⑧上藩文人字 SHANGHAI JIAO TONG UNIVERSITY 1896 1920 2006 Chapter 12 object Recognition 口影好回 驾越现觉到 Deep vis 40m0男驾
1896 1920 1987 2006 Chapter 12 Object Recognition
Digital Image Processing 121 Patterns and Pattern Classes Three types of iris flowers described by 2.5 △ Iris virginica two measurements 口 Iris versicolor o Iris setosa △△Δ△ △△ △△M△△ 2.0 △ △△ △△△△ △ BM△ 口口口 1.0 日日口 0.5 3 Petal length(cm)
Digital Image Processing 12.1 Patterns and Pattern Classes Three types of iris flowers described by two measurements
Digital Image Processing 121 Patterns and Pattern Classes a pattern is an arrangement of descriptors The name feature is used often in the pattern recognition literature to denote a descriptor a pattern class is a family of patterns that share some common properties
Digital Image Processing 12.1 Patterns and Pattern Classes • A pattern is an arrangement of descriptors • The name feature is used often in the pattern recognition literature to denote a descriptor • A pattern class is a family of patterns that share some common properties
Digital Image Processing 121 Patterns and Pattern Classes Noisy object and signature x1=T(61),x2=r(02)…,xn=r(6n) 丌亓3丌丌5丌3丌7丌2丌
Digital Image Processing 12.1 Patterns and Pattern Classes Noisy Object and Signature 𝒙𝟏 = 𝒓 𝜽𝟏 , 𝒙𝟐 = 𝒓 𝜽𝟐 , … , 𝒙𝒏 = 𝒓 𝜽𝒏
Digital Image processing 121 Patterns and Pattern Classes Staircase structure String description abababa b
Digital Image Processing 12.1 Patterns and Pattern Classes Staircase Structure String description …abababa…
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)
