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Image Categorization Computer Vision CS 543 / ECE 549 University of Illinois Derek Hoiem 03/11/10
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Image Categorization

Mar 21, 2016

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03/11/10. Image Categorization. Computer Vision CS 543 / ECE 549 University of Illinois Derek Hoiem. Last classes. Object recognition: localizing an object instance in an image Face recognition: matching one face image to another. Today’s class: categorization. - PowerPoint PPT Presentation
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Page 1: Image Categorization

Image Categorization

Computer VisionCS 543 / ECE 549

University of Illinois

Derek Hoiem

03/11/10

Page 2: Image Categorization

Last classes

• Object recognition: localizing an object instance in an image

• Face recognition: matching one face image to another

Page 3: Image Categorization

Today’s class: categorization

• Overview of image categorization

• Representation– Image histograms

• Classification– Important concepts in machine learning– What the classifiers are and when to use them

Page 4: Image Categorization

Image Categorization

Training Labels

Training Images

Classifier Training

Training

Image Features

Trained Classifier

Page 5: Image Categorization

Image Categorization

Training Labels

Training Images

Classifier Training

Training

Image Features

Image Features

Testing

Test Image

Trained Classifier

Trained Classifier Outdoor

Prediction

Page 6: Image Categorization

Part 1: Image features

Training Labels

Training Images

Classifier Training

Training

Image Features

Trained Classifier

Page 7: Image Categorization

General Principles of Representation• Coverage

– Ensure that all relevant info is captured

• Concision– Minimize number of features

without sacrificing coverage

• Directness– Ideal features are independently

useful for prediction

Image Intensity

Page 8: Image Categorization

Space Shuttle Cargo Bay

Image Representations: Histograms

Global histogram• Represent distribution of features

– Color, texture, depth, …

Images from Dave Kauchak

Page 9: Image Categorization

Image Representations: Histograms

• Joint histogram– Requires lots of data– Loss of resolution to

avoid empty bins

Images from Dave Kauchak

Marginal histogram• Requires independent features• More data/bin than

joint histogram

Histogram: Probability or count of data in each bin

Page 10: Image Categorization

EASE Truss Assembly

Space Shuttle Cargo Bay

Image Representations: Histograms

Images from Dave Kauchak

Clustering

Use the same cluster centers for all images

Page 11: Image Categorization

Computing histogram distance

Chi-squared Histogram matching distance

K

m ji

jiji mhmh

mhmhhh

1

22

)()()]()([

21),(

K

mjiji mhmhhh

1

)(),(min1),histint(

Histogram intersection (assuming normalized histograms)

Cars found by color histogram matching using chi-squared

Page 12: Image Categorization

Histograms: Implementation issues

Few BinsNeed less dataCoarser representation

Many BinsNeed more dataFiner representation

• Quantization– Grids: fast but only applicable with few dimensions– Clustering: slower but can quantize data in higher

dimensions

• Matching– Histogram intersection or Euclidean may be faster– Chi-squared often works better– Earth mover’s distance is good for when nearby bins

represent similar values

Page 13: Image Categorization

What kind of things do we compute histograms of?• Color

• Texture (filter banks or HOG over regions)

L*a*b* color space HSV color space

Page 14: Image Categorization

What kind of things do we compute histograms of?• Histograms of gradient

• Visual words

SIFT – Lowe IJCV 2004

Page 15: Image Categorization

Image Categorization: Bag of WordsTraining1. Extract keypoints and descriptors for all training images2. Cluster descriptors3. Quantize descriptors using cluster centers to get “visual words”4. Represent each image by normalized counts of “visual words” 5. Train classifier on labeled examples using histogram values as features

Testing1. Extract keypoints/descriptors and quantize into visual words2. Compute visual word histogram3. Compute label or confidence using classifier

Page 16: Image Categorization

But what about layout?

All of these images have the same color histogram

Page 17: Image Categorization

Spatial pyramid

Compute histogram in each spatial bin

Page 18: Image Categorization

Part 2: Classifiers

Training Labels

Training Images

Classifier Training

Training

Image Features

Trained Classifier

Page 19: Image Categorization

Learning a classifier• Given some set features with corresponding

labels, learn a function to predict the labels from the features

x x

x x

x

xx

x

oo

o

o

o

x2

x1

Page 20: Image Categorization

Many classifiers to choose from• SVM• Neural networks• Naïve Bayes• Bayesian network• Logistic regression• Randomized Forests• Boosted Decision Trees• K-nearest neighbor• RBMs• Etc.

Which is the best one?

Page 21: Image Categorization

No Free Lunch Theorem

Page 23: Image Categorization

Bias and Variance

Many training examples

Few training examples

Complexity Low BiasHigh Variance

High BiasLow Variance

Test

Err

or

Error = bias2 + variance

Page 24: Image Categorization

Choosing the trade-off• Need validation set• Validation set not same as test set

Training error

Test error

Complexity Low BiasHigh Variance

High BiasLow Variance

Err

or

Page 25: Image Categorization

Effect of Training Size

Testing

TrainingNumber of Training Examples

Err

or

Generalization Error

Fixed classifier

Page 26: Image Categorization

How to measure complexity?• VC dimension

Training error +

Upper bound on generalization error

N: size of training seth: VC dimension: 1-probability

Page 27: Image Categorization

How to reduce variance?

