CS558 COMPUTER VISIONLecture XI: Object Recognition (2)

Slides adapted from S. Lazebnik

OUTLINE

Object recognition: overview and history Object recognition: a learning based approach Object recognition: bag of features representation Object recognition: classification algorithms

BAG-OF-FEATURES MODELS

ORIGIN 1: TEXTURE RECOGNITION

Texture is characterized by the repetition of basic elements or textons

For stochastic textures, it is the identity of the textons, not their spatial arrangement, that matters

Julesz, 1981; Cula & Dana, 2001; Leung & Malik 2001; Mori, Belongie & Malik, 2001; Schmid 2001; Varma & Zisserman, 2002, 2003; Lazebnik, Schmid & Ponce, 2003

ORIGIN 1: TEXTURE RECOGNITION

Universal texton dictionary

histogram

Julesz, 1981; Cula & Dana, 2001; Leung & Malik 2001; Mori, Belongie & Malik, 2001; Schmid 2001; Varma & Zisserman, 2002, 2003; Lazebnik, Schmid & Ponce, 2003

ORIGIN 2: BAG-OF-WORDS MODELS Orderless document representation: frequencies of

words from a dictionary Salton & McGill (1983)

ORIGIN 2: BAG-OF-WORDS MODELS

US Presidential Speeches Tag Cloudhttp://chir.ag/phernalia/preztags/

Orderless document representation: frequencies of words from a dictionary Salton & McGill (1983)

ORIGIN 2: BAG-OF-WORDS MODELS

US Presidential Speeches Tag Cloudhttp://chir.ag/phernalia/preztags/

Orderless document representation: frequencies of words from a dictionary Salton & McGill (1983)

ORIGIN 2: BAG-OF-WORDS MODELS

US Presidential Speeches Tag Cloudhttp://chir.ag/phernalia/preztags/

Orderless document representation: frequencies of words from a dictionary Salton & McGill (1983)

1. Extract features

2. Learn “visual vocabulary”

3. Quantize features using visual vocabulary

4. Represent images by frequencies (counts) of “visual words”

BAG-OF-FEATURES STEPS

1. FEATURE EXTRACTION

Regular grid or interest regions

Normalize patch

Detect patches

Compute descriptor

Slide credit: Josef Sivic

1. FEATURE EXTRACTION

…

1. FEATURE EXTRACTION

Slide credit: Josef Sivic

2. LEARNING THE VISUAL VOCABULARY

…

Slide credit: Josef Sivic

2. LEARNING THE VISUAL VOCABULARY

Clustering

…

Slide credit: Josef Sivic

2. LEARNING THE VISUAL VOCABULARY

Clustering

…

Slide credit: Josef Sivic

Visual vocabulary

K-MEANS CLUSTERING• Want to minimize sum of squared Euclidean

distances between points xi and their nearest cluster centers mk

Algorithm:• Randomly initialize K cluster centers• Iterate until convergence:

Assign each data point to the nearest center Recompute each cluster center as the mean of all

points assigned to it

k

ki

ki mxMXDcluster

clusterinpoint

2),(

CLUSTERING AND VECTOR QUANTIZATION

• Clustering is a common method for learning a visual vocabulary or codebook Unsupervised learning process Each cluster center produced by k-means becomes

a codevector Codebook can be learned on separate training set Provided the training set is sufficiently

representative, the codebook will be “universal”

• The codebook is used for quantizing features A vector quantizer takes a feature vector and maps

it to the index of the nearest codevector in a codebook

Codebook = visual vocabulary Codevector = visual word

EXAMPLE CODEBOOK

…

Source: B. Leibe

Appearance codebook

ANOTHER CODEBOOK

Appearance codebook…

………

…

Source: B. Leibe

Yet another codebook

Fei-Fei et al. 2005

VISUAL VOCABULARIES: ISSUES

• How to choose vocabulary size? Too small: visual words not representative of all

patches Too large: quantization artifacts, overfitting

• Computational efficiency Vocabulary trees

(Nister & Stewenius, 2006)

SPATIAL PYRAMID REPRESENTATION Extension of a bag of features Locally orderless representation at several levels of resolution

level 0

Lazebnik, Schmid & Ponce (CVPR 2006)

Extension of a bag of features Locally orderless representation at several levels of resolution

SPATIAL PYRAMID REPRESENTATION

level 0 level 1

Lazebnik, Schmid & Ponce (CVPR 2006)

Extension of a bag of features Locally orderless representation at several levels of resolution

SPATIAL PYRAMID REPRESENTATION

level 0 level 1 level 2

Lazebnik, Schmid & Ponce (CVPR 2006)

SCENE CATEGORY DATASET

Multi-class classification results(100 training images per class)

CALTECH101 DATASET

http://www.vision.caltech.edu/Image_Datasets/Caltech101/Caltech101.html

Multi-class classification results (30 training images per class)

BAGS OF FEATURES FOR ACTION RECOGNITION

Juan Carlos Niebles, Hongcheng Wang and Li Fei-Fei, Unsupervised Learning of Human Action Categories Using Spatial-Temporal Words, IJCV 2008.

