Finding ridges and valleys in a discrete surface using a modified MLS approximation

Implicit surface fitting is a promising approach to finding ridges and valleys in discrete surfaces, but existing techniques are time-consuming and rely on user-supplied tuning parameters. We use a modified MLS (moving-least-squares) approximation technique to estimate the local differential information near a vertex by means of an approximating surface. Ridge and valley vertices are easily detected as zero-crossings, and can then be connected along the direction of principal curvature. Our method, demonstrated on several large meshed models, produces a good fit which leads to improved visualization. It does not oscillate and is quick to compute.