set_functions {segmetric}

Set functions

Description

These functions compute subsets required to calculate segmentation metrics as described in Clinton et al. (2010) and Costa et al. (2017).

• sm_ref() returns the set of n polygons of reference, represented by X = \{x_{i}: i = 1, ....., n\}

• sm_seg() returns the set of m segmentation polygons, represented by Y = \{y_{j}: j = 1, ....., m\}

• sm_ytilde() returns \tilde{Y}_{i}, a subset of Y, where \tilde{Y}_{i} = \{y_{j}: \rm{area}(x_{i} \cap y_{j}) \neq 0\}

• sm_xtilde() returns \tilde{X}_{j}, a subset of X, where \tilde{X}_{j} = \{x_{i}: \rm{area}(y_{j} \cap x_{i}) \neq 0\}

• sm_yprime() returns Y'_{i}, a subset of Y, where Y'_{i} = \{y_{j}: max(\rm{area}(x_{i} \cap y_{j}))\}

• sm_xprime() returns X'_{j}, a subset of X, where X'_{j} = \{x_{i}: max(\rm{area}(y_{j} \cap x_{i}))\}

• sm_ya() returns Y\!a_{i}, a subset of \tilde{Y}_{i}, where Y\!a_{i} = \{y_{j}: \rm{centroid}(x_{i}) \:\rm{in}\: y_{j}\}

• sm_yb() returns Y\!b_{i}, a subset of \tilde{Y}_{i}, where Y\!b_{i} = \{y_{j}: \rm{centroid}(y_{j}) \:\rm{in}\: x_{i}\}

• sm_yc() returns Y\!c_{i}, a subset of \tilde{Y}_{i}, where Y\!c_{i} = \{y_{j}: \rm{area}(x_{i} \cap y_{j}) / \rm{area}(y_{j}) > 0.5\}

• sm_yd() returns Y\!d_{i}, a subset of \tilde{Y}_{i}, where Y\!d_{i} = \{y_{j}: \rm{area}(x_{i} \cap y_{j}) / \rm{area}(x_{i}) > 0.5\}

• sm_ystar() returns {Y}^{*}_{i}, where {Y}^{*}_{i} = Y\!a_{i} \cup Y\!b_{i} \cup Y\!c_{i} \cup Y\!c_{i}

• sm_ycd() returns Y\!cd_{i}, where Y\!cd_{i} = Y\!c_{i} \cup Y\!d_{i}

• sm_ye() returns Y\!e_{i}, a subset of \tilde{Y}_{i}, where Y\!e_{i} = \{y_{j}: \rm{area}(x_{i} \cap y_{j}) / \rm{area}(y_{j}) = 1\}

• sm_yf() returns Y\!f_{i}, a subset of \tilde{Y}_{i}, where Y\!f_{i} = \{y_{j}: \rm{area}(x_{i} \cap y_{j}) / \rm{area}(y_{j}) > 0.55\}

• sm_yg() returns Y\!g_{i}, a subset of \tilde{Y}_{i}, where Y\!g_{i} = \{y_{j}: \rm{area}(x_{i} \cap y_{j}) / \rm{area}(y_{j}) > 0.75\}

Usage

sm_ytilde(m)

sm_xtilde(m)

sm_yprime(m)

sm_xprime(m)

sm_ya(m)

sm_yb(m)

sm_yc(m)

sm_yd(m)

sm_ystar(m)

sm_ycd(m)

sm_ye(m)

sm_yf(m)

sm_yg(m)

Arguments

m

A segmetric object.

Value

• sm_ref(): Return an object of class ref_sf (inherited from sf) containing identification (ref_id) and geometry (geometry) columns.

• sm_seg(): Return an object of class seg_sf (inherited from sf) containing identification (seg_id) and geometry (geometry) columns.

• sm_ytilde(), sm_xtilde(), sm_yprime(), sm_xprime(), sm_ya(), sm_yb(), sm_yc(), sm_yd(), sm_ystar(), sm_ycd(), sm_ye(), sm_yf(), and sm_yg(): Return an object of class subset_sf (inherited from sf) containing identification (ref_id and seg_id), and geometry (geometry) columns.

References

Clinton, N., Holt, A., Scarborough, J., Yan, L., & Gong, P. (2010). Accuracy Assessment Measures for Object-based Image Segmentation Goodness. Photogrammetric Engineering & Remote Sensing, 76(3), 289–299. doi: 10.14358/PERS.76.3.289.

Costa, H., Foody, G. M., & Boyd, D. S. (2018). Supervised methods of image segmentation accuracy assessment in land cover mapping. Remote Sensing of Environment, 205(December 2017), 338–351. doi: 10.1016/j.rse.2017.11.024.