Space-time interest points

BAGS OF FEATURES FOR ACTION RECOGNITION

Juan Carlos Niebles, Hongcheng Wang and Li Fei-Fei, Unsupervised Learning of Human Action Categories Using Spatial-Temporal Words, IJCV 2008.

IMAGE CLASSIFICATION

• Given the bag-of-features representations of images from different classes, how do we learn a model for distinguishing them?

OUTLINE

Object recognition: overview and history Object recognition: a learning based approach Object recognition: bag of features representation Object recognition: classification algorithms

CLASSIFIERS Learn a decision rule assigning bag-of-features

representations of images to different classes

Zebra

Non-zebra

Decisionboundary

CLASSIFICATION Assign any input vector to one of two or more

classes Any decision rule divides an input space into

decision regions separated by decision boundaries

NEAREST NEIGHBOR CLASSIFIER

Assign the label of the nearest training data point to each test data point

Voronoi partitioning of feature space for two-category 2D and 3D data

from Duda et al.

Source: D. Lowe

For a new point, find the k closest points from a training data set.

The labels of the k points “vote” to classify the new point. Works well provided that there is lots of data and the

distance/similarity function is good.

k-Nearest Neighbors

k = 5

Source: D. Lowe

FUNCTIONS FOR COMPARING HISTOGRAMS

• L1 distance:

• χ2 distance:

• Quadratic distance (cross-bin distance):

• Histogram intersection (similarity function):

N

i

ihihhhD1

2121 |)()(|),(

N

i ihih

ihihhhD

1 21

221

21 )()(

)()(),(

ji

ij jhihAhhD,

22121 ))()((),(

N

i

ihihhhI1

2121 ))(),(min(),(

LINEAR CLASSIFIERS

• Find a linear function (hyperplane) to separate positive and negative examples

0:negative

0:positive

b

b

ii

ii

wxx

wxx

Which hyperplaneis best?

SUPPORT VECTOR MACHINES

• Find hyperplane that maximizes the margin between the positive and negative examples

C. Burges, A Tutorial on Support Vector Machines for Pattern Recognition, Data Mining and Knowledge Discovery, 1998

SUPPORT VECTOR MACHINES

• Find a hyperplane that maximizes the margin between the positive and negative examples

1:1)(negative

1:1)( positive

by

by

iii

iii

wxx

wxx

MarginSupport vectors

C. Burges, A Tutorial on Support Vector Machines for Pattern Recognition, Data Mining and Knowledge Discovery, 1998

Distance between point and hyperplane: ||||

||

w

wx bi

For support vectors, 1 bi wx

Therefore, the margin is 2 / ||w||

FINDING THE MAXIMUM MARGIN HYPERPLANE

1. Maximize the margin 2/||w||

2. Correctly classify all training examples:

Quadratic programming problem:

Minimize

Subject to yi(w·xi+b) ≥ 1

C. Burges, A Tutorial on Support Vector Machines for Pattern Recognition, Data Mining and Knowledge Discovery, 1998

wwT

2

1

1:1)(negative

1:1)( positive

by

by

iii

iii

wxx

wxx

FINDING THE MAXIMUM MARGIN HYPERPLANE• Solution:

i iii y xw

C. Burges, A Tutorial on Support Vector Machines for Pattern Recognition, Data Mining and Knowledge Discovery, 1998

Support vector

learnedweight

FINDING THE MAXIMUM MARGIN HYPERPLANE

• Solution:

b = yi – w·xi for any support vector

• Classification function (decision boundary):

• Notice that it relies on an inner product between the test point x and the support vectors xi

• Solving the optimization problem also involves computing the inner products xi · xj between all pairs of training points

i iii y xw

C. Burges, A Tutorial on Support Vector Machines for Pattern Recognition, Data Mining and Knowledge Discovery, 1998

bybi iii xxxw

• Datasets that are linearly separable work out great:

• But what if the dataset is just too hard?

• We can map it to a higher-dimensional space:

0 x

0 x

0 x

x2

NONLINEAR SVMS

Slide credit: Andrew Moore

• General idea: the original input space can always be mapped to some higher-dimensional feature space where the training set is separable:

Φ: x → φ(x)

NONLINEAR SVMS

Slide credit: Andrew Moore

• The kernel trick: instead of explicitly computing the lifting transformation φ(x), define a kernel function K such that

K(xi , xj) = φ(xi ) · φ(xj)

(To be valid, the kernel function must satisfy Mercer’s condition)

• This gives a nonlinear decision boundary in the original feature space:

NONLINEAR SVMS

bKybyi

iiii

iii ),()()( xxxx

C. Burges, A Tutorial on Support Vector Machines for Pattern Recognition, Data Mining and Knowledge Discovery, 1998

NONLINEAR KERNEL: EXAMPLE

• Consider the mapping ),()( 2xxx

22

2222

),(

),(),()()(

yxxyyxK

yxxyyyxxyx

x2

Polynomial kernel

KERNELS FOR BAGS OF FEATURES

• Histogram intersection kernel:

• Generalized Gaussian kernel:

• D can be L1 distance, Euclidean distance, χ2 distance, etc.

