Object Recognition

So what does object recognition involve?

Verification: is that a bus?

Detection: are there cars?

Identification: is that a picture of Mao?

Object categorization

sky

building

flag

wallbanner

bus

cars

bus

face

street lamp

Challenges 1: view point variation

Michelangelo 1475-1564

Challenges 2: illumination

slide credit: S. Ullman

Challenges 3: occlusion

Magritte, 1957

Challenges 4: scale

Challenges 5: deformation

Xu, Beihong 1943

Challenges 7: intra-class variation

Two main approaches

Part-basedGlobal sub-window

Global Approaches

x1 x2 x3

Vectors in high-dimensional space

Aligned images

x1 x2 x3

Vectors in high-dimensional space

Global Approaches

Training

Involves some dimensionality

reduction

Detector

– Scale / position range to search over

Detection

Detection– Scale / position range to search over

Detection– Scale / position range to search over

Detection– Combine detection over space and scale.

PROJECT 1

• Turk and Pentland, 1991• Belhumeur et al. 1997• Schneiderman et al. 2004• Viola and Jones, 2000• Keren et al. 2001• Osadchy et al. 2004

• Amit and Geman, 1999• LeCun et al. 1998• Belongie and Malik, 2002

• Schneiderman et al. 2004• Argawal and Roth, 2002• Poggio et al. 1993

Object DetectionProblem:

Locate instances of object category in a given image. Asymmetric classification

problem!

Background Object (Category)

Very large Relatively small

Complex (thousands of categories)

Simple (single category)

Large prior to appear in an image

Small prior

Easy to collect (not easy to learn from examples)

Hard to collect

All images

Intuition

Denote H to be the acceptance region of a classifier. We propose to minimize the

Pr(All images) ( Pr(bkg)) in H except for the object samples.

Background

Object class

All images Background

We have a prior on the distribution of all natural images

Image smoothness measureLower probability

Lower probability

Distribution of Natural Images – Boltzmann distribution

dxdyIII yx22exp)Pr(

lklkxlk

,

2,

22exp)xPr(

In frequency domain:

Antiface

Lower probability

Lower probability

Ω

d

object images

Acceptance region

Main Idea Claim: for random natural images viewed as

unit vectors,

yx, y x,

is large on average.is large on average.

– for all positive classxd , x

– d is smooth

xd , is large on average for random natural image.

Anti-Face detector is defined as a vector d satisfying:

Discrimination

x

xxd ,

xd ,

x

SMALL

LARGE

If x is an image and is a target class:

Cascade of Independent Detectors

1d

2d

3d

7 inner products

4 inner products

Example

Samples from the training set

4 Anti-Face Detectors

4 Anti-face Detectors4 Anti-face Detectors

Eigenface method with the subspace of dimension 100

Ensemble Learning• Bagging

– reshuffle your training data to create k different training sets and learn f1(x),f2(x),…,fk(x)

– Combine the k different classifiers by majority voting

fFINAL(x) =sign[ 1/k fi(x) ]

• Boosting– Assign different weights to training samples in a “smart”

way so that different classifiers pay more attention to different samples

– Weighted majority voting, the weight of individual classifier is proportional to its accuracy

– Ada-boost (1996) was influenced by bagging, and it is superior to bagging

Boosting - Motivation

• It is usually hard to design an accurate classifier which generalizes well

• However it is usually easy to find many “rule of thumb” weak classifiers– A classifier is weak if it is only slightly better

than random guessing

• Can we combine several weak classifiers to produce an accurate classifier?– Question people have been working on since

1980’s

Ada Boost• Let’s assume we have 2-class classification

problem, with yi -1,1• Ada boost will produce a discriminant function:

T

ttt xfxg

1

where ft(x) is the “weak” classifier

The final classifier is the sign of the discriminant function, that is ffinal(x) = sign[g(x)]

Idea Behind Ada Boost

• Algorithm is iterative• Maintains distribution of weights over the training

examples• Initially distribution of weights is uniform• At successive iterations, the weight of misclassified

examples is increased, forcing the weak learner to focus on the hard examples in the training set

PROJECT 2

Training with small number of Examples

• Majority of object detection method require a large number of training examples.

• Goal: to design a classifier that can learn from a small number of examples

• Use small number in a existing classifiers

Overfiting: learns by hart the training examples, performs poor on unseen examples.

Linear SVM

Maximal margin

Enough training data

Class 1

Class 2

Not Enough training data

Linear SVM –Detection Task

Class 1

Class 2

0 xwx b

MM with prior

0xwx B b

margin wide3)

H samples postive )2

Hin images) natural(min)1

P

Object class

PROJECT 4

Part-Based Approaches

ObjectObject

Bag of ‘words’Bag of ‘words’

Constellation of partsConstellation of parts

Of all the sensory impressions proceeding to the brain, the visual experiences are the dominant ones. Our perception of the world around us is based essentially on the messages that reach the brain from our eyes. For a long time it was thought that the retinal image was transmitted point by point to visual centers in the brain; the cerebral cortex was a movie screen, so to speak, upon which the image in the eye was projected. Through the discoveries of Hubel and Wiesel we now know that behind the origin of the visual perception in the brain there is a considerably more complicated course of events. By following the visual impulses along their path to the various cell layers of the optical cortex, Hubel and Wiesel have been able to demonstrate that the message about the image falling on the retina undergoes a step-wise analysis in a system of nerve cells stored in columns. In this system each cell has its specific function and is responsible for a specific detail in the pattern of the retinal image.

