V2EX level set

Level Set

释义 Definition

level set(常译:等值集合 / 水平集):在数学中,指对某个函数 \(f(x)\),所有满足 \(f(x)=c\)(其中 \(c\) 为常数)的点所组成的集合。常见于多元微积分、偏微分方程、图像处理与计算机视觉中的“水平集方法(level set method)”。

发音 Pronunciation (IPA)

/lvl st/

例句 Examples

The contour line on the map is a level set of elevation.
地图上的等高线是海拔高度的一个等值集合。

In level set methods, the moving boundary is represented implicitly as the zero level set of a function, which helps handle merging or splitting shapes.
在水平集方法中,运动边界常被隐式表示为某个函数的“零水平集”,这有助于处理形状的合并或分裂等变化。

词源 Etymology

level 原意与“平的、同一高度/水平”相关;set 表示“集合”。合起来 level set 字面意思是“处在同一水平(数值)上的点的集合”,因此在数学语境中引申为“函数取同一常值时的点集”。

相关词 Related Words

文学与作品 Literary Works

  • Level Set Methods and Fast Marching Methods(J. A. Sethian)
  • Level Set Methods and Dynamic Implicit Surfaces(Stanley Osher & Ronald Fedkiw)
  • Geometric Partial Differential Equations and Image Analysis(Guillermo Sapiro)
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