling in manifolds with bounded curvature |
| title_auth |
Cone Fields and Topological Sampling in Manifolds with Bounded Curvature |
| abstract |
Abstract A standard reconstruction problem is how to discover a compact set from a noisy point cloud that approximates it. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the Hausdorff distance between two compact sets, for when certain offsets of these two sets are homotopic in terms of the absence of μ-critical points in an annular region. We reduce the problem of reconstructing a subset from a point cloud to the existence of a deformation retraction from the offset of the subset to the subset itself. The ambient space can be any Riemannian manifold but we focus on ambient manifolds which have nowhere negative curvature (this includes Euclidean space). We get an improvement on previous bounds for the case where the ambient space is Euclidean whenever μ≤0.945 (μ∈(0,1) by definition). In the process, we prove stability theorems for μ-critical points when the ambient space is a manifold. © SFoCM 2013 |
| abstractGer |
Abstract A standard reconstruction problem is how to discover a compact set from a noisy point cloud that approximates it. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the Hausdorff distance between two compact sets, for when certain offsets of these two sets are homotopic in terms of the absence of μ-critical points in an annular region. We reduce the problem of reconstructing a subset from a point cloud to the existence of a deformation retraction from the offset of the subset to the subset itself. The ambient space can be any Riemannian manifold but we focus on ambient manifolds which have nowhere negative curvature (this includes Euclidean space). We get an improvement on previous bounds for the case where the ambient space is Euclidean whenever μ≤0.945 (μ∈(0,1) by definition). In the process, we prove stability theorems for μ-critical points when the ambient space is a manifold. © SFoCM 2013 |
| abstract_unstemmed |
Abstract A standard reconstruction problem is how to discover a compact set from a noisy point cloud that approximates it. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the Hausdorff distance between two compact sets, for when certain offsets of these two sets are homotopic in terms of the absence of μ-critical points in an annular region. We reduce the problem of reconstructing a subset from a point cloud to the existence of a deformation retraction from the offset of the subset to the subset itself. The ambient space can be any Riemannian manifold but we focus on ambient manifolds which have nowhere negative curvature (this includes Euclidean space). We get an improvement on previous bounds for the case where the ambient space is Euclidean whenever μ≤0.945 (μ∈(0,1) by definition). In the process, we prove stability theorems for μ-critical points when the ambient space is a manifold. © SFoCM 2013 |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2088 GBV_ILN_4277 |
| container_issue |
6 |
| title_short |
Cone Fields and Topological Sampling in Manifolds with Bounded Curvature |
| url |
https://doi.org/10.1007/s10208-013-9176-6 |
| remote_bool |
false |
| ppnlink |
330598139 |
| mediatype_str_mv |
n |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| doi_str |
10.1007/s10208-013-9176-6 |
| up_date |
2024-07-03T17:02:57.593Z |
| _version_ |
1803578169197854720 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2057961826</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230502175656.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2013 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10208-013-9176-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2057961826</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10208-013-9176-6-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="a">004</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.76$jNumerische Mathematik</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">54.10$jTheoretische Informatik</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Turner, Katharine</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Cone Fields and Topological Sampling in Manifolds with Bounded Curvature</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2013</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© SFoCM 2013</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract A standard reconstruction problem is how to discover a compact set from a noisy point cloud that approximates it. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the Hausdorff distance between two compact sets, for when certain offsets of these two sets are homotopic in terms of the absence of μ-critical points in an annular region. We reduce the problem of reconstructing a subset from a point cloud to the existence of a deformation retraction from the offset of the subset to the subset itself. The ambient space can be any Riemannian manifold but we focus on ambient manifolds which have nowhere negative curvature (this includes Euclidean space). We get an improvement on previous bounds for the case where the ambient space is Euclidean whenever μ≤0.945 (μ∈(0,1) by definition). In the process, we prove stability theorems for μ-critical points when the ambient space is a manifold.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Distance function</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Surface and manifold reconstruction</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Deformation retraction</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fibre bundle</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Foundations of computational mathematics</subfield><subfield code="d">Springer US, 2001</subfield><subfield code="g">13(2013), 6 vom: 23. Okt., Seite 913-933</subfield><subfield code="w">(DE-627)330598139</subfield><subfield code="w">(DE-600)2050531-0</subfield><subfield code="w">(DE-576)094479291</subfield><subfield code="x">1615-3375</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:13</subfield><subfield code="g">year:2013</subfield><subfield code="g">number:6</subfield><subfield code="g">day:23</subfield><subfield code="g">month:10</subfield><subfield code="g">pages:913-933</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s10208-013-9176-6</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2002</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4277</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">31.76$jNumerische Mathematik</subfield><subfield code="q">VZ</subfield><subfield code="0">106408194</subfield><subfield code="0">(DE-625)106408194</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">54.10$jTheoretische Informatik</subfield><subfield code="q">VZ</subfield><subfield code="0">106418815</subfield><subfield code="0">(DE-625)106418815</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">13</subfield><subfield code="j">2013</subfield><subfield code="e">6</subfield><subfield code="b">23</subfield><subfield code="c">10</subfield><subfield code="h">913-933</subfield></datafield></record></collection>
|
| score |
7.3985367 |