1. Chapter 12 Object Recognition
智能视觉理解
实验室

2. 12.1 Patterns and Pattern Classes
Three types of iris flowers described by two measurements

3. A pattern is an arrangement of descriptors
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

4. 12.1 Patterns and Pattern Classes
Noisy Object and Signature
𝒙 𝟏 =𝒓 𝜽 𝟏 , 𝒙 𝟐 =𝒓 𝜽 𝟐 ,…, 𝒙 𝒏 =𝒓 𝜽 𝒏

5. 12.1 Patterns and Pattern Classes
Staircase Structure
String description
…abababa…

6. 12.1 Patterns and Pattern Classes
Satellite image of a heavily built downtown area and surrounding residential areas.
Tree Description

7. 12.2 Recognition Based on Decision-Theoretic Methods
Let 𝒙= 𝒙 𝟏 , 𝒙 𝟐 ,…, 𝒙 𝒏 𝑻 for 𝑾 pattern class 𝝎 𝟏 , 𝝎 𝟐 ,…, 𝝎 𝑾
𝒅 𝒊 𝒙 > 𝒅 𝒋 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, 𝒅 𝒊 𝒙 yields the largest numerical value.

8. Minimum Distance Classifier
Matching
Minimum Distance Classifier
Define the prototype of each pattern class
𝒎 𝒋 = 𝟏 𝑵 𝒋 𝒙∈ 𝝎 𝒋 𝒙 𝒋
Assign x to class 𝝎 𝒋 if 𝑫 𝒋 (𝒙) is the smallest distance.
𝑫 𝒋 𝒙 = 𝒙− 𝒎 𝒋

9. Assign x to class 𝝎 𝒋 if 𝒅 𝒋 (𝒙) is the largest numerical value.
Matching
Selecting the smallest distance is equivalent to evaluating the functions
𝒅 𝒋 𝒙 = 𝒙 𝑻 𝒎 𝒋 − 𝟏 𝟐 𝒎 𝒋 𝑻 𝒎 𝒋
Assign x to class 𝝎 𝒋 if 𝒅 𝒋 (𝒙) is the largest numerical value.

10. Matching
Decision boundary of minimum distance classifier. (Dark dot and square are the means)

11. Matching
American Bankers Association E-13B font character set and corresponding waveforms.

12. Matching by Correlation
𝒄 𝒙,𝒚 = 𝒔 𝒕 𝒇 𝒔,𝒕 𝒘(𝒙+𝒔, 𝒚+𝒕)
Correlation Coefficient:
𝜸 𝒙,𝒚 = 𝒔 𝒕 𝒇 𝒔,𝒕 − 𝒇 𝒔,𝒕 𝒘 𝒙+𝒔, 𝒚+𝒕 − 𝒘 𝒔 𝒕 𝒇 𝒔,𝒕 − 𝒇 𝒔,𝒕 𝟐 𝒔 𝒕 𝒘 𝒙+𝒔, 𝒚+𝒕 − 𝒘 𝟐 𝟏 𝟐

13. Matching
The mechanics of template matching

14. Location of the best match Correlation Coefficient
Matching
Satellite image
Template
Location of the best match
Correlation Coefficient

15. 12.2.2 Optimum Statistical Classifiers
Conditional Average Risk
𝒓 𝒋 𝒙 = 𝒌=𝟏 𝑾 𝑳 𝒌𝒋 𝒑( 𝝎 𝒌 |𝒙)
The classifier that minimizes the total average loss is called the Bayes Classifier.
Assign pattern x to class 𝝎 𝒊 if
𝒌=𝟏 𝑾 𝑳 𝒌𝒊 𝒑 𝒙| 𝝎 𝒌 𝑷 𝝎 𝒌 < 𝒒=𝟏 𝑾 𝑳 𝒒𝒋 𝒑 𝒙| 𝝎 𝒒 𝑷( 𝝎 𝒒 )
for 𝒋=𝟏,𝟐,…,𝑾;𝒋≠𝒊

