Evolving Curves: General Flow

A closed curve moving under its curvature, shrinks to a circle and disappears. This Java Applet provides a tool to examine a more general speed law.

This time, imagine a curve moving perpendicular to itself with speed F. Curvature flow comes from letting F=-K, where K is the curvature. A more general speed law is given by F=(1-Alpha) + Alpha * K
The two extreme cases are

• Alpha=0.0: then the curve uniformly expands, and grows bigger and bigger.
• Alpha=1.0: then the curve moves under curvature, and shrinks into a circle and disappears.

Instructions:
To explore various flows, first input a value for Alpha between 0 and 1. Be sure to then press Enter/Return on your keyboard. Then, draw the curve in the box below. Instructions: Using your mouse, click several points on the white panel to define the vertices of a polygon. When you are finished entering the points, press the "Draw Curve" button. At any time prior to pressing "Draw Curve" you can change the alpha value by enter a new number and pressing return. Once Draw Curve is clicked, the vertices will connect and the Level Set Evolution process will start. Press "Stop" to end the program before completion. To do it again, reload the page.

Some things to watch out for:

• If the evolving curve hits the side of the box, it will keep on expanding.
• Starting with a perfect circle and the right choice for "Alpha" the competition between expansion and shrinkage will be balanced, and the curve will just sit there.