On the Local Connectivity Number of Stationary Random Closed Sets View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2005

AUTHORS

Evgueni Spodarev , Volker Schmidt

ABSTRACT

Random closed sets (RACS) in the d—dimensional Euclidean space are considered, whose realizations belong to the extended convex ring. A family of nonparametric estimators is investigated for the simultaneous estimation of the vector of all specific Minkowski functionals (or, equivalently, the specific intrinsic volumes) of stationary RACS. The construction of these estimators is based on a representation formula for the expected local connectivity number of stationary RACS intersected with spheres, whose radii are small in comparison with the size of the whole sampling window. Asymptotic properties of the estimators are given for unboundedly increasing sampling windows. Numerical results are provided as well. More... »

PAGES

343-354

Book

TITLE

Mathematical Morphology: 40 Years On

ISBN

1-4020-3442-3

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/1-4020-3443-1_31

DOI

http://dx.doi.org/10.1007/1-4020-3443-1_31

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1020635014


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0104", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Statistics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Ulm", 
          "id": "https://www.grid.ac/institutes/grid.6582.9", 
          "name": [
            "Abteilung Stochastik, Universit\u00e4t Ulm, D-89069\u00a0Ulm, Germany"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Spodarev", 
        "givenName": "Evgueni", 
        "id": "sg:person.014255731127.42", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014255731127.42"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Ulm", 
          "id": "https://www.grid.ac/institutes/grid.6582.9", 
          "name": [
            "Abteilung Stochastik, Universit\u00e4t Ulm, D-89069\u00a0Ulm, Germany"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Schmidt", 
        "givenName": "Volker", 
        "id": "sg:person.01051347101.48", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01051347101.48"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1002/mana.200310032", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020550099"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1287/moor.25.3.485.12217", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064724250"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2005", 
    "datePublishedReg": "2005-01-01", 
    "description": "Random closed sets (RACS) in the d\u2014dimensional Euclidean space are considered, whose realizations belong to the extended convex ring. A family of nonparametric estimators is investigated for the simultaneous estimation of the vector of all specific Minkowski functionals (or, equivalently, the specific intrinsic volumes) of stationary RACS. The construction of these estimators is based on a representation formula for the expected local connectivity number of stationary RACS intersected with spheres, whose radii are small in comparison with the size of the whole sampling window. Asymptotic properties of the estimators are given for unboundedly increasing sampling windows. Numerical results are provided as well.", 
    "editor": [
      {
        "familyName": "Ronse", 
        "givenName": "Christian", 
        "type": "Person"
      }, 
      {
        "familyName": "Najman", 
        "givenName": "Laurent", 
        "type": "Person"
      }, 
      {
        "familyName": "Decenci\u00e8re", 
        "givenName": "Etienne", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/1-4020-3443-1_31", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "1-4020-3442-3"
      ], 
      "name": "Mathematical Morphology: 40 Years On", 
      "type": "Book"
    }, 
    "name": "On the Local Connectivity Number of Stationary Random Closed Sets", 
    "pagination": "343-354", 
    "productId": [
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/1-4020-3443-1_31"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "625262e9442376f03b83d2ddb1572f1d4881d471de99cf938482fb34ee54334d"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1020635014"
        ]
      }
    ], 
    "publisher": {
      "location": "Berlin/Heidelberg", 
      "name": "Springer-Verlag", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/1-4020-3443-1_31", 
      "https://app.dimensions.ai/details/publication/pub.1020635014"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-15T22:55", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8695_00000256.jsonl", 
    "type": "Chapter", 
    "url": "http://link.springer.com/10.1007/1-4020-3443-1_31"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/1-4020-3443-1_31'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/1-4020-3443-1_31'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/1-4020-3443-1_31'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/1-4020-3443-1_31'


 

This table displays all metadata directly associated to this object as RDF triples.

