Isovalue

An isovalue is a specific scalar value used to define a level set of a scalar field. If a scalar field F assigns a numerical value to every point in a domain, then the set of points where F(x)=c, for a chosen constant c, is called the isovalue c, and the geometric set is a level set at that value. In two dimensions, the level set F(x,y)=c forms a contour line; in three dimensions, it forms an isosurface.

Isovalue-based visualization identifies features of the field by tracing where the field reaches the same value. The choice of c determines the geometry of the resulting curve or surface, and progressively varying c reveals the field's structure. In data processing, isovalues are used for thresholding, segmentation, or topology analysis.

Computational methods include marching squares for 2D contours and marching cubes or related algorithms for 3D isosurfaces, which approximate the level set with polygonal facets. These methods are common in computer graphics, scientific visualization, and medical imaging.

In applications, isovalues are often tied to physical quantities such as elevation, temperature, pressure, or density. For instance, elevation values yield contour lines on topographic maps, while MRI or CT data use isosurfaces at certain intensity values to delineate anatomical structures. The appropriate choice of isovalue depends on the analysis goal and data resolution, and multiple isovalues may be examined to study topology and features.