Compute the difference between the current pixel value and its neighboring values. This uses classic definitions of curvature based on derivative values. This method is more stable than Angle Deficit for smooth inputs, such as a parameterization of hemisphere.

Treat each pixel as a vertex in a polygonal height field. This calculates the sum of the angles formed at each pixel by its neighboring vertices. The angle sum equals 2𝜋 in flat regions, but the sum is less in curved areas and results in an angle deficit that’s used to estimate local curvature. This method performs more robustly when the input includes complex or non-uniform variations.

This curvature is positive in both convex and concave regions. It becomes negative at saddle points, where the surface curves in opposite directions (concave in one direction and convex in the other). Gaussian curvature is useful for distinguishing simple convex and concave shapes from regions with saddle-like geometry.

This curvature is positive in convex regions and negative in concave regions. Mean curvature is useful for distinguishing convex, concave, and flat regions.

The maximal principal curvature represents the largest normal curvature at a point. Although it’s not a direct measure of convexity, it often emphasizes geometrically prominent, outward-curving features.

The minimal principal curvature represents the smallest normal curvature at a point. Although it’s not a direct measure of concavity, it often emphasizes geometrically recessed, inward-curving features.

Outputs the entire computed curvature.

Outputs the convex regions based on the selected curvature.

Outputs the concave regions based on the selected curvature.