Beyond the Hough transform: further properties of the R, Theta mapping and their applications
Abstract: "The Hough transform is a standard technique for finding features such as lines in images. Typically, points or edgels [sic] are mapped into a partitioned parameter or Hough space as individual votes where peaks denote the feature of interest. The standard mapping used for line detect...
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Edinburgh
1996
|
| Schriftenreihe: | University <Edinburgh> / Department of Artificial Intelligence: DAI research paper
785 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "The Hough transform is a standard technique for finding features such as lines in images. Typically, points or edgels [sic] are mapped into a partitioned parameter or Hough space as individual votes where peaks denote the feature of interest. The standard mapping used for line detection is the R[theta] mapping and the key property the Hough transform exploits is that lines in the image map to points in Hough space. In this paper we introduce and explore three further properties of the R[theta] mapping and suggest applications for them. Firstly, we show that points in Hough space with maximal R for any value of [theta] are on the convex hull of the object in image space. It is shown that approximate hulls of 2D and 3D hulls of objects can be constructed in linear time using this approach. Secondly, it is shown that a simple relationship exists between the occluding contour of an object and the R[theta] mapping and that this could in principle be used to generate approximate aspect graphs of objects whose geometry was known. Thirdly, it is shown that antipodal points on object boundaries, (which are optimal robot grasp points), can be found by translation and reflection of the R[theta] representation. In addition we show the relationship between the R[theta] mapping used in the Hough transform and the classical mathematical theory of duals. We use this analysis to prove formally stated properties of the R[theta] mapping from image space to Hough space and in particular the relationship to the convex hull." |
| Beschreibung: | 15 S. |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV011049467 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 961111s1996 |||| 00||| engod | ||
| 035 | |a (OCoLC)35590598 | ||
| 035 | |a (DE-599)BVBBV011049467 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G | ||
| 245 | 1 | 0 | |a Beyond the Hough transform |b further properties of the R, Theta mapping and their applications |c Wright, M. ... |
| 264 | 1 | |a Edinburgh |c 1996 | |
| 300 | |a 15 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a University <Edinburgh> / Department of Artificial Intelligence: DAI research paper |v 785 | |
| 520 | 3 | |a Abstract: "The Hough transform is a standard technique for finding features such as lines in images. Typically, points or edgels [sic] are mapped into a partitioned parameter or Hough space as individual votes where peaks denote the feature of interest. The standard mapping used for line detection is the R[theta] mapping and the key property the Hough transform exploits is that lines in the image map to points in Hough space. In this paper we introduce and explore three further properties of the R[theta] mapping and suggest applications for them. Firstly, we show that points in Hough space with maximal R for any value of [theta] are on the convex hull of the object in image space. It is shown that approximate hulls of 2D and 3D hulls of objects can be constructed in linear time using this approach. Secondly, it is shown that a simple relationship exists between the occluding contour of an object and the R[theta] mapping and that this could in principle be used to generate approximate aspect graphs of objects whose geometry was known. Thirdly, it is shown that antipodal points on object boundaries, (which are optimal robot grasp points), can be found by translation and reflection of the R[theta] representation. In addition we show the relationship between the R[theta] mapping used in the Hough transform and the classical mathematical theory of duals. We use this analysis to prove formally stated properties of the R[theta] mapping from image space to Hough space and in particular the relationship to the convex hull." | |
| 650 | 7 | |a Pattern recognition, image processing and remote sensing |2 sigle | |
| 650 | 4 | |a Computer vision | |
| 650 | 4 | |a Hough functions | |
| 650 | 4 | |a Transformations (Mathematics) | |
| 700 | 1 | |a Wright, M. |e Sonstige |4 oth | |
| 810 | 2 | |a Department of Artificial Intelligence: DAI research paper |t University <Edinburgh> |v 785 |w (DE-604)BV010450646 |9 785 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007399931 | ||
Datensatz im Suchindex
| _version_ | 1804125539111272448 |
|---|---|
| any_adam_object | |
| building | Verbundindex |
| bvnumber | BV011049467 |
| ctrlnum | (OCoLC)35590598 (DE-599)BVBBV011049467 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02661nam a2200325 cb4500</leader><controlfield tag="001">BV011049467</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">961111s1996 |||| 00||| engod</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)35590598</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV011049467</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Beyond the Hough transform</subfield><subfield code="b">further properties of the R, Theta mapping and their applications</subfield><subfield code="c">Wright, M. ...