Biomimetics Pattern Recognition aBiomimetics Pattern Recognition a

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Machine Thinking in ImageMachine Thinking in Image

Lab of Artificial Neural Networks & Machine Thinking in Image, Institute of Semiconductors, CAS

( 中科院半导体所神经网络与形象思维实验室 )

Wang Shoujue(王守觉 )

2004.6

1. Development of 1. Development of Information Information

sciences in recent sciences in recent five decadesfive decades

Comparison between 1950 and 2000

computing speed, storage capacity, computing speed, storage capacity, quality of intelligencequality of intelligence

computing speed : thousands billion calculation per second, corresponds to about 1012 times of human brain, as 100 times of total number of human being all over the world.

storage capacity : a 100G hard disk corresponds to all information included in a library with 100000 books.

quality of intelligence : not even comparable with an animal

aa 、、 Thinking in LogicThinking in Logic b b 、、 Thinking in ImageThinking in Image

Two kinds of thinking in human brain

3.14159265358… ?whole life paid for ‘’ calculating

Baby recognizes its mother

but doesn’t know 1+1=?

the Way to Solve the Image problemthe Way to Solve the Image problem

to solve image problem by

symbolic logic description

to solve image problem by connectionism computing ( artificial neural networks)

2. Discussion on a 2. Discussion on a Basic Problem of Basic Problem of

Information SciencesInformation Sciences

（（ 11 ）） What’s What’s InformationInformation

In digital world, any In digital world, any information should be described information should be described

as large amounts of digital as large amounts of digital numbersnumbers

a picture, a photo, a picture, a photo, a speech, a knowledge a speech, a knowledge

each of them corresponds each of them corresponds to a point in the High to a point in the High Dimensional SpaceDimensional Space

Basic general problem in Basic general problem in

information sciences ——information sciences ——

Point Set Analysis in the Point Set Analysis in the

High Dimensional SpaceHigh Dimensional Space

(2) A brief review of (2) A brief review of conventional concepts , conventional concepts , from point set analysis in from point set analysis in

the High Dimensional the High Dimensional SpaceSpace

signal in time domain corresponds to a point in high dimensional space

(x1,x2,……xn)

A signal in time domain—large amount of digital numbers — a point in the High Dimensional Space

x1 x5

nx

x

a point in Rn

Fourier Transformation

0 20 40 60 80 100-1

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0 20 40 60 80 100-1

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......

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sin, sin2, sin3, …...

cos, cos2, cos3, …...

O

“there are no more than n lines existed, which perpendicular to each

other, in n-dimensional space”

Nyquist Sampling Theorem Theorem

Principal Component Analysis

( P C A )

（（ 33 ）） high dimensional high dimensional geometrical concepts are geometrical concepts are useful for developing new useful for developing new algorithms for Point Sets algorithms for Point Sets

AnalysisAnalysis

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A new method to get A new method to get sharper picture from sharper picture from

a blur picturea blur picture

Original picture( blur )

Final picture( sharper )

blur sharper

3. 3. Biomimetics Pattern Biomimetics Pattern RecognitionRecognition ————

application of High Dimensional Geometricaapplication of High Dimensional Geometrical Point Set Analysis in pattern recognitionl Point Set Analysis in pattern recognition

(1) discussing a (1) discussing a basic conceptionbasic conception

What’s the job of What’s the job of Pattern RecognitionPattern Recognition

(2) The Conceptional Start Point of Biomimetics Pattern

Recognition

Pattern Recognition classification separation

（ conventional

Pattern Recognition ）

cognition ( Biomimetics Pattern Recognition )

（（ better close to the fact of human better close to the fact of human beingbeing ））

(3) Theoretical starting point of the Biomimetics Pattern Recognition

The Principle of HomologThe Principle of Homology-Continuity (PHC).y-Continuity (PHC).

The difference between two The difference between two samples of the same class samples of the same class must be gradually changed. must be gradually changed. So every sample in the So every sample in the gradually changing sequence gradually changing sequence between two samples, must be between two samples, must be belonging to the same class.belonging to the same class.

