Digital Image Processing 121 Patterns and Pattern Classes Satellite image of a heavily built downtown area and surrounding residential areas Tree Description Downtown Residential Building Highways Housing Shopping Highways malls High Large Multiple Numerous Loops densitity structures intersections Low Small Wooded Single Few density structures areas intersections
Digital Image Processing 12.1 Patterns and Pattern Classes Satellite image of a heavily built downtown area and surrounding residential areas. Tree Description
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
Digital Image Processing 12.21 Matching Minimum distance classifier Define the prototype of each pattern class 1 N x∈ Assign x to class w; if Di(r) is thesmallest distance D, (x)=lx
Digital Image Processing 12.2.1 Matching Minimum Distance Classifier • Define the prototype of each pattern class 𝒎𝒋 = 𝟏 𝑵𝒋 𝒙∈𝝎𝒋 𝒙𝒋 • Assign x to class 𝝎𝒋 if 𝑫𝒋 (𝒙) is the smallest distance. 𝑫𝒋 𝒙 = 𝒙 − 𝒎𝒋
Digital Image Processing 12.21 Matching Selecting the smallest distance is equivalent to evaluating the functions 1 di x=xm Assign x to class wj if di(r)isthe largestnumerical value
Digital Image Processing 12.2.1 Matching • Selecting the smallest distance is equivalent to evaluating the functions 𝒅𝒋 𝒙 = 𝒙 𝑻𝒎𝒋 − 𝟏 𝟐 𝒎𝒋 𝑻𝒎𝒋 • Assign x to class 𝝎𝒋 if 𝒅𝒋 (𝒙) is the largest numerical value
Digital Image Processing 12.2.1 Matching 口 Iris versicolo o Iris setosa 20 28x1+1.0 8.9=0 口口口 51.5 二 口口口 s10 日日口口 0.5 o Ee Petal length(cm) Decision boundary of minimum distance classifier. Dark dot and square are the means)
Digital Image Processing 12.2.1 Matching Decision boundary of minimum distance classifier. (Dark dot and square are the means)