Table 2 List of generated features,...

Table 2

List of generated features, their descriptions and formulas

Feature	Description	Formula
Area (m²)	Area of each given object	–
Perimeter (m)	Perimeter of each given object	–
Longest axis length (m)	The length of the longest axis of each given object; the axis is defined as the diameter of a minimal circumscribed circle around the convex hull	$\max {d 1, d 2, \dots, d n}$
Circular compactness	Area of each given object divided by the corresponding area of the enclosing circle	$\frac{A r e a}{A r e a o f e n c l o s i n g c i r c l e}$
Convexity	Area of each given object divided by the corresponding area of the convex hull	$\frac{A r e a}{C o n v e x h u l l a r e a}$
Elongation	The elongation of each given object is regarded as elongation of its minimum bounding rectangle, where a is the area of the object and p is its perimeter	$\frac{\frac{p - \sqrt{p^{2} - 16 a}}{4}}{\frac{p}{2} - \frac{p - \sqrt{p^{2} - 16 a}}{4}}$
Equivalent rectangular index	The equivalent rectangular index of each object, where BC is the bounding rectangle and BR is the bounding rectangle	$\frac{\sqrt{a r e a}}{a r e a B C} * \frac{p e r i m e t e r B R}{p e r i m e t e r}$
Fractal dimension	The fractal dimension of each given object	$\frac{2 \log (\frac{P e r i m e t e r}{4})}{\log (A r e a)}$
Rectangularity	The rectangularity of each given object, where RRA is the rotated rectangle area	$\frac{A r e a}{m i n i m u m b o u n d i n g R R A}$
Shape index	The shape index of each given object	$\frac{\sqrt{\frac{A r e a}{π}}}{0.5 * l o n g e s t a x i s}$
Square compactness	The square compactness of each given object	${(\frac{4 \sqrt{A r e a}}{P e r i m e t e r})}^{2}$
Orientation	An orientation of the longest axis of the bounding rectangle in the range of 0–45°	–
Corners	The number of corners of each given object	$\sum c o r n e r$
Centroid corners	The number of centroid corners of each given object	$\sum c e n t r o i d c o r n e r$
Centroid corners mean	The mean distance of the centroid corners, where n is the number of centroid corners	$\frac{1}{n} (\sum_{i = 1}^{n} {d i s t a n c e}_{i})$
Centroid corners standard deviation	The standard deviation of the distance of the centroid corners, where n is the number of centroid corners and x is the distance	$\sqrt{\frac{\sum {\| x - \overset{̅}{x} \|}^{2}}{n}}$

Feature	Description	Formula
Area (m²)	Area of each given object	–
Perimeter (m)	Perimeter of each given object	–
Longest axis length (m)	The length of the longest axis of each given object; the axis is defined as the diameter of a minimal circumscribed circle around the convex hull	$\max {d 1, d 2, \dots, d n}$
Circular compactness	Area of each given object divided by the corresponding area of the enclosing circle	$\frac{A r e a}{A r e a o f e n c l o s i n g c i r c l e}$
Convexity	Area of each given object divided by the corresponding area of the convex hull	$\frac{A r e a}{C o n v e x h u l l a r e a}$
Elongation	The elongation of each given object is regarded as elongation of its minimum bounding rectangle, where a is the area of the object and p is its perimeter	$\frac{\frac{p - \sqrt{p^{2} - 16 a}}{4}}{\frac{p}{2} - \frac{p - \sqrt{p^{2} - 16 a}}{4}}$
Equivalent rectangular index	The equivalent rectangular index of each object, where BC is the bounding rectangle and BR is the bounding rectangle	$\frac{\sqrt{a r e a}}{a r e a B C} * \frac{p e r i m e t e r B R}{p e r i m e t e r}$
Fractal dimension	The fractal dimension of each given object	$\frac{2 \log (\frac{P e r i m e t e r}{4})}{\log (A r e a)}$
Rectangularity	The rectangularity of each given object, where RRA is the rotated rectangle area	$\frac{A r e a}{m i n i m u m b o u n d i n g R R A}$
Shape index	The shape index of each given object	$\frac{\sqrt{\frac{A r e a}{π}}}{0.5 * l o n g e s t a x i s}$
Square compactness	The square compactness of each given object	${(\frac{4 \sqrt{A r e a}}{P e r i m e t e r})}^{2}$
Orientation	An orientation of the longest axis of the bounding rectangle in the range of 0–45°	–
Corners	The number of corners of each given object	$\sum c o r n e r$
Centroid corners	The number of centroid corners of each given object	$\sum c e n t r o i d c o r n e r$
Centroid corners mean	The mean distance of the centroid corners, where n is the number of centroid corners	$\frac{1}{n} (\sum_{i = 1}^{n} {d i s t a n c e}_{i})$
Centroid corners standard deviation	The standard deviation of the distance of the centroid corners, where n is the number of centroid corners and x is the distance	$\sqrt{\frac{\sum {\| x - \overset{̅}{x} \|}^{2}}{n}}$

Note(s): Each of the features are calculated for each building's footprint, tessellation and corresponding block. In total, 48 features are generated and used as the training dataset. All features are calculated using the momepy package

Source(s): Fleischmann (2019)

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