Curvaturebased

Curvaturebased, also written curvature-based, describes methods and formulations that use curvature information as the central criterion or constraint. Curvature is a measure of how a geometric object deviates from a straight line or a flat plane; in 2D curves, curvature describes bending; on surfaces, mean and Gaussian curvature characterize bending and intrinsic curvature. In discrete settings, curvature values are estimated from sampled data such as pixels, mesh vertices, or point clouds.

In image processing and computer vision, curvature-based approaches are used to guide segmentation, smoothing, denoising, and shape analysis. Energy functionals may include terms that penalize curvature, promoting smooth contours with controlled bends, or curvature terms may drive evolution in processes such as mean curvature flow. Active contour models and snakes with curvature regularization yield stable boundaries. Curvature measures serve as features for corner or shape detection.

In graphics and geometry, curvature-based models support surface fairing, mesh smoothing, and shape reconstruction. Mean curvature flow evolves surfaces toward minimal surfaces, removing noise and irregularities while preserving volume to some extent. Gaussian curvature helps classify surface types and detect flat regions or ridges.

Computation and challenges: Curvature estimates are sensitive to sampling and noise; discrete differential geometry provides tools to compute approximate curvatures on meshes or voxel grids. Regularization, pre-smoothing, and robust estimators improve stability; high curvature regions can be prone to artifacts and require careful handling.

See also curvature, mean curvature, Gaussian curvature, curvature flow, active contour, variational methods.