Computation of Lacunarity from Covariance of Spatial Binary Maps
We consider a spatial binary coverage map (binary pixel image) which might represent the spatial pattern of the presence and absence of vegetation in a landscape. ‘Lacunarity’ is a generic term for the nature of gaps in the pattern: a popular choice of summary statistic is the ‘gliding-box lacunarit...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
SPRINGER
2019
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| Subjects: | |
| Online Access: | http://purl.org/au-research/grants/arc/DP130104470 http://hdl.handle.net/20.500.11937/91579 |
| _version_ | 1848765553905238016 |
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| author | Hingee, K. Baddeley, Adrian Caccetta, P. Nair, G. |
| author_facet | Hingee, K. Baddeley, Adrian Caccetta, P. Nair, G. |
| author_sort | Hingee, K. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We consider a spatial binary coverage map (binary pixel image) which might represent the spatial pattern of the presence and absence of vegetation in a landscape. ‘Lacunarity’ is a generic term for the nature of gaps in the pattern: a popular choice of summary statistic is the ‘gliding-box lacunarity’ (GBL) curve. GBL is potentially useful for quantifying changes in vegetation patterns, but its application is hampered by a lack of interpretability and practical difficulties with missing data. In this paper we find a mathematical relationship between GBL and spatial covariance. This leads to new estimators of GBL that tolerate irregular spatial domains and missing data, thus overcoming major weaknesses of the traditional estimator. The relationship gives an explicit formula for GBL of models with known spatial covariance and enables us to predict the effect of changes in the pattern on GBL. Using variance reduction methods for spatial data, we obtain statistically efficient estimators of GBL. The techniques are demonstrated on simulated binary coverage maps and remotely sensed maps of local-scale disturbance and meso-scale fragmentation in Australian forests. Results show in some cases a fourfold reduction in mean integrated squared error and a twentyfold reduction in sensitivity to missing data. Supplementary materials accompanying the paper appear online and include a software implementation in the R language. |
| first_indexed | 2025-11-14T11:37:05Z |
| format | Journal Article |
| id | curtin-20.500.11937-91579 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:37:05Z |
| publishDate | 2019 |
| publisher | SPRINGER |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-915792023-05-11T04:47:01Z Computation of Lacunarity from Covariance of Spatial Binary Maps Hingee, K. Baddeley, Adrian Caccetta, P. Nair, G. Science & Technology Life Sciences & Biomedicine Physical Sciences Biology Mathematical & Computational Biology Statistics & Probability Life Sciences & Biomedicine - Other Topics Mathematics Forest disturbance Fractal Gliding box Image analysis Random set Spatial statistics MICROSTRUCTURE MOSAICS We consider a spatial binary coverage map (binary pixel image) which might represent the spatial pattern of the presence and absence of vegetation in a landscape. ‘Lacunarity’ is a generic term for the nature of gaps in the pattern: a popular choice of summary statistic is the ‘gliding-box lacunarity’ (GBL) curve. GBL is potentially useful for quantifying changes in vegetation patterns, but its application is hampered by a lack of interpretability and practical difficulties with missing data. In this paper we find a mathematical relationship between GBL and spatial covariance. This leads to new estimators of GBL that tolerate irregular spatial domains and missing data, thus overcoming major weaknesses of the traditional estimator. The relationship gives an explicit formula for GBL of models with known spatial covariance and enables us to predict the effect of changes in the pattern on GBL. Using variance reduction methods for spatial data, we obtain statistically efficient estimators of GBL. The techniques are demonstrated on simulated binary coverage maps and remotely sensed maps of local-scale disturbance and meso-scale fragmentation in Australian forests. Results show in some cases a fourfold reduction in mean integrated squared error and a twentyfold reduction in sensitivity to missing data. Supplementary materials accompanying the paper appear online and include a software implementation in the R language. 2019 Journal Article http://hdl.handle.net/20.500.11937/91579 10.1007/s13253-019-00351-9 English http://purl.org/au-research/grants/arc/DP130104470 SPRINGER fulltext |
| spellingShingle | Science & Technology Life Sciences & Biomedicine Physical Sciences Biology Mathematical & Computational Biology Statistics & Probability Life Sciences & Biomedicine - Other Topics Mathematics Forest disturbance Fractal Gliding box Image analysis Random set Spatial statistics MICROSTRUCTURE MOSAICS Hingee, K. Baddeley, Adrian Caccetta, P. Nair, G. Computation of Lacunarity from Covariance of Spatial Binary Maps |
| title | Computation of Lacunarity from Covariance of Spatial Binary Maps |
| title_full | Computation of Lacunarity from Covariance of Spatial Binary Maps |
| title_fullStr | Computation of Lacunarity from Covariance of Spatial Binary Maps |
| title_full_unstemmed | Computation of Lacunarity from Covariance of Spatial Binary Maps |
| title_short | Computation of Lacunarity from Covariance of Spatial Binary Maps |
| title_sort | computation of lacunarity from covariance of spatial binary maps |
| topic | Science & Technology Life Sciences & Biomedicine Physical Sciences Biology Mathematical & Computational Biology Statistics & Probability Life Sciences & Biomedicine - Other Topics Mathematics Forest disturbance Fractal Gliding box Image analysis Random set Spatial statistics MICROSTRUCTURE MOSAICS |
| url | http://purl.org/au-research/grants/arc/DP130104470 http://hdl.handle.net/20.500.11937/91579 |