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Harti dasar '''random field''' nyaeta daftar [[random number|wilangan acak]] numana nileyna dipetakeun kana rohangan ([[dimensions|dimensi]]-n). Nilai dina random field ilahar pakait sacara spatial antara hiji niley jeung nu sejenna, dina harti dasarna bisa oge niley ieu teu pati beda jeung niley saterusna. Contona keur kasus struktur [[covariance]], numana sababaraha tipe kovarian nu beda ieu bisa dimodelkeun make random field.
== MathematicallySacara Matematika ==
InDina [[probability theory]], letanggap ''S'' = {''X''<sub>1</sub>, ..., ''X''<sub>''n''</sub>}, with thenumana ''X''<sub>''i''</sub> indina {0, 1, ..., ''G'' − 1}, bedisusun a set ofsalaku [[randomvariabel variableacak]]s ondi thejero [[sample space|sampel ruang]] Ω = {0, 1, ..., ''G'' − 1}<sup>''n''</sup>. AUkuran probability measureprobabiliti π is anyaeta '''random field''' iflamun
: <math>\pi(\omega)>0\,</math>
forkeur allsakabeh ω indina Ω. SeveralSababaraha kinds oftipe random fields existnu ilahar, among themdiantara [[Markov random field]]s (MRF), [[Gibbs random field]]s (GRF), [[conditional random field]]s(CRF), andsarta [[Gaussian random field]]s. A MRF exhibitsnembongkeun thepasipatan Markovian property
:<math>\pi (X_i=x_i|X_j=x_j, i\neq j) = \pi (X_i=x_i|\partial_i), \,</math>
wheredimana <math>\partial_i</math> isnyaeta asusunan setpangdeukeutna oftina neighboursvariable of the random variableacak ''X''<sub>''i''</sub>. InDina otherkalimah wordssejen, theprobabiliti probabilityvariabel aacak randomdianggap variable assumes a value depends on theniley othernu randomgumantung variableskana onlyvariabel throughacak thesejenna onesngaliwatan thatnilai arepangdeukeutna itsnu immediatekapanggih neighborssaanggeusna. Probabiliti Avariabel probabilityacak of a random variable in adina MRF is showed byditembongkeun theku equationpersamaan 1, Ω' issarua thejeung sameniley realization ofreal Ω, exceptiwal forti randomkeur variablevariabel acak ''X''<sub>''i''</sub>. ItGampang isditempo easyyen tohese seediitung thatgedena itieu isniley difficultmigunakeun topersamaan calculatedi with this equationluhur. TheSolusi solutionkeur toieu thismasalah problemdiusulkeun was proposed byku Besag indina 1974, when henumana mademanehna anyieun relationhubungan betweenantara MRF andjeung GRF.
:<math> \pi (X_i=x_i|\partial_i) = \frac{\pi(\omega)}{\sum_{\omega'}\pi(\omega')} \;\;\;\;(1) </math>
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