Object Recognizing

Object Classes

Individual Recognition

Object parts

Headlight

Window

Door knob

Back wheel

Mirror

Front wheel Headlight

Window

Bumper

Class Non-class

Class Non-class

Unsupervised Training Data

Features and Classifiers

Same features with different classifiersSame classifier with different features

Generic Features

Simple (wavelets) Complex (Geons)

Class-specific Features: Common Building Blocks

Mutual information

H(C) when F=1 H(C) when F=0

I(C;F) = H(C) – H(C/F)

F=1 F=0

H(C)

))(()()( cPLogcPcH

Mutual Information I(C,F)

Class: 1 1 0 1 0 1 0 0

Feature: 1 0 0 1 1 1 0 0

I(F,C) = H(C) – H(C|F)

Optimal classification features

• Theoretically: maximizing delivered information minimizes classification error

• In practice: informative object components can be identified in training images

Mutual Info vs. Threshold

0.00 20.00 40.00

Detection threshold

Mu

tu

al

Info

forehead

hairline

mouth

eye

nose

nosebridge

long_hairline

chin

twoeyes

Selecting Fragments

Adding a New Fragment(max-min selection)

?

MIΔ

MI = MI [Δ ;class] - MI [ ;class ]Select: Maxi Mink ΔMI (Fi, Fk)

)Min. over existing fragments, Max. over the entire pool(

);(),;(min);(),;( jjiij

i FCMIFFCMIFCMIFFCMI

Horse-class features

Car-class features

Pictorial features Learned from examples

Star model

Detected fragments ‘vote’ for the center location

Find location with maximal vote

In variations, a popular state-of-the art scheme

Fragment-based Classification

Fergus, Perona, Zisserman 2003Agarwal, Roth 2002Ullman, Sali 1999

Variability of Airplanes Detected

Recognition Features in the Brain

Class-fragments and Activation

Malach et al 2008

EEG

ERP

FACE FEATURES

milliseconds0 200 400 600 0 200 400 600

milliseconds

Left Hemisphere Right Hemisphere

Posterior-Temporal sites

FACE FEATURES

milliseconds0 200 400 600 0 200 400 600

milliseconds

Left Hemisphere Right Hemisphere

Posterior-Temporal sites

MI 1— MI 2— MI 3— MI 4— MI 5—

Harel, Ullman,Epshtein, Bentin Vis Res 2007

Bag of words

ObjectObject Bag of ‘words’Bag of ‘words’

Bag of visual words A large collection of image patches

–

1.Feature detection 1.Feature detection and representationand representation

•Regular grid– & VogelSchiele ,2003

–Fei- ,Fei & Perona2005

Generate a dictionary using K-means clustering

Each class has its words historgram

–

–

–

Limited or no GeometrySimple and popular, no longer state-of-the art .

Classifiers

SVM – linear separation in feature space

Optimal Separation

SVM

Find a separating plane such that the closest points are as far as possible

Advantages of SVM :

Optimal separation Extensions to the non-separable case: Kernel SVM

Separating line: w ∙ x + b = 0 Far line: w ∙ x + b = +1Their distance: w ∙ ∆x = +1 Separation: |∆x| = 1/|w|Margin: 2/|w|

0+1

-1 The Margin

Max Margin Classification

)Equivalently, usually used

How to solve such constraint optimization ?

The examples are vectors xi

The labels yi are +1 for class, -1 for non-class

Using Lagrange multipliers :

Using Lagrange multipliers: Minimize LP =

With αi > 0 the Lagrange multipliers

Minimizing the Lagrangian

Minimize Lp :

Set all derivatives to 0:

Also for the derivative w.r.t. αi

Dual formulation: Maximize the Lagrangian w.r.t. the αi and the above two conditions.

Solved in ‘dual’ formulation

Maximize w.r.t αi :

With the conditions:

Put into Lp

W will drop out of the expression

Dual formulation

Mathematically equivalent formulation: Can maximize the Lagrangian with respect to the αi

After manipulations – concise matrix form :

SVM: in simple matrix form

We first find the α. From this we can find: w, b, and the support vectors.

The matrix H is a simple ‘data matrix’: Hij = yiyj <xi∙xj>

Final classification: w∙x + b ∑αi yi <xi x> + b

Because w = ∑αi yi xi Only <xi x> with support vectors are used

DPM Felzenszwalb

• Felzenszwalb, McAllester, Ramanan CVPR 2008. A Discriminatively Trained, Multiscale, Deformable Part Model

• Many implementation details, will describe the main points.

HoG descriptor

HoG Descriptor

Dallal, N & Triggs, B. Histograms of Oriented Gradients for Human Detection

Using patches with HoG descriptors and classification by SVM

Person model: HoG

Object model using HoG

A bicycle and its ‘root filter ’The root filter is a patch of HoG descriptor Image is partitioned into 8x8 pixel cells In each block we compute a histogram of gradient orientations

The filter is searched on a pyramid of HoG descriptors, to deal with unknown scale

Dealing with scale: multi-scale analysis

A part Pi = (Fi, vi, si, ai, bi) .

Fi is filter for the i-th part, vi is the center for a box of possible positions for part i relative to the root position, si the size of this box

ai and bi are two-dimensional vectors specifying coefficients of a quadratic function measuring a score for each possible placement of the i-th part. That is, ai and bi are two numbers each, and the penalty for deviation ∆x, ∆y from the expected location is a1 ∆ x + a2 ∆y + b1 ∆x2 + b2 ∆y2

Adding Parts

Bicycle model: root, parts, spatial map

Person model

The full score of a potential match is:  ∑ Fi ∙ Hi + ∑ ai1 xi + ai2 yi

+ bi1xi2 + bi2yi

2  

Fi ∙ Hi is the appearance part

xi, yi, is the deviation of part pi from its expected location in the model. This is the spatial part.

Match Score

search with gradient descent over the placement. This includes also the levels in the hierarchy. Start with the root filter, find places of high score for it. For these high-scoring locations, each for the optimal placement of the parts at a level with twice the resolution as the root-filter, using GD.

Final decision β∙ψ > θ implies class

Recognition

Essentially maximize ∑Fi Hi + ∑ ai1 xi + ai2 y + bi1x2 + bi2y2

Over placements (xi yi)

‘Pascal Challenge’ Airplanes

Obtaining human-level performance ?

All images contain at least 1 bike

Bike Recognition