## Description

This tool calculates the shape index (Koenderink and van Doorn, 1992) from a digital elevation model (DEM). This variable ranges from -1 to 1, with positive values indicative of convex landforms, negative values corresponding to concave landforms (Florinsky, 2017). Absolute values from 0.5 to 1.0 are associated with elliptic surfaces (hills and closed depressions), while absolute values from 0.0 to 0.5 are typical of hyperbolic surface form (saddles). Shape index is a dimensionless variable and has utility in landform classification applications.

Koenderink and vsn Doorn (1992) make the following observations about the shape index:

- Two shapes for which the shape index differs merely by sign represent complementary pairs that will fit together as ‘stamp’ and ‘mould’ when suitably scaled;

- The shape for which the shape index vanishes - and consequently has indeterminate sign - represents the objects which are congruent to their own moulds;

- Convexities and concavities find their places on opposite sides of the shape scale. These basic shapes are separated by those shapes which are neither convex nor concave, that are the saddle-like objects. The transitional shapes that divide the convexities/concavities from the saddle-shapes are the cylindrical ridge and the cylindrical rut.

The user must specify the name of the input DEM (`dem`) and the output raster (`output`). The The Z conversion factor (`zfactor`) is only important when the vertical and horizontal units are not the same in the DEM. When this is the case, the algorithm will multiply each elevation in the DEM by the Z Conversion Factor.

For DEMs in projected coordinate systems, the tool uses the 3rd-order bivariate Taylor polynomial method described by Florinsky (2016). Based on a polynomial fit of the elevations within the 5x5 neighbourhood surrounding each cell, this method is considered more robust against outlier elevations (noise) than other methods. For DEMs in geographic coordinate systems (i.e. angular units), the tool uses the 3x3 polynomial fitting method for equal angle grids also described by Florinsky (2016).

## References

Florinsky, I. (2016). Digital terrain analysis in soil science and geology. Academic Press.

Florinsky, I. V. (2017). An illustrated introduction to general geomorphometry. Progress in Physical Geography, 41(6), 723-752.

Koenderink, J. J., and Van Doorn, A. J. (1992). Surface shape and curvature scales. Image and vision computing, 10(8), 557-564.

curvedness, minimal_curvature, maximal_curvature, tangential_curvature, profile_curvature, mean_curvature, gaussian_curvature

## Function Signature

`def shape_index(self, dem: Raster, z_factor: float = 1.0) -> Raster: ...`

## Project Links

WbW Homepage User Manual Support WbW