Isosurface

Isosurfaces of an iron protein

Isosurface in the density field of an MRT image of a human head.
The area was extracted with marching cubes .

Isosurfaces are surfaces that connect neighboring points in space with the same characteristics or values ​​of a certain size such as temperature or density. They are the three-dimensional counterpart to isolines that connect points on a surface.

The importance of isosurfaces lies in the computer graphic visualization of scalar fields or grids.

In medicine, isosurfaces from data sets with density values ​​are used to represent organ surfaces. The data sets are created, for example, from computer tomography measurements. Another application is the representation of molecules whose atomic position has been determined by electron microscopy.

The most common method for representing isosurfaces is called Marching Cubes and was introduced by Lorensen and Cline in 1987.

definition

The isosurface to a scalar field at the iso value is the amount . ${\displaystyle S_{c}}$ ${\displaystyle \varphi :\mathbb {R} ^{n}\rightarrow \mathbb {R} }$ ${\displaystyle c\in \mathbb {R} }$ ${\displaystyle S_{c}:=\{\mathbf {v} \in \mathbb {R} ^{n}|\varphi (\mathbf {v} )=c\}}$

Three-dimensional isosurfaces are usually approximated from a finite set of data points ( grids ), for example by means of triangular networks . ${\displaystyle {\mathcal {P}}\subset \mathbb {R} ^{3}\times \mathbb {R} }$

See also

• implicit area
• Triangulation (area)

literature

• Hansen, Charles D., Johnson, Chris R .: The Visualization Handbook. Elsevier Academic Press, 2005, ISBN 0-12-387582-X , p. 39ff