sensory, brain, visual, perception,

retinal, cerebral cortex,eye, cell, optical

nerve, imageHubel, Wiesel

China is forecasting a trade surplus of $90bn (£51bn) to $100bn this year, a threefold increase on 2004's $32bn. The Commerce Ministry said the surplus would be created by a predicted 30% jump in exports to $750bn, compared with a 18% rise in imports to $660bn. The figures are likely to further annoy the US, which has long argued that China's exports are unfairly helped by a deliberately undervalued yuan. Beijing agrees the surplus is too high, but says the yuan is only one factor. Bank of China governor Zhou Xiaochuan said the country also needed to do more to boost domestic demand so more goods stayed within the country. China increased the value of the yuan against the dollar by 2.1% in July and permitted it to trade within a narrow band, but the US wants the yuan to be allowed to trade freely. However, Beijing has made it clear that it will take its time and tread carefully before allowing the yuan to rise further in value.

China, trade, surplus, commerce,

exports, imports, US, yuan, bank, domestic,

foreign, increase, trade, value

Bag of ‘words’ analogy to documents

Interest Point Detectors

• Basic requirements:– Sparse– Informative – Repeatable

• Invariance– Rotation– Scale (Similarity)– Affine

Popular Detectors

Scale Invariant

Affine Invariant

Harris-Laplace Affine

Difference of Gaussians Laplace of Gaussians Scale Saliency (Kadir-Braidy)

Harris-Laplace

Difference of Gaussians

Affine

Laplace of Gaussians

Affine

Affine Saliency (Kadir-Braidy)

The are many others…

See:

1) “Scale and affine invariant interest point detectors” K. Mikolajczyk, C. Schmid,

IJCV, Volume 60, Number 1 - 2004

2) “A comparison of affine region detectors”, K. Mikolajczyk, T. Tuytelaars, C. Schmid, A. Zisserman, J. Matas, F. Schaffalitzky, T. Kadir and L. Van Gool, http://www.robots.ox.ac.uk/~vgg/research/affine/det_eval_files/vibes_ijcv2004.pdf

Representation of appearance:Local Descriptors

• Invariance– Rotation– Scale – Affine

• Insensitive to small deformations

• Illumination invariance– Normalize out

SIFT – Scale Invariant Feature Transform

• Descriptor overview:– Determine scale (by maximizing DoG in scale and in space),

local orientation as the dominant gradient direction.Use this scale and orientation to make all further computations invariant to scale and rotation.

– Compute gradient orientation histograms of several small windows (128 values for each point)

– Normalize the descriptor to make it invariant to intensity change

David G. Lowe, "Distinctive image features from scale-invariant keypoints,“ International Journal of Computer Vision, 60, 2 (2004), pp. 91-110.

Feature Detection and Representation

Normalize patch

Detect patches[Mikojaczyk and Schmid ’02]

[Matas et al. ’02]

[Sivic et al. ’03]

Compute SIFT

descriptor

[Lowe’99]

Slide credit: Josef Sivic

…

Feature Detection and Representation

Codewords dictionary formationCodewords dictionary formation

…

Codewords dictionary formationCodewords dictionary formation

Vector quantization

…

Slide credit: Josef Sivic

Codewords dictionary formationCodewords dictionary formation

Fei-Fei et al. 2005

Image patch examples of codewordsImage patch examples of codewords

Sivic et al. 2005

Vector X

Representation

Learning

positive negative

SVM classifier

positive negative

SVM classification

SVM classification

Recognition

SVM(X)

Contains object

Vector X

Representation

Doesn’t contain object

PROJECT 3

Pros/Cons• Pros.

– Fast and simple. – Insensitive to pose variation.– No segmentation required during learning.

• Cons.– No localization.– Requires discriminative or no background.

• An object in an image is represented by a collection of parts, characterized by both their visual appearances and locations.

• Object categories are modeled by the appearance and spatial distributions of these characteristic parts.

Constellation of Parts

The correspondence problem• Model with P parts• Image with N possible locations for each part

• NP combinations!!!Slide credit: Rob Fergus

How to model location?

• Explicit: Probability density functions

• Implicit: Voting scheme

• Probability densities– Continuous (Gaussians)– Analogy with springs

• Parameters of model, and – Independence corresponds to zeros in

Explicit shape model

Slide credit: Rob Fergus

Different graph structures

1

3

4 5

6

2

1

3

4 5

6

2

Fully connected Star structure

1

3

4

5

6

2

Tree structure

O(N6) O(N2) O(N2)

• Sparser graphs cannot capture all interactions between parts

Slide credit: Rob Fergus

Implicit shape model

Spatial occurrence distributionsx

y

s

x

y

sx

y

s

x

y

s

Probabilistic Voting

Interest PointsMatched Codebook Entries

Recognition

Learning• Learn appearance codebook

– Cluster over interest points on training images

• Learn spatial distributions– Match codebook to training images– Record matching positions on object– Centroid is given

• Use Hough space voting to find object • Leibe and Schiele ’03,’05

Slide credit: Rob Fergus

Pros/Cons

• Pros– Principle modeling– Models appearance and shape– Provides localization

• Cons– Computationally expensive – Small number of parts (learning on

unsegmented images) or requires bounding box during learning.

Week Shape Model

• Model parts arrangements

• Allows many parts but the model is computationally effective

• context distributions – see each part in the context of other parts.

PROJECT 4