Konturvolumen

Konturvolumen is a measure used in geometry, geographic information systems, and image analysis to denote the three-dimensional volume enclosed by a contour. It arises when a two-dimensional boundary is associated with a height function or when a surface is reconstructed from contour data.

If the contour lies on a base plane and is paired with a height function z = f(x,y) over the interior domain D, the konturvolumen equals the integral of f over D. For contours that bound a closed surface, the volume can be computed by standard surface-integral methods or by voxelizing the region and summing voxel volumes.

Common computation methods include voxel-based summation, cross-sectional integration from a stack of slices, and mesh-based techniques that apply the divergence theorem to convert a surface integral into a volume integral.

Applications include estimating organ or lesion volumes in medical imaging, evaluating terrain or geologic volumes in GIS and geoscience, and contributing to design and quality control in computer graphics and architectural modeling.

Limitations include dependence on how the height is assigned to the interior, the requirement that the contour be closed (or that it defines a well-posed region), and sensitivity to data resolution and discretization, which can introduce errors or ambiguity when multiple disjoint regions exist.

See also: area, volume, level set, voxelization, marching cubes.