Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Mathematical morphology
open-in-new
<p>Mathematical morphology (MM) is a theory and technique for the analysis and processing of <a href="/facts/Geometry/wTQf5ffQ">geometrical</a> structures, based on <a href="/facts/Set_theory/1ptfsvUP">set theory</a>, <a href="/facts/Lattice_theory/5ak6ufky">lattice theory</a>, <a href="/facts/Topology/2EqW47cU">topology</a>, and <a href="/facts/Random_function/Ng1n1dnB">random functions</a>. MM is most commonly applied to <a href="/facts/Digital_image/3TNT47Mv">digital images</a>, but it can be employed as well on <a href="/facts/Graph_(discrete_mathematics)/kw3eIBUe">graphs</a>, <a href="/facts/Polygon_mesh/6WLD80ER">surface meshes</a>, <a href="/facts/Solid_geometry/tHH3JFoq">solids</a>, and many other spatial structures. </p><p><a href="/facts/Topology/2EqW47cU">Topological</a> and <a href="/facts/Geometry/wTQf5ffQ">geometrical</a> <a href="/facts/Continuum_(theory)/oz3r6kvm">continuous</a>-space concepts such as size, <a href="/facts/Shape/nww0x85d">shape</a>, <a href="/facts/Convex_set/vdAuJRJl">convexity</a>, <a href="/facts/Connectedness/P5w33wdx">connectivity</a>, and <a href="/facts/Geodesic_distance/EmQFKvqa">geodesic distance</a>, were introduced by MM on both continuous and <a href="/facts/Discrete_space/hpvXA23u">discrete spaces</a>. MM is also the foundation of morphological <a href="/facts/Image_processing/zenalNCf">image processing</a>, which consists of a set of operators that transform images according to the above characterizations. </p><p>The basic morphological operators are <a href="/facts/Erosion_(morphology)/CkHHo65Q">erosion</a>, <a href="/facts/Dilation_(morphology)/P3NbEmoS">dilation</a>, <a href="/facts/Opening_(morphology)/tss6523A">opening</a> and <a href="/facts/Closing_(morphology)/PjW0c7en">closing</a>. </p><p>MM was originally developed for <a href="/facts/Binary_image/qaKaPntY">binary images</a>, and was later extended to <a href="/facts/Grayscale/Tjb9kR8v">grayscale</a> <a href="/facts/Function_(mathematics)/CdReEKCh">functions</a> and images. The subsequent generalization to <a href="/facts/Complete_lattice/pQbphWeR">complete lattices</a> is widely accepted today as MM's theoretical foundation. </p>