The GeoMap representation: on topologically correct sub-pixel image analysis
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| Format: | Abschlussarbeit Buch |
| Sprache: | German |
| Veröffentlicht: |
Heidelberg
Akadem. Verl.-Ges.
2009
|
| Schriftenreihe: | Dissertationen zur künstlichen Intelligenz
323 |
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| 020 | |a 9783898383233 |9 978-3-89838-323-3 | ||
| 020 | |a 9781586039813 |9 978-1-58603-981-3 | ||
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| 100 | 1 | |a Meine, Hans |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The GeoMap representation: on topologically correct sub-pixel image analysis |c Hans Meine |
| 264 | 1 | |a Heidelberg |b Akadem. Verl.-Ges. |c 2009 | |
| 300 | |a XVI, 220 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Dissertationen zur künstlichen Intelligenz |v 323 | |
| 502 | |a Zugl.: Hamburg, Univ., Diss., 2008 | ||
| 650 | 4 | |a Bildsegmentierung | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Geospatial data |x Data processing | |
| 650 | 4 | |a Image analysis |x Data processing | |
| 650 | 0 | 7 | |a Bildsegmentierung |0 (DE-588)4145448-0 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Bildsegmentierung |0 (DE-588)4145448-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Dissertationen zur künstlichen Intelligenz |v 323 |w (DE-604)BV005345280 |9 323 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017141605&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017141605&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017141605&sequence=000007&line_number=0003&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-017141605 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 DAT 700d 2001 A 894 |
|---|---|
| DE-BY-TUM_katkey | 1678610 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010146253 |
| _version_ | 1820896103820689408 |
| adam_text | Contents
1 Introduction 1
1.1 Structure of the Thesis............................................... 5
1.2 Related Publications.................................................... 5
2 Previous Work 7
2.1 Topological Formalisms.................................................. 7
2.1.1 Region Adjacency Graphs.......................................... 8
2.1.2 Cellular Complexes............................................. 9
2.1.3 Dual Image Graphs .............................................. 10
2.1.4 Combinatorial Maps............................................ 11
2.1.5 Extended Planar Maps............................................ 14
2.1.6 Comparison of Topological Formalisms.......................... 16
2.2 Topology in Digital Images............................................. 17
2.2.1 Inter-pixel Boundaries........................................ 17
2.2.2 8-Connected Pixel Boundaries.................................... 19
2.2.3 Summary......................................................... 21
2.3 Hierarchical Image Analysis............................................ 21
2.3.1 Regular Pyramids................................................ 22
2.3.2 Irregular Pyramids.............................................. 24
3 The GeoMap Representation 27
3.1 Combining Topology and Geometry ....................................... 27
3.1.1 Requirement Analysis.......................................... 28
3.1.2 The GeoMap: A Unified Representation............................ 29
3.2 Modifying GeoMaps...................................................... 31
3.2.1 Euler Operators ................................................ 31
3.2.2 Using a Small Basis of Elementary Operations.................... 32
3.2.3 More Complex Composed Operations................................ 37
3.2.4 Managing Statistics on Cells ................................. 40
3.2.5 GeoMap Pyramids................................................. 43
3.3 Pixel-based Realization ............................................... 47
3.3.1 Cell Image Representation....................................... 47
3.4 Sub-pixel Representation.............................................. 49
3.4.1 Structure of the GeoMap......................................... 51
3.4.2 Inspection of the Topology ..................................... 52
3.4.3 Inspection of the Geometry...................................... 54
xiii
Contents
3.4.4 Modifications via Euler Operations................................ 59
3.4.5 Initializing a Sub-pixel GeoMap................................... 64
3.5 Conclusions.............................................................. 67
4 Initial GeoMap Segmentations 69
4.1 Geo Maps from Label Images............................................. 69
4.1.1 Mid-crack Maps.................................................. 72
4.1.2 Euclidean Paths................................................... 73
4.2 Level Contours........................................................ 75
