Cao Mengfei

2009.7

*Cluster Spectrum*

*Correspondence*

Semantic Analysis

Recognition

Ⅰ.Warm-ups:

Ⅱ. abstract

Ⅲ. a special example and its counterpart

Ⅳ. extension

Recognition: based on feature but what if what you get

is not what you really want?

Semantic Analysis: various methods; however it will be great when something happens like this:

Warm-ups:

“Hierarchical Semantics of Objects ”

----ICCV2005

Related saying: " 一般的点模式匹配问题是模式识别中的一个有名的难题 , 人们对一般的点模式匹配问题提出过很多的算法 ,像 Sanjay Ranade 等人的松弛算法、 Shih-hsu Chang 等人的基于二维聚类的快速算法、 Zsolt Miklós 等人的三角匹配的算法、 Xudong Jiang 等人[9] 的基于局部和全局结构的匹配算法 ." 摘抄自 ------自动指纹识别中的图像增强和细节匹配算法

My feeling: search for the pairwise through similarities of objective-data

About Correspondence Matching(1):

according to the ways of making use of the similarites:

About Correspondence Matching(2):

Direct Comparison •Distance of feature, similarity of inter_data instead of intra_data•eg. enumerate

Consistency Constraints

•Groupwise of Pairwise based on distance•Groupwise of Pairwise based on more sophisticated geometric properties

j

ij’

i’

Compare the Similarity: (i-i’),(i-j’),(j-i’),(j-j’)

j

ij’

i’

Compare Consistency: (i-j) v.s. (i’-j’)

Ⅰ.

Ⅱ.

?calculation

accuracy

+

（ 1 ） to find out the outliers in the first set;

（ 2 ） to find out the outliers in the second set;robust to the outliers

（ 3 ） to find out all the correct correspondent pairwises.

robust to the noise Affine transformation, translation, scalar

transformation illumination, rotation, diversity``````

issues to be taken into accounts:

Spectrum of Matrix: Magical Mathematical Object-properties, instead of pure Consciousness.

objective, descriptive, essential

Based on eigen values & eigen vectors.

Related saying: music is dynamic, while score is static;movement is dynamic, while law is static

About spectral method:

Graph

Adjacency Matrix

Spectrum

Model the reality

Calculation, Accuracy

image

matrixgraph

Advantages:

Based on math and reality

Basic problem in the field of pattern recognition

Various methods used in various situations

after all, to cluster is to aggregate the objects with similar properties

how to combine it to the former issues?

About clustering:

Marius Leordeanu and Martial Hebert International Conference of Computer Vision (ICCV), October, 2005

“A Spectral Technique for Correspondence Problems Using Pairwise Constraints”

PhD Student, RIVision and Autonomous Systems Center (VASC)The Robotics Institute

ProfessorEfficient techniques for object/category recognition Use of contextual information, in particular 3-D geometry from images, for scene analysis Detection, tracking, and prediction in dynamic environments

A Spectral Technique for Correspondence Problems Using Pairwise Constraints:

Based on spectral theory, build the

wanted matrix(similarity)

Spectral Clustering

Get the Correspondence

j

ij’

i’

Compare the Similarity: (i-i’),(i-j’),(j-i’),(j-j’)

j

ij’

i’

Compare Consistency: (i-j) v.s. (i’-j’)

Ⅰ.

Ⅱ.

?calculation

accuracy

+

A Spectral Technique for Correspondence Problems Using Pairwise Constraints:

Based on spectral theory, build the

wanted matrix(similarity)

Spectral Clustering

Get the Correspondence

(if)Has a main strongly connected cluster formed by

the correctassignments that tend to establish agreement links

• first find the principal eigenvector of M

incorrect assignments outside of the cluster or weakly connected to it,

which do not form strongly connected clusters due to their small probability of establishing agreement

links and random, unstructured way in which

they form these links.

• keep rejecting the assignments of low association

Fundamental thoughts:

the graph associated with matrix M

main clusters

linprog-based method:

Matrix H represents the cost matrix of the individual correspondence (the factor ), vector x represent the corresponding indicatory correspondence. Anyway, x’*H*x stands for the correspondence-cost; thus the thing is that , as for the value, the smaller, the better, which comes to the problem of Integer Quadratic Programming--NP-complete… thus linear I.P.

University of California,

Berkeley

 

CVPR

 

geometric distortion between pairs of

corresponding feature points

edge feature

how similar feature points are to their corresponding

feature points

how much the spatial arrangement

of the feature points is changed.

Comparison (1):

occlusion and clutter

Ⅰ. What’s special?

Compared to the former

Ⅱ. Emulation:1. deformations using white noise

Comparison (2):

Ratio of time ≈ 4 : 1

2. considering the scalar and translationtheoretically ， translation invariant is

necessaryAs for the scalar transformation:Spectral:

Comparison (3):

Comparison (4): translationL

eft: sp

ectra

l righ

t: linp

rog

Comparison (5): scaleU

pp

er: sp

ectra

l dow

n: lin

pro

g

3. robust to the outliers

Comparison (6):

15-data, 1-15

outliers each

30 times sampling

σ=2

Red: linprog

method,

4235s

Blue: spectral method, 13650s

More experiments:

“our method is orders of magnitude faster then linprog: over 400 times faster on 20 points problem sets (average time of 0.03 sec. vs 13 sec) and over650 faster on 30 points problem sets (0.25 sec. vs 165 sec.), on a 2.4 GHz Pentium computer”

Ⅲ. Practice:

Comparison (7):Spectral Clustering Based

Comparison (8):Linprog-based recognition:

Extension:

Recognizing objects from low resolution images:

Providing the semantic layout of the scene, learnt hSOs can have several useful applications such as compact scene representation for scene category classification and providing context forenhanced object detection:

Ⅰ.

Ⅱ.

Extension(2): Combined with direction:Affine transform

j

ij’

k

i’k’

What tools to use, how to use(spectral clustering)

Single parameter

properties

Represent the

relationship

among data

Ⅲ.

Ⅳ.

Thanks a lot ...