Digital Image Processing 12.2 Recognition Based on Decision-Theoretic Methods Let x=(x1, x2,, xn)for W pattern class 1,02, W d1(x)>d1(x)j=1,2,…,W;j≠i In other words, an unknown pattern x is said to belong to the ith pattern class if, upon substitution of x into all decision functions di (x) yields the largest numerical value.Digital Image Processing 12.2 Recognition Based on Decision-Theoretic Methods • Let 𝒙 = 𝒙𝟏, 𝒙𝟐, … , 𝒙𝒏 𝑻 for 𝑾 pattern class 𝝎𝟏, 𝝎𝟐,… , 𝝎𝑾 𝒅𝒊 𝒙 > 𝒅𝒋 𝒙 𝒋 = 𝟏, 𝟐, … , 𝑾;𝒋 ≠ 𝒊 • In other words, an unknown pattern 𝒙 is said to belong to the ith pattern class if, upon substitution of 𝒙 into all decision functions, 𝒅𝒊 𝒙 yields the largest numerical value