4.2.1 Pixel-based Level Lines........................................... 77
4.2.2 Marching Squares ................................................. 78
4.2.3 Predictor-Corrector Methods....................................... 81
4.2.4 Conclusion........................................................ 83
4.3 Watershed Segmentations.................................................. 85
4.3.1 Pixel-based Watersheds............................................ 86
4.3.2 Subpixel Watersheds............................................... 88
4.4 Conclusions..............................................................107
5 Tools within the GeoMap Framework 111
5.1 Image Segmentation and Relevance Filtering...............................Ill
5.1.1 The Superpixel Approach...........................................112
5.1.2 Relevance Measures................................................114
5.1.3 Boundary Indicators...............................................115
5.1.4 Edge Significance from Boundary Indicators........................119
5.1.5 Region-based Edge Significance....................................122
5.1.6 Geometric Significance Measures...................................128
5.1.7 Relations between Cost Measures...................................132
5.1.8 Conclusions.......................................................133
5.2 Geo MAP-based Segmentation Algorithms....................................134
5.2.1 Seeded Region Growing.............................................134
5.2.2 Automatic Region Merging..........................................137
5.2.3 Waterfall.........................................................144
5.2.4 Intelligent Scissors..............................................148
5.2.5 Active Paintbrush............................................... 153
5.2.6 Conclusions..................................................... 155
5.3 Integrated Interactive Environment.......................................157
5.3.1 Managing a History of Euler Operations............................157
5.3.2 Separating Manual and Automatic Actions . ........................163
5.3.3 Edge Protection ..................................................166
5.3.4 Controlling Automatic Methods with a Slider.......................167
5.3.5 Conclusions.......................................................169
5.4 Triangulation............................................................170
5.5 Skeletonization..........................................................174
5.5.1 Chordal Axis Transform............................................174
5.5.2 Rectifications....................................................178
xiv
Contents
5.5.3 Skeleton Pruning................................................178
5.6 Boundary Reconstruction using Alpha Shapes........................... 180
5.6.1 Motivation: Limitations of Superpixel-based Image Segmentation . 181
5.6.2 Computing Alpha Shapes of an Edgel Set..........................183
5.6.3 (a,/?)-Boundary Reconstruction .................................185
5.6.4 Recovering a Thin Boundary......................................190
5.6.5 Handling 2D Image Features......................................191
5.6.6 Conclusions.....................................................195
5.7 Conclusions............................................................196
6 Conclusions and Outlook 199
6.1 Contributions .... 200
6.2 Future Work ......................................................203
Bibliography 209
xv
This thesis introduces a new, unified representation (termed GeoMap)
for capturing both the geometrical and the topological aspects of a
segmentation result. This representation is not static, but suitable for
all intermediate working states of a segmentation process, and serves
as a common representation for a multitude of algorithms. Throughout
a segmentation process, our GeoMap maintains the consistency
between the topological and geometrical information and the duality of
regions and boundaries.
Our main contribution is a new, sub-pixel precise GeoMap realization
and a corresponding watershed segmentation algorithm, which we use
to produce an oversegmentation into sub-pixel precise superpixels
(data-dependent picture elements that are independent of the
sampling grid).
Furthermore, we introduce an integrated environment for image
segmentation based on a relevance filtering process that reduces the
number of irrelevant boundaries within a GeoMap using a combination
of region- or boundary- based, automatic or (semi-)interactive
segmentation tools in order to produce the final result.
Finally, we show that since our new sub-pixel GeoMap does not suffer
from certain limitations imposed on previous representations by the
pixel grid, it becomes flexible enough to be suitable for applications
beyond image segmentation, e.g. triangulations, skeletonization, or a
new boundary reconstruction method based on a-shapes.
