Digital geometry

Digital geometry deals with <a href="/facts/Discrete_space/hpvXA23u">discrete</a> sets (usually discrete <a href="/facts/Point_(geometry)/6YPAvX2a">point</a> sets) considered to be <a href="/facts/Digitizing/RRdE9Ma9">digitized</a> <a href="/facts/Scale_model/YgCtlwqb">models</a> or <a href="/facts/Image/hbjEdTXK">images</a> of objects of the 2D or 3D <a href="/facts/Euclidean_space/R2UbzmzM">Euclidean space</a>. 
Simply put, digitizing is replacing an object by a discrete set of its points. The images we see on the TV screen, the <a href="/facts/Raster_graphics/HkXNc8oI">raster</a> display of a computer, or in newspapers are in fact <a href="/facts/Digital_data/JChckAvr">digital</a> images.
Its main application areas are <a href="/facts/Computer_graphics/lapBE8wv">computer graphics</a> and <a href="/facts/Image_analysis/woLB8cX7">image analysis</a>.
Main aspects of study are:

<ul><li>Constructing digitized representations of objects, with the emphasis on precision and efficiency (either by means of synthesis, see, for example, <a href="/facts/Bresenham%2527s_line_algorithm/G1fcMKEF">Bresenham's line algorithm</a> or digital disks, or by means of digitization and subsequent processing of digital images).</li>
<li>Study of properties of digital sets; see, for example, <a href="/facts/Pick%2527s_theorem/rvk9rFDG">Pick's theorem</a>, digital convexity, digital straightness, or digital planarity.</li>
<li>Transforming digitized representations of objects, for example (A) into simplified shapes such as (i) skeletons, by repeated removal of simple points such that the <a href="/facts/Digital_topology/UdhbeLPD">digital topology</a> of an image does not change, or (ii) medial axis, by calculating local maxima in a distance transform of the given digitized object representation, or (B) into modified shapes using <a href="/facts/Mathematical_morphology/qVpYux75">mathematical morphology</a>.</li>
<li>Reconstructing "real" objects or their properties (area, length, curvature, volume, surface area, and so forth) from digital images.</li>
<li>Study of digital curves, digital surfaces, and <a href="/facts/Digital_manifold/3xDA87xz">digital manifolds</a>.</li>
<li>Designing tracking algorithms for digital objects.</li>
<li>Functions on digital space.</li>
<li>Curve sketching, a method of drawing a curve pixel by pixel.</li></ul>

Digital geometry heavily overlaps with <a href="/facts/Discrete_geometry/Ixnl3GBc">discrete geometry</a> and may be considered as a part thereof.

Digital geometry open-in-new

Digital geometry