The Mathematical Description of PHC:

If A is a point set including all samples in class A in feature space, there must be a set B:

B={ x1, x2, x3, …, xn| x1= x, xn= y, n N,

ρ(xm, xm+1) <ε, ε> 0, n-1 m 1, m N } ,

B A

Conventional Pattern Recognition——oConventional Pattern Recognition——optimal classification of many classes ptimal classification of many classes

Biomimetics Pattern Recognition —— Biomimetics Pattern Recognition ——cognizing different classes one by one, cognizing different classes one by one, by the connectivity of samples in the saby the connectivity of samples in the sa

me classme class(point set analysis in the High Dimensio(point set analysis in the High Dimensio

nal Space)nal Space)

(4) Actual results of(4) Actual results of BiBiomimetics Pattern Reomimetics Pattern Recognitioncognition compared wi compared with SVM (Support Vectth SVM (Support Vect

or Machine )or Machine )

(a) Experiments on recognition of o(a) Experiments on recognition of omnidirectionally oriented rigid objectmnidirectionally oriented rigid object

s on a planes on a plane

objects for recognition objects for recognition

objects for rejection testing objects for rejection testing

procedure in experimentprocedure in experiment

number of training samples: number of training samples: 338 338 ~ ~ 169 169

totally for totally for 88 objects objects

testing sample set A: testing sample set A: 3200 samples for 8 3200 samples for 8

objects ( training samples included )objects ( training samples included )

testing sample set B: testing sample set B: 3200 samples for 8 3200 samples for 8

objects ( no training samples included )objects ( no training samples included )

testing sample set C: testing sample set C: 2400 samples for 6 2400 samples for 6

objects for correct rejection test objects for correct rejection test

（（ bb ）） human face human face recognizing recognizing

Olivetti Research Laboratory face database

40 persons, 10 pictures per each

ten pictures from one human face in ORL face database

35 persons, 3 pictures / each

105 pictures as training set

testing set A: remained 7 pictures per each of the 35 persons.

7 × 35 ＝ 245 pictures

testing set B: 10 pictures per each of the remained 5 persons.

10 × 5 ＝ 50 picturesfor correct rejection testing

Results comparison of different Results comparison of different recognition methodsrecognition methods

methods

correct recognition test

correct rejection test

testing set A

error rate

testing set B

error rate

Minimum Distance

（ RBF ）4.90% 22%

Support Vector Machine ( SVM)

1.64% 10%

Biomimetics PatterBiomimetics Pattern Recognition ( BPn Recognition ( BP

R )R )0.81% 2%

4. Tools forTools for point set point set analysis in the High Danalysis in the High D

imensional Spaceimensional Space

（ 1 ） High DimensionHigh Dimensionalal descriptive geometrydescriptive geometry

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（（ 22 ）） multi-weight neural netmulti-weight neural networks for high dimensional poiworks for high dimensional poi

nt set computing nt set computing

mathematicalmathematical model of neuron in the CASSANmodel of neuron in the CASSANN-II neurocomputerN-II neurocomputer

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Wi : DIRECTION weight

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mathematical model of a conventional neuron mathematical model of a conventional neuron

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Generalized mathematical model of Generalized mathematical model of an artificial neuronan artificial neuron

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Y = F { distance from X to a manifoldY = F { distance from X to a manifold }}

the equation of the manifoldthe equation of the manifold is as follows: is as follows:

Display in three Display in three dimension casedimension case

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in 100 dimensional feature space

if D2 ＝ D1

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V1 V2 times hundred billion billion billion( 1029 )

1

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D1L

5. Make MachineThinking in Image

Recognition of Imperfect Pictures

Experiment 1

For random Imperfection

0%

5% 10% 15% 20% 25%

30% 35% 40% 45% 50%

拒识率％

判别阈值

误识率％

拒识率％

误识率％

判别阈值

Experiment 2

For Imperfection in the middle

0% 4.35% 8.70% 13.04% 17.39% 21.74%

26.09% 30.43% 34.78% 39.13% 43.48% 47.83%

成片缺损比例

拒识率％

误识率％

判别阈值

拒识率％

误识率％

判别阈值

Experiment 3

For Imperfection on one side

0% 4.35% 8.70% 13.04% 17.39% 21.74%

26.09% 30.43% 34.78% 39.13% 43.48% 47.83%

成片缺损比例

拒识率％

误识率％

判别阈值

拒识率％

误识率％

判别阈值

6. Conclusion6. Conclusion(1) Geometrical method of point set analysis in thpoint set analysis in th

e High Dimensional Space may be a new tool e High Dimensional Space may be a new tool for making “ machine thinking in image” for making “ machine thinking in image”

(2)(2) Biomimetics Pattern Recognition ( BPR ), an aBiomimetics Pattern Recognition ( BPR ), an application of point set analysis in the High Dipplication of point set analysis in the High Dimensional Space, is much better than conventimensional Space, is much better than conventional pattern recognition such as SVM, RBF, etonal pattern recognition such as SVM, RBF, etc. c.

Thank you for Thank you for your attention!your attention!