Level-set method: Difference between revisions

Revision as of 00:46, 15 April 2024

Revision as of 14:48, 17 April 2024

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==Example==

Consider a unit circle in <math display="inline">\mathbb{R}^2</math>, shrinking in on itself at a constant rate, i.e. each point on the boundary of the circle moves along its inwards pointing normalnormally at some fixed speed. The circle will shrink and eventually collapse down to a point. If an initial distance field is constructed (i.e. a function whose value is the signed [[Euclidean distance]] to the boundary, positive interior, negative exterior) on the initial circle, the normalized gradient of this field will be the circle normal.

If the field has a constant value subtracted from it in time, the zero level (which was the initial boundary) of the new fields will also be circular and will similarly collapse to a point. This is due to this being effectively the temporal integration of the [[Eikonal equation]] with a fixed front [[velocity]].