Contents
1 Introduction 1
1.1 Structure of the Thesis................................................. 5
1.2 Related Publications.................................................... 5
2 Previous Work 7
2.1 Topological Formalisms.................................................. 7
2.1.1 Region Adjacency Graphs.......................................... 8
2.1.2 Cellular Complexes............................................... 9
2.1.3 Dual Image Graphs .............................................. 10
2.1.4 Combinatorial Maps.............................................. 11
2.1.5 Extended Planar Maps............................................ 14
2.1.6 Comparison of Topological Formalisms............................ 16
2.2 Topology in Digital Images............................................. 17
2.2.1 Inter-pixel Boundaries.......................................... 17
2.2.2 8-Connected Pixel Boundaries.................................... 19
2.2.3 Summary......................................................... 21
2.3 Hierarchical Image Analysis............................................ 21
2.3.1 Regular Pyramids................................................ 22
2.3.2 Irregular Pyramids.............................................. 24
3 The GeoMap Representation 27
3.1 Combining Topology and Geometry ....................................... 27
3.1.1 Requirement Analysis............................................ 28
3.1.2 The GeoMap: A Unified Representation............................ 29
3.2 Modifying GeoMaps...................................................... 31
3.2.1 Euler Operators ................................................ 31
3.2.2 Using a Small Basis of Elementary Operations.................... 32
3.2.3 More Complex Composed Operations................................ 37
3.2.4 Managing Statistics on Cells ................................... 40
3.2.5 GeoMap Pyramids................................................. 43
3.3 Pixel-based Realization ............................................... 47
3.3.1 Cell Image Representation....................................... 47
3.4 Sub-pixel Representation............................................... 49
3.4.1 Structure of the GeoMap......................................... 51
3.4.2 Inspection of the Topology...................................... 52
3.4.3 Inspection of the Geometry . ................................... 54
Contents
by
3.4.4 Modifications via Euler Operations............................. ^
3.4.5 Initializing a Sub-pixel ......................................... ^
3.5 Conclusions...........................................................
69
4 Initial GeoMap Segmentations 6g
4.1 GeoMaps from Label Images................................................ ^
4.1.1 Mid-crack Maps ................................................
4.1.2 Euclidean Paths................................................
4.2 Level Contours........................................................... ^
4.2.1 Pixel-based Level Lines.......................................... «g
4.2.2 Marching Squares ................................................. ^
4.2.3 Predictor-Corrector Methods....................................... ^
4.2.4 Conclusion........................................................ ^
4.3 Watershed Segmentations................................................. «g
4.3.1 Pixel-based Watersheds........................................... gg
4.3.2 Subpixel Watersheds................................................^
4.4 Conclusions...........................................................
5 Tools within the GeoMap Framework ^
5.1 Image Segmentation and Relevance Filtering .......................* ^
5.1.1 The Superpixel Approach............................................^
5.1.2 Relevance Measures.................................................^
5.1.3 Boundary Indicators...........................................
5.1.4 Edge Significance from Boundary Indicators....................* ^
5.1.5 Region-based Edge Significance...........................•••***
5.1.6 Geometric Significance Measures................................^
5.1.7 Relations between Cost Measures...............................‘
5.1.8 Conclusions...................................................‘ ^
5.2 GEoMAP-based Segmentation Algorithms..............................* * * ^
5.2.1 Seeded Region Growing......................................... ^
5.2.2 Automatic Region Merging......................................* ^
5.2.3 Waterfall..........................................................^
148
5.2.4 Intelligent Scissors...........................................
5.2.5 Active Paintbrush..............................................^
5.2.6 Conclusions...............................................* • * * „
157
5.3 Integrated Interactive Environment...................................* *
157
5.3.1 Managing a History of Euler Operations ........................
5.3.2 Separating Manual and Automatic Actions......................* *
5.3.3 Edge Protection...............................................* ^
5.3.4 Controlling Automatic Methods with a Slider....................A
5.3.5 Conclusions........................................................^
5.4 Triangulation........................................................* ^
5.5 Skeletonization.......................................................^
