xDEM: cross-DEM analysis

In xDEM, bias-correction methods are transformations used to correct systematic elevation errors and spatially-structured random errors. Unlike affine coregistration, bias corrections are not limited to elevation data; they can incorporate external variables (e.g., land cover type, processing metrics) to identify and correct biases.

While many methods rely on coordinates (e.g., deramping) or terrain (e.g., curvature-dependent corrections) derived from the elevation data, the framework allows for any number of simultaneous dimensions to be used for correction.

xDEM is a Python package for analyzing Digital Elevation Models (DEMs) and Elevation Point Clouds (EPCs). The library is built around two primary data abstractions:

• DEM: The central class for manipulating digital elevation models (rasters).
• EPC: The central class for manipulating elevation point clouds.

Terrain analysis is implemented modularly, re-implementing tools found in gdalDEM. For complex workflows like 3D rigid coregistration or bias corrections, xDEM uses modular Coreg objects that interface with one another.

Additionally, xDEM inherits geospatial functionalities from GeoUtils, including implicit loading, numerical interfacing, and object-based methods for reprojection, cropping, and vector masking. It relies on Rasterio, GeoPandas, Pyproj, NumPy, and SciPy for its underlying computations.

When a single coregistration method is insufficient, you can combine multiple methods sequentially using the xdem.coreg.CoregPipeline object. This object follows a pattern similar to SciKit-Learn's Pipeline. You can construct a pipeline by passing a list of methods to the constructor or by using the + operator to sum them. A pipeline exposes the same interface as a single Coreg object (e.g., .fit(), .apply(), .fit_and_apply()) and its results can be exported using .to_matrix().

# Option 1: List sequential methods
pipeline = xdem.coreg.CoregPipeline([xdem.coreg.ICP(), xdem.coreg.NuthKaab()])

# Option 2: Sum methods
pipeline = xdem.coreg.ICP() + xdem.coreg.NuthKaab()

# Apply the pipeline
aligned_dem = pipeline.fit_and_apply(ref_dem, tba_dem_shifted_rotated)

Curvatures describe the convexity or concavity of terrain using second derivatives of elevation. xDEM provides six basic curvatures: profile, tangential, planform, flowline, maximal/maximum, and minimal/minimum.

Calculation Systems

You can choose between two mathematical systems using the curv_method parameter:

• "geometric" (default): Suitable for most users; defines curvature via the radius of a circle.
• "directional": Defines curvatures as directional derivatives of the elevation field.

Requirements

All curvature calculations require second-order derivatives ($z_{xx}$, $z_{xy}$, or $z_{yy}$). Therefore, you must use either the "ZevenbergThorne" or "Florinsky" surface_fit methods. The "Horn" method is incompatible with curvatures.

Note: Curvature values are returned in units of $m^{-1}$ but are multiplied by 100 by convention for easier handling.

The xdem.EPC class represents an Estimated Point Cloud. It inherits all point cloud methods and attributes from geoutils.PointCloud.

Core Capabilities:

• Creation: Create from XYZ arrays, tuples, or standard arrays via .from_xyz(), .from_tuples(), or .from_array().
• I/O: Open/save via EPC() or EPC.to_file().
• Georeferencing: Reproject, crop, or subsample using .reproject(), .crop(), and .subsample().
• Raster Interface: Convert to a grid via .grid() or rasterize via .rasterize().
• Coregistration: Perform 3D coregistration using .coregister_3d().
• Vertical Referencing: Manage VCRS using .set_vcrs() and .to_vcrs().

import xdem

# Example: Creating an EPC from XYZ data
x, y, z = [0, 1], [0, 1], [10, 11]
epc = xdem.EPC.from_xyz(x, y, z)
print(epc.point_count)