16. 12.2.2 Optimum Statistical Classifiers
Bayes Classifier for Gaussian Pattern Classes
𝒅 𝒋 𝒙 =𝒑 𝒙 𝝎 𝒋 𝑷 𝝎 𝒋 = 𝟏 𝟐𝝅 𝝈 𝒋 𝒆 − 𝒙− 𝒎 𝒋 𝟐 𝟐 𝝈 𝒋 𝟐
𝒑 𝒙 𝝎 𝒋 = 𝟏 𝟐𝝅 𝒏 𝟐 𝑪 𝒋 𝒏 𝟐 𝒆 − 𝟏 𝟐 𝒙− 𝒎 𝒋 𝑻 𝑪 𝒋 −𝟏 (𝒙− 𝒎 𝒋 )
𝑪 𝒋 = 𝑬 𝒋 𝒙− 𝒎 𝒋 𝒙− 𝒎 𝒋 𝑻 , 𝒎 𝒋 = 𝑬 𝒋 𝒙
Bayes decision function for class 𝝎 𝒊 is
𝒅 𝒋 𝒙 =𝐥𝐧𝑷 𝝎 𝒋 + 𝒙 𝑻 𝑪 −𝟏 𝒎 𝒋 − 𝟏 𝟐 𝒎 𝒋 𝑻 𝑪 −𝟏 𝒎 𝒋

17. 12.2.2 Optimum Statistical Classifiers
Probability density functions for two 1-D pattern classes. The point x0 shown is the decision boundary if the two classes are equally likely to occur.

18. Two Simple Pattern Classes and their Bayes Decision Boundary
Optimum Statistical Classifiers
Two Simple Pattern Classes and their Bayes Decision Boundary

19. 12.2.2 Optimum Statistical Classifiers
Formation of a pattern vector from registered pixels of four digital images generated by a multispectral scanner.

20. Near Infrared Wavelengths Mask Result of Classification
Visible Blue
Visible Green
Visible Red
Near Infrared Wavelengths
Mask
Result of Classification
All Classified as Water
As Urban development
As Vegetations

21. 12.2.3 Neural Networks 𝒅 𝒙 = 𝒊=𝟏 𝒏 𝒘 𝒊 𝒙 𝒊 + 𝒘 𝒏+𝟏
𝒅 𝒙 = 𝒊=𝟏 𝒏 𝒘 𝒊 𝒙 𝒊 + 𝒘 𝒏+𝟏
Two equivalent representations of the perceptron model for two pattern classes

22. Patterns Belonging to Two Classes
Neural Networks
Patterns Belonging to Two Classes
Decision Boundary

23. Multilayer Feedforward Neural Network
Neural Networks
Multilayer Feedforward Neural Network

24. 12.2.3 Neural Networks Sigmoidal Activation
𝒉 𝒋 𝑰 𝒋 = 𝟏 𝟏+ 𝒆 −( 𝑰 𝒋 + 𝜽 𝒋 )/ 𝜽 𝟎

25. Typical Noisy Shapes Used in Training
Neural Networks
Reference Shapes
Typical Noisy Shapes Used in Training

26. Three-layer Neural Network
Neural Networks
Three-layer Neural Network

27. Neural Networks
Performance of the neural network as a function of noise level.

28. Neural Networks
Improvement in performance for Rt=0.4 by increasing the number of training patterns (the curve for Rt=0.3 is shown for reference).

29. Examples of Decision Boundaries
Neural Networks
Two-input Two-layer
Examples of Decision Boundaries

30. Types of decision regions that can be formed by single- and multilayer feedforward neural networks.

31. Hypothetical Similarity Tree
Matching Shape Number
Shapes
Hypothetical Similarity Tree
Similarity Matrix

32. String Matching
Sample boundaries of two different object classes
Polygonal approximations
Tabulations of R

33. 12.3.3 Syntactic Recognition of Strings

34. 12.3.3 Syntactic Recognition of Strings
Finite Automaton

35. 12.3.4 Syntactic Recognition of Tree
Primitives

36. Processing Stages of a Frontier-to-root Tree
Syntactic Recognition of Tree
Processing Stages of a Frontier-to-root Tree

37. A Bubble Chamber Photograph
Syntactic Recognition of Tree
A Bubble Chamber Photograph

38. 12.3.4 Syntactic Recognition of Tree
Tree Representation
Coded Event

39. 12.3.4 Syntactic Recognition of Tree
State Diagram

41. State Diagram for Af (R+, 1)
Syntactic Recognition of Tree
State Diagram for Af (R+, 1)

42. 智能视觉理解
实验室