Ke Chen1, Shaogang Gong1, Tao Xiang1, Chen Change Loy2

1. Queen Mary, University of London2. The Chinese University of Hong Kong

VGG reading group presentation by Minh Hoai

Cumulative Attribute Space for Age and Crowd Density Estimation

Tasks

How old are they?

How many people?

What is the head angle?

A Regression FrameworkInput images

AAM feature

Segment feature

Edge feature

Texture feature

Feature extraction

Features Label space

Label (age, count)Learn the mapping

Regression

Data distribution of FG-NET Dataset

Challenge – Sparse and Unbalanced data

Data distribution of UCSD Dataset

Challenge – Sparse and Unbalanced data

Proposed Approach

Solution:• Attribute Learning can address data sparsity problem --

Exploits the shared characteristics between classesHas sematic meaning

Question to address:• How to exploit cumulative dependent nature of labels in

regression?

…… …… ……

Age 20 Age 21 Age 60

Cumulative Attribute

Age 20

1

1

0

1

…20

0…0

the rest

Cumulative attribute (dependent)

Vs.

0

1

…

20th

0…

0

Non-cumulative attribute (independent)

0

0

Limitation of Non-cumulative Attribute

Age 200

1

…

20th

0

…0

Age 60

60th0

…

0

0

0

1

…

0

…

0

0…0

0

21st

0

1

…

0

…

0

0

0

0

Age 21

Age 21

Advantages of Cumulative Attribute

Age 20

1

1

0

1

…20

0

…0

the rest

Age 60

1

1

1

…60

0…

0

1

0

… 1…1 attribute changes

1

1…21

0

…

0

1

1

0

40 attributes change

Proposed Framework

xiFeature vector (e.g., intensity)

yiLabel

(e.g., age)

1

1

1

… …0

0

aiCumulative

attribute

yi

1

2

The task

Regressor Regressor

Proposed Framework

xiFeature vector (e.g., intensity)

yiLabel

(e.g., age)

1

1

1

… …0

0

aiCumulative

attribute

yi

1

2

Our task

Regressor Regressor

How are these regressors learned?

Can use any regression method: Support Vector Regression, Ridge Regression

See next slide!

Regressor for Cumulative Attributes

Regularization Regression error

# of training dataCumulative

attribute Image feature

vectorParameters

to learn

Closed-form solution:

Experiments

Baseline Methods and Name Abbreviation

xiFeature vector

yiLabel

Cumulative attributes

Non-Cumulative attributes

Support Vector Regression (SVR)

SVR

SVR

CA-SVR

NCA-SVR

…1 1 0 0…1

1 2 yi

…1 0 0…00

1 2 yi

Cumulative (CA) vs. Non-cumulative (NCA)

Age Estimation

Mean absolute error(lower is better)

Percentage of prediction within 5 years(higher is better)

Cumulative (CA) vs. Non-cumulative (NCA)

Crowd Counting

Mean absolute error(lower is better)

Mean squared error(lower is better)

Mean deviation error(lower is better)

Crowd Counting Results

CA-RR: our method; LSSVR: Suykens et al, IJCNN, 2001; KRR: An et al, CVPR, 2007; RFR: Liaw et al, R News, 2002; GPR: Chan et al, CVPR, 2008; RR: Chen et al, BMVC, 2012;

Based on regression

Proposed method, RR: Ridge Regression

Ridge Regression without attributes

Age Estimation Results

CA-SVR: our method; AGES: Geng et al, TPAMI, 2007; RUN: Yan et al, ICCV, 2007; Ranking: Yan et al, ICME, 2007; RED-SVM: Chang et al, ICPR, 2010; LARR: Guo et al, TIP, 2008; MTWGP: Zhang et al, CVPR, 2010; OHRank: Chang et al, CVPR, 2011; SVR: Guo et al, TIP, 2008;

Proposed method, SVR: Support Vector Regression

Not based on regression

What is OHRank?

OHRank - Ordinal Hyperplanes Ranker

SVM score for older than k

Delta 0/1 function

This is 104 slower than closed-form solution of regression

Robustness Against Sparse and Unbalanced Data

Age Estimation

Crowd Counting

(Effects of removing random/certain label groups)

Feature Selection by Attributes

Shape plays a more important role than texture for younger ages.

Summary

• Has a simple and neat idea • Exploits cumulative dependent nature of label space• Addresses sparse and unbalanced data problem

Support Vector Regression

Datasets