• A kernel function must be a similarity function.

N

i

ihihhhI1

2121 ))(),(min(),(

2

2121 ),(1

exp),( hhDA

hhK

J. Zhang, M. Marszalek, S. Lazebnik, and C. Schmid, Local Features and Kernels for Classifcation of Texture and Object Categories: A Comprehensive Study, IJCV 2007

SUMMARY: SVMS FOR IMAGE CLASSIFICATION

1. Pick an image representation (in our case, bag of features)

2. Choose a kernel function for that representation3. Compute the matrix of kernel values between all

pairs of training examples4. Feed the kernel matrix into your favorite SVM

solver to obtain support vectors and weights5. At test time: compute kernel values between your

test example and all support vectors, and combine them with the learned weights to yield the value of the final decision function

WHAT ABOUT MULTI-CLASS SVMS?

• Unfortunately, there is no “definitive” multi-class SVM formulation

• In practice, we have to obtain a multi-class SVM by combining multiple binary (two-class) SVMs

• One vs. others Training: learn an SVM for each class vs. the others Testing: apply each SVM to test example and assign

to it the class of the SVM that returns the highest decision value

• One vs. one Training: learn an SVM for each pair of classes Testing: each learned SVM “votes” for a class to

assign to the test example

SVMS: PROS AND CONS

• Pros Many publicly available SVM packages:

http://www.kernel-machines.org/software Kernel-based framework is very powerful, flexible SVMs work very well in practice, even with very

small training sample sizes

• Cons No “direct” multi-class SVM, must combine two-

class SVMs Computation, memory

During training time, must compute a matrix of kernel values between all pairs of examples ( training time >= O(n^2) )

Training SVMs can take a very long time for large-scale problems (actually kernel SVMs can typically handle ~100K training examples on a single machine)

SUMMARY: CLASSIFIERS

• Nearest-neighbor and k-nearest-neighbor classifiers L1 distance, χ2 distance, quadratic distance, histogram

intersection• Support vector machines

Linear classifiers Margin maximization The kernel trick Kernel functions: histogram intersection, generalized

Gaussian, pyramid match Multi-class

• Of course, there are many other classifiers out there Neural networks, boosting, decision trees, … Deep neural networks, convolutional neural networks:

jointly learning feature representation and classifiers

PROJECT #4Visual Recognition Challenge:

DATA SET:

Graz02 Bike, Cars, Person, None (background)

TRAIN/VALIDATION/TEST

Use the Train dataset to train the classifiers for recognizing the three object categories;

Use the validation dataset to tune any parameters;

Fix the parameters you tuned and report your final classification accuracy on the test images.

FEATURE EXTRACTION

Sample fixed-size image patches on regular grid of the image. You can use a single fixed image patch size, or have several different sizes.

Sample random-size patches at random locations

Sample fixed-size patches around the feature locations from, e.g., your own Harris corner detector or any other feature detector you found online. Note if you used code you downloaded online, please cite it clearly in your report.

FEATURE DESCRIPTION

It is recommended that you implement the SIFT descriptor described in the lecture slides for each image patch you generated. But you may also use other feature descriptors, such as the raw pixel values (bias-gain normalized). You don’t need to make your SIFT descriptor to be rotation invariant if you don’t want to do so.

DICTIONARY COMPUTATION

Run K-means clustering on all training feature descriptors to learn the dictionary. Setting K to be 500-1000 should be sufficient. You may experiment with different sizes.

IMAGE REPRESENTATION

Given the features extracted from any training/validation/test image, quantize each feature to its closest codevector in the dictionary. For each image, you can accumulate a histogram by counting how many features are quantized to each code in the dictionary. This is your image representation (bag-of-features).

CLASSIFIER TRAINING

Given the histogram representation of all images, you may use a k-NN classifier or any other classifier you wish to use. If you wanted to push for recognition, you mean consider training an SVM classifier. Please feel free to find any SVM library to train your classifier. You may use the Matlab Toolbox provided in this link (http://theoval.cmp.uea.ac.uk/~gcc/svm/toolbox/).

RECOGNITION QUALITY

After you train the classifier, please report recognition accuracy on the test image set. It is the ratio of images you recognize correctly. Please also generate the so-called confusion matrix to enumerate, e.g., how many images you mis-classify from one category to another category. You will need to report results from both the validation and test datasets to see how well your algorithm generalizes to test data.

IMPORTANT NOTE

Please follow the train/validation/test protocol and don’t heavily tune parameters on the test dataset. You will be asked to report recognition accuracy on both the validation and test datasets. Tuning parameters on the test dataset is considered to be cheating, and not allowed.