5.5.1 Chordal Axis Transform.............................................^
5.5.2 Rectifications................................................• 1^8
Contents
5.5.3 Skeleton Pruning................................................178
5.6 Boundary Reconstruction using Alpha Shapes............180
5.6.1 Motivation: Limitations of Superpixel-based Image Segmentation . 181
5.6.2 Computing Alpha Shapes of an Edgel Set..........................183
5.6.3 (a,/3)-Boundary Reconstruction .................................185
5.6.4 Recovering a Thin Boundary......................................190
5.6.5 Handling 2D Image Features......................................191
5.6.6 Conclusions.....................................................195
5.7 Conclusions............................................................196
6 Conclusions and Outlook 199
6.1 Contributions..........................................................200
6.2 Future Work............................................................203
Bibliography 209
This thesis introduces a new, unified representation (termed GeoMap)
for capturing both the geometrical and the topological aspects of a
segmentation result. This representation is not static, but suitable for
all intermediate working states of a segmentation process, and serves
as a common representation for a multitude of algorithms. Throughout
a segmentation process, our GeoMap maintains the consistency
between the topological and geometrical information and the duality of
regions and boundaries.
Our main contribution is a new, sub-pixel precise GeoMap realization
and a corresponding watershed segmentation algorithm, which we use
to produce an oversegmentation into sub-pixel precise superpixels
(data-dependent picture elements that are independent of the
sampling grid).
Furthermore, we introduce an integrated environment for image
segmentation based on a relevance filtering process that reduces the
number of irrelevant boundaries within a GeoMap using a combination
of region- or boundary- based, automatic or (semi-)interactive
segmentation tools in order to produce the final result.
Finally, we show that since our new sub-pixel GeoMap does not suffer
from certain limitations imposed on previous representations by the
pixel grid, it becomes flexible enough to be suitable for applications
beyond image segmentation, e.g. triangulations, skeletonization, or a
new boundary reconstruction method based on cr-shapes.
|
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| author_facet | Meine, Hans |
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| classification_rvk | ST 330 |
| classification_tum | DAT 700d DAT 764d GEO 007d |
| ctrlnum | (OCoLC)313654135 (DE-599)BSZ303123710 |
| discipline | Informatik Geographie |
| format | Thesis Book |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV035337253 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T21:26:50Z |
| institution | BVB |
| isbn | 9783898383233 9781586039813 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017141605 |
| oclc_num | 313654135 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-188 DE-355 DE-BY-UBR |
| owner_facet | DE-91G DE-BY-TUM DE-188 DE-355 DE-BY-UBR |
| physical | XVI, 220 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Akadem. Verl.-Ges. |
| record_format | marc |
| series | Dissertationen zur künstlichen Intelligenz |
| series2 | Dissertationen zur künstlichen Intelligenz |
| spellingShingle | Meine, Hans The GeoMap representation: on topologically correct sub-pixel image analysis Dissertationen zur künstlichen Intelligenz Bildsegmentierung Datenverarbeitung Geospatial data Data processing Image analysis Data processing Bildsegmentierung (DE-588)4145448-0 gnd |
| subject_GND | (DE-588)4145448-0 (DE-588)4113937-9 |
| title | The GeoMap representation: on topologically correct sub-pixel image analysis |
| title_auth | The GeoMap representation: on topologically correct sub-pixel image analysis |
| title_exact_search | The GeoMap representation: on topologically correct sub-pixel image analysis |
| title_full | The GeoMap representation: on topologically correct sub-pixel image analysis Hans Meine |
| title_fullStr | The GeoMap representation: on topologically correct sub-pixel image analysis Hans Meine |
| title_full_unstemmed | The GeoMap representation: on topologically correct sub-pixel image analysis Hans Meine |
| title_short | The GeoMap representation: on topologically correct sub-pixel image analysis |
| title_sort | the geomap representation on topologically correct sub pixel image analysis |
| topic | Bildsegmentierung Datenverarbeitung Geospatial data Data processing Image analysis Data processing Bildsegmentierung (DE-588)4145448-0 gnd |
| topic_facet | Bildsegmentierung Datenverarbeitung Geospatial data Data processing Image analysis Data processing Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017141605&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017141605&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017141605&sequence=000007&line_number=0003&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017141605&sequence=000008&line_number=0004&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005345280 |
| work_keys_str_mv | AT meinehans thegeomaprepresentationontopologicallycorrectsubpixelimageanalysis |