• Choose a simpler classifier

• Regularize the parameters

• Get more training data

Page 28: Image Categorization

The perfect classification algorithm

• Objective function: solves what you want to solve

• Parameterization: makes assumptions that fit the problem

• Regularization: right level of regularization for amount of training data

• Training algorithm: can find parameters that maximize objective on training set

• Inference algorithm: can solve for objective function in evaluation

Page 29: Image Categorization

Generative vs. Discriminative Classifiers

Generative• Training

– Maximize joint likelihood of data and labels

– Assume (or learn) probability distribution and dependency structure

– Can impose priors

• Testing– P(y=1, x) / P(y=0, x) > t?

• Examples– Foreground/background GMM – Naïve Bayes classifier– Bayesian network

Discriminative• Training

– Learn to directly predict the labels from the data

– Assume form of boundary– Margin maximization or

parameter regularization

• Testing– f(x) > t ; e.g., wTx > t

• Examples– Logistic regression– SVM– Boosted decision trees

Page 30: Image Categorization

Generative Classifier: Naïve Bayes• Objective• Parameterization• Regularization• Training• Inference

x1 x2 x3

y

Page 31: Image Categorization

Using Naïve Bayes

• Simple thing to try for categorical data

• Very fast to train/test

Page 32: Image Categorization

Classifiers: Logistic Regression• Objective• Parameterization• Regularization• Training• Inference

x x

x x

x

xx

x

oo

o

o

o

x2

x1

Page 33: Image Categorization

Using Logistic Regression

• Quick, simple classifier (try it first)

• Use L2 or L1 regularization– L1 does feature selection and is robust to

irrelevant features

Page 34: Image Categorization

Classifiers: Linear SVM

• Objective• Parameterization• Regularization• Training• Inference

x x

x x

x

xx

x

oo

o

o

o

x2

x1

Page 35: Image Categorization

Classifiers: Linear SVM

• Objective• Parameterization• Regularization• Training• Inference

x x

x x

x

xx

x

oo

o

o

o

x2

x1

Page 36: Image Categorization

Classifiers: Linear SVM

• Objective• Parameterization• Regularization• Training• Inference

x x

x x

x

xx

xo

oo

o

o

o

x2

x1

Page 37: Image Categorization

Classifiers: Kernelized SVM

• Objective• Parameterization• Regularization• Training• Inference

xx xx oo ox

x

x

x

x

o

oo

x

x2

Page 38: Image Categorization

Using SVMs• Good general purpose classifier

– Generalization depends on margin, so works well with many weak features

– No feature selection– Usually requires some parameter tuning

• Choosing kernel– Linear: fast training/testing – start here– RBF: related to neural networks, nearest neighbor– Chi-squared, histogram intersection: good for histograms

(but slower, esp. chi-squared)– Can learn a kernel function

Page 39: Image Categorization

Classifiers: Decision Trees

• Objective• Parameterization• Regularization• Training• Inference

x x

x x

x

xx

xo

oo

o

o

oo

x2

x1

Page 40: Image Categorization

Ensemble Methods: Boosting

figure from Friedman et al. 2000

Page 41: Image Categorization

Boosted Decision Trees

Gray?

High inImage?

Many LongLines?

Yes

No

NoNo

No

Yes Yes

Yes

Very High Vanishing

Point?

High in Image?

Smooth? Green?

Blue?

Yes

No

NoNo

No

Yes Yes

Yes

Ground Vertical Sky

[Collins et al. 2002]

P(label | good segment, data)

Page 42: Image Categorization

Using Boosted Decision Trees• Flexible: can deal with both continuous and

categorical variables• How to control bias/variance trade-off

– Size of trees– Number of trees

• Boosting trees often works best with a small number of well-designed features

• Boosting “stubs” can give a fast classifier

Page 43: Image Categorization

K-nearest neighbor

x x

x x

x

xx

xo

oo

o

o

oo

x2

x1

• Objective• Parameterization• Regularization• Training• Inference

+

+

Page 44: Image Categorization

1-nearest neighbor

x x

x x

x

xx

xo

oo

o

o

oo

x2

x1

+

+

Page 45: Image Categorization

3-nearest neighbor

x x

x x

x

xx

xo

oo

o

o

oo

x2

x1

+

+

Page 46: Image Categorization

5-nearest neighbor

x x

x x

x

xx

xo

oo

o

o

oo

x2

x1

+

+

Page 47: Image Categorization

Using K-NN

• Simple, so another good one to try first

• With infinite examples, 1-NN provably has error that is at most twice Bayes optimal error

Page 48: Image Categorization

Clustering (unsupervised)

x x

x xx

xo

o

o

o

o

x1

x

x2

+ +

+ +

+

++

+

+

+

+

x2

x1

+

Page 49: Image Categorization

What to remember about classifiers

• No free lunch: machine learning algorithms are tools, not dogmas

• Try simple classifiers first

• Better to have smart features and simple classifiers than simple features and smart classifiers

• Use increasingly powerful classifiers with more training data (bias-variance tradeoff)

Page 50: Image Categorization

Next class• Object category detection overview

Page 51: Image Categorization

Some Machine Learning References

• General– Tom Mitchell, Machine Learning, McGraw Hill, 1997– Christopher Bishop, Neural Networks for Pattern

Recognition, Oxford University Press, 1995

• Adaboost– Friedman, Hastie, and Tibshirani, “Additive logistic

regression: a statistical view of boosting”, Annals of Statistics, 2000

• SVMs– http://www.support-vector.net/icml-tutorial.pdf