Occupancy Field

Definition

An occupancy field is a function that defines whether a point in space lies inside or outside a surface.

Formula

$$o:{\mathbb{R}}^3\to \{0,1\},o(\mathbf{x})=\{\begin{array}{ll}1& \mathbf{x}\text{ inside}\\ 0& \mathbf{x}\text{ outside}\end{array}$$

Unlike a voxel grid, the function is continuous: it can be queried at any 3D point, not only at grid cells. Inside and outside are only well defined for closed (watertight) surfaces. Poisson surface reconstruction approximates exactly this kind of indicator function before it extracts the surface.

Appears in

• Lecture 1, 3D representations: one of the five representations; the indicator function in Poisson reconstruction
• Lecture 5, Implicit function: occupancy with threshold $\tau$
• Lecture 5, Poisson: the indicator function
• Lecture 6.1, Neural Fields: Occupancy Networks, $f(\mathbf{z},\mathbf{p})\mapsto [0,1]$
• Lecture 7, UniSurf: ${\alpha }_i$ as occupancy

Related concepts

• Neural Field
• Marching Cubes
• Signed Distance Function
• Voxel Grid
• Implicit and Explicit Representations