</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Edinburgh</subfield><subfield code="c">1996</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">15 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">University <Edinburgh> / Department of Artificial Intelligence: DAI research paper</subfield><subfield code="v">785</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">Abstract: "The Hough transform is a standard technique for finding features such as lines in images. Typically, points or edgels [sic] are mapped into a partitioned parameter or Hough space as individual votes where peaks denote the feature of interest. The standard mapping used for line detection is the R[theta] mapping and the key property the Hough transform exploits is that lines in the image map to points in Hough space. In this paper we introduce and explore three further properties of the R[theta] mapping and suggest applications for them. Firstly, we show that points in Hough space with maximal R for any value of [theta] are on the convex hull of the object in image space. It is shown that approximate hulls of 2D and 3D hulls of objects can be constructed in linear time using this approach. Secondly, it is shown that a simple relationship exists between the occluding contour of an object and the R[theta] mapping and that this could in principle be used to generate approximate aspect graphs of objects whose geometry was known. Thirdly, it is shown that antipodal points on object boundaries, (which are optimal robot grasp points), can be found by translation and reflection of the R[theta] representation. In addition we show the relationship between the R[theta] mapping used in the Hough transform and the classical mathematical theory of duals. We use this analysis to prove formally stated properties of the R[theta] mapping from image space to Hough space and in particular the relationship to the convex hull."</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Pattern recognition, image processing and remote sensing</subfield><subfield code="2">sigle</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computer vision</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hough functions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Transformations (Mathematics)</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wright, M.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="810" ind1="2" ind2=" "><subfield code="a">Department of Artificial Intelligence: DAI research paper</subfield><subfield code="t">University <Edinburgh></subfield><subfield code="v">785</subfield><subfield code="w">(DE-604)BV010450646</subfield><subfield code="9">785</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007399931</subfield></datafield></record></collection> |
| id | DE-604.BV011049467 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:03:10Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007399931 |
| oclc_num | 35590598 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | 15 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| record_format | marc |
| series2 | University <Edinburgh> / Department of Artificial Intelligence: DAI research paper |
| spelling | Beyond the Hough transform further properties of the R, Theta mapping and their applications Wright, M. ... Edinburgh 1996 15 S. txt rdacontent n rdamedia nc rdacarrier University <Edinburgh> / Department of Artificial Intelligence: DAI research paper 785 Abstract: "The Hough transform is a standard technique for finding features such as lines in images. Typically, points or edgels [sic] are mapped into a partitioned parameter or Hough space as individual votes where peaks denote the feature of interest. The standard mapping used for line detection is the R[theta] mapping and the key property the Hough transform exploits is that lines in the image map to points in Hough space. In this paper we introduce and explore three further properties of the R[theta] mapping and suggest applications for them. Firstly, we show that points in Hough space with maximal R for any value of [theta] are on the convex hull of the object in image space. It is shown that approximate hulls of 2D and 3D hulls of objects can be constructed in linear time using this approach. Secondly, it is shown that a simple relationship exists between the occluding contour of an object and the R[theta] mapping and that this could in principle be used to generate approximate aspect graphs of objects whose geometry was known. Thirdly, it is shown that antipodal points on object boundaries, (which are optimal robot grasp points), can be found by translation and reflection of the R[theta] representation. In addition we show the relationship between the R[theta] mapping used in the Hough transform and the classical mathematical theory of duals. We use this analysis to prove formally stated properties of the R[theta] mapping from image space to Hough space and in particular the relationship to the convex hull." Pattern recognition, image processing and remote sensing sigle Computer vision Hough functions Transformations (Mathematics) Wright, M. Sonstige oth Department of Artificial Intelligence: DAI research paper University <Edinburgh> 785 (DE-604)BV010450646 785 |
| spellingShingle | Beyond the Hough transform further properties of the R, Theta mapping and their applications Pattern recognition, image processing and remote sensing sigle Computer vision Hough functions Transformations (Mathematics) |
| title | Beyond the Hough transform further properties of the R, Theta mapping and their applications |
| title_auth | Beyond the Hough transform further properties of the R, Theta mapping and their applications |
| title_exact_search | Beyond the Hough transform further properties of the R, Theta mapping and their applications |
| title_full | Beyond the Hough transform further properties of the R, Theta mapping and their applications Wright, M. ... |
| title_fullStr | Beyond the Hough transform further properties of the R, Theta mapping and their applications Wright, M. ... |
| title_full_unstemmed | Beyond the Hough transform further properties of the R, Theta mapping and their applications Wright, M. ... |
| title_short | Beyond the Hough transform |
| title_sort | beyond the hough transform further properties of the r theta mapping and their applications |
| title_sub | further properties of the R, Theta mapping and their applications |
| topic | Pattern recognition, image processing and remote sensing sigle Computer vision Hough functions Transformations (Mathematics) |
| topic_facet | Pattern recognition, image processing and remote sensing Computer vision Hough functions Transformations (Mathematics) |
| volume_link | (DE-604)BV010450646 |
| work_keys_str_mv | AT wrightm beyondthehoughtransformfurtherpropertiesoftherthetamappingandtheirapplications |