87 TRIPLES      23 PREDICATES      29 URIs      20 LITERALS      8 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/1-4020-3443-1_31 schema:about anzsrc-for:01
2 anzsrc-for:0104
3 schema:author N46a571b3d30d4ab4993bb434ac0aefb7
4 schema:citation https://doi.org/10.1002/mana.200310032
5 https://doi.org/10.1287/moor.25.3.485.12217
6 schema:datePublished 2005
7 schema:datePublishedReg 2005-01-01
8 schema:description Random closed sets (RACS) in the d—dimensional Euclidean space are considered, whose realizations belong to the extended convex ring. A family of nonparametric estimators is investigated for the simultaneous estimation of the vector of all specific Minkowski functionals (or, equivalently, the specific intrinsic volumes) of stationary RACS. The construction of these estimators is based on a representation formula for the expected local connectivity number of stationary RACS intersected with spheres, whose radii are small in comparison with the size of the whole sampling window. Asymptotic properties of the estimators are given for unboundedly increasing sampling windows. Numerical results are provided as well.
9 schema:editor Nce2b79b9ac6849928b06906e5bc941f3
10 schema:genre chapter
11 schema:inLanguage en
12 schema:isAccessibleForFree false
13 schema:isPartOf N0098d7a384fe44f9b249fd1962abac2b
14 schema:name On the Local Connectivity Number of Stationary Random Closed Sets
15 schema:pagination 343-354
16 schema:productId Na95f8afff0214cf4a544a65cce4fef55
17 Ne26a504fae3b433899875425cc763a5d
18 Nfaf03a17792d4f73b25a40be2c5e2a95
19 schema:publisher N28b9469361d04bdabb6f934541637471
20 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020635014
21 https://doi.org/10.1007/1-4020-3443-1_31
22 schema:sdDatePublished 2019-04-15T22:55
23 schema:sdLicense https://scigraph.springernature.com/explorer/license/
24 schema:sdPublisher N85844d1bb4894341894d84ef4af5ca91
25 schema:url http://link.springer.com/10.1007/1-4020-3443-1_31
26 sgo:license sg:explorer/license/
27 sgo:sdDataset chapters
28 rdf:type schema:Chapter
29 N0098d7a384fe44f9b249fd1962abac2b schema:isbn 1-4020-3442-3
30 schema:name Mathematical Morphology: 40 Years On
31 rdf:type schema:Book
32 N28b9469361d04bdabb6f934541637471 schema:location Berlin/Heidelberg
33 schema:name Springer-Verlag
34 rdf:type schema:Organisation
35 N46a571b3d30d4ab4993bb434ac0aefb7 rdf:first sg:person.014255731127.42
36 rdf:rest Ne424919f782e40229be2098a03ca8913
37 N4eb0cbf0d36e40e09fc8a4aa1da17acf schema:familyName Decencière
38 schema:givenName Etienne
39 rdf:type schema:Person
40 N85844d1bb4894341894d84ef4af5ca91 schema:name Springer Nature - SN SciGraph project
41 rdf:type schema:Organization
42 N979d056db9e044bbbf67a3bf9a821d15 rdf:first Ndfdd816b53ba470587a975deafbb9fe5
43 rdf:rest Nea3da507b2354fdd9cb1ffd169bf25b5
44 Na95f8afff0214cf4a544a65cce4fef55 schema:name doi
45 schema:value 10.1007/1-4020-3443-1_31
46 rdf:type schema:PropertyValue
47 Nc1c6d3d5bbc04cebb5bba60f615120a0 schema:familyName Ronse
48 schema:givenName Christian
49 rdf:type schema:Person
50 Nce2b79b9ac6849928b06906e5bc941f3 rdf:first Nc1c6d3d5bbc04cebb5bba60f615120a0
51 rdf:rest N979d056db9e044bbbf67a3bf9a821d15
52 Ndfdd816b53ba470587a975deafbb9fe5 schema:familyName Najman
53 schema:givenName Laurent
54 rdf:type schema:Person
55 Ne26a504fae3b433899875425cc763a5d schema:name readcube_id
56 schema:value 625262e9442376f03b83d2ddb1572f1d4881d471de99cf938482fb34ee54334d
57 rdf:type schema:PropertyValue
58 Ne424919f782e40229be2098a03ca8913 rdf:first sg:person.01051347101.48
59 rdf:rest rdf:nil
60 Nea3da507b2354fdd9cb1ffd169bf25b5 rdf:first N4eb0cbf0d36e40e09fc8a4aa1da17acf
61 rdf:rest rdf:nil
62 Nfaf03a17792d4f73b25a40be2c5e2a95 schema:name dimensions_id
63 schema:value pub.1020635014
64 rdf:type schema:PropertyValue
65 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
66 schema:name Mathematical Sciences
67 rdf:type schema:DefinedTerm
68 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
69 schema:name Statistics
70 rdf:type schema:DefinedTerm
71 sg:person.01051347101.48 schema:affiliation https://www.grid.ac/institutes/grid.6582.9
72 schema:familyName Schmidt
73 schema:givenName Volker
74 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01051347101.48
75 rdf:type schema:Person
76 sg:person.014255731127.42 schema:affiliation https://www.grid.ac/institutes/grid.6582.9
77 schema:familyName Spodarev
78 schema:givenName Evgueni
79 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014255731127.42
80 rdf:type schema:Person
81 https://doi.org/10.1002/mana.200310032 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020550099
82 rdf:type schema:CreativeWork
83 https://doi.org/10.1287/moor.25.3.485.12217 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064724250
84 rdf:type schema:CreativeWork
85 https://www.grid.ac/institutes/grid.6582.9 schema:alternateName University of Ulm
86 schema:name Abteilung Stochastik, Universität Ulm, D-89069 Ulm, Germany
87 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...