NOISEPROOF EDGE DETECTOR NOISEPROOF EDGE DETECTOR

ON BASE OF NEURON NET ON BASE OF NEURON NET

Alex Astapkovitch,Alex Astapkovitch, Head of the Student Design CentHead of the Student Design Centerer

State University of Aerospace InstrumentationState University of Aerospace InstrumentationSaint-Petersburg,RussiaSaint-Petersburg,Russia

20102010

Student research project Phoenix-3

STUDENT RESEARCH PROJECTS “Phoenix-X” HISTORYSTUDENT RESEARCH PROJECTS “Phoenix-X” HISTORY

Real robots:Real robots:

PHOENIX-XPHOENIX-X

Virtual robots:Virtual robots:

2006 - 20072006 - 2007 2007 - 20082007 - 2008 2008 - 20092008 - 2009 20102010

SOFA-2009Virtual robotbenchmark

model

Neuron net Noise proofEdge Detector

- Distant immobilizer;- Video system;

- Details on site guap.ru/english version/student design center

PHOENIX-X PHILOSOPHY

•Vision system is necessary part of most modern robot ;

•Edge detector is a part of robot vision system ;

LEGEND OF PHOENIX-3 PROJECT:Autonomic robot Phoenix-3 is designing to be able to patrol the determined area with the purpose of detection the centers of the flame. In case of the flame detection the robot should come nearer and use the onboard fire extinguisher to eliminate flaming. For orientation the video shock-proof camera with the rotary mechanism and a zoom lens is supposed to be used.

- The strategic goal of the “Phoenix-X” projects is a developing of the understanding of the supervised learning for the control system on base of a neuron net.

LAPLAS EDGE FILTERLAPLAS EDGE FILTER

NOISY_TEST

TEST_FIG

0 -1 0

-1 4 -1

0 -1 0

CLEAN IMAGE “DOG AND BALL”

LF_FIG_1

NOISY IMAGE (UNIFORM NOISE MODEL )

FILTERED

LF_NTEST_FIG

CONCEPT OF THE NEURON FILTER CONCEPT OF THE NEURON FILTER

GLOSSARYGLOSSARY

- “ - “ LEARNING” stands for the procedure of the determination LEARNING” stands for the procedure of the determination meanings of weight vector W and thresholds of activation function ;meanings of weight vector W and thresholds of activation function ;

““SUPERVISED LEARNINGSUPERVISED LEARNING “ stands for LEARNING with set of “ stands for LEARNING with set of “SAMPLES” ; “SAMPLES” ;

- SAMPLE is pair of frames: RAW FRAME and RESULTING FRAME ;

S1

S2

SNSEN

1

(S,W)

RESi,j

S1 S2 S3

S4 S5 S6

S7 S8 S9

FRAME

FILTER

Piecewise linear activation function

F(x)

THmin THmax

ONE STEP SUPERVIZED LEARNING PROCEDURE ONE STEP SUPERVIZED LEARNING PROCEDURE

S1(0,0) S2(0,0)

S1(0,1) S2(0,1) ................. 1……………………………….. S1(i,j) S2(i,j ) Snsen(i,j) 1

…………………………………

w1

w2

wnsen+1

F(0,0)

F(0,1)

…..

………F( i,j)………

* =

min F(w) = (SW - F, SW – F) + (W,W) w

Tichonov regularization provides stable solution

W = (ST S + E) –1 ST F

Weights calculation is one step procedure :

S * W = F - the bad posed problem for W

S - rectangular matrix, formed from RAW sample, F - sample vector ;

W - unknown neuron filter weight vector ;

MULTISAMPLE LEARNING PROCEDUREMULTISAMPLE LEARNING PROCEDURE

ONE STEP WEIGHT CALCULATION PROCEDURE W = (ST S + E) –1 ST F

Sample_1 : S1 F1

Sample_2 : S2 F2

S =

S1

S2 F =

F1

F2

MULTISAMPLE LEARNING

Let us introduce :Sek = ∑ Sk

TSk - experience matrix for k samplesFek = ∑ SkTFk - experience vector for k samples

Wk+1 = (Sek + S k+1T Sk+1 + E) –1 * (Fek+Sk+1

T Fk+1)

W1 = (S1T S1 + E) –1 * S1 T F1

W2 = (S1T S1 + S 2

T S2 + E) –1 * (S1T F1+S2

T F2)

ONE SAMPLE LEARNING

TWO SAMLE LEARNING

TWO SAMPLE CASE

LEARNING WITH HEURISTICLEARNING WITH HEURISTIC

50 50 50 50 50 50

50 50 50 50 50 5050 50 250 250 250 25050 50 250 250 250 25050 50 250 250 250 250

RESULTING FRAME is LAPLAS FILTERING OF RAW FRAME

SAMPLE_1 RAW FRAME

TEST OF THE LEARNING PROCEDURERAW FRAME : NOISY_REC1RES FRAME : LAPLAS FILTERED NOISY FRAME

LF_CLEAN_REC1CLEAN_REC1

NOISY_REC1 LF_NOISY_REC1

LN_WEIGTHS

W1_L0

W1_L3

W1_L6

W1_L1

W1_L4

W1_L7

W1_L2

W1_L5

W1_L8

1.269 106

1

1.269 106

1

4

1

1.269 106

1

1.269 106

LN_WEIGHTS_CONST W1_L9

2.392 1013

0 0 0 0 0 0

0 0 -200 -200 -200 -2000 -200 400 200 200 2000 -200 200 0 0 00 -200 200 0 0 00 -200 200 0 0 0

-100*100 bmp artificially formed sample was used;

- 10th sensor of constant part was added;

NEURONLIKE LAPLAS EDGE FILTER NEURONLIKE LAPLAS EDGE FILTER

NOISY_TESTTEST_FIG

LF_NFIG_1

CLEAN AND NOISY BMP IMAGE “DOG AND BALL”

LF_FIG_1

FILTERING WITH PURE LAPLAS

THmin = 60

- UNIFORM NOISE MODEL ;

- NOISE AMPLITUDE 60 ;

- DOG BODY AMPLITUDE 150 ;

LF_NTEST_FIG

THmin = -20

NEURONLIKE LAPLAS EDGE FILTER WITH THRESHOLDS

LF_NFIG_1

NEURON “LINEAR” FILTER LEARNINGNEURON “LINEAR” FILTER LEARNING

WHAT LENGTH OF FILTER HAS TO BE USED ?

Due to symmetry conditions - 3*3 neuron filter has the 3 free weights - 5*5 neuron filter has the 3+3 = 6 free weights - 7*7 neuron filter has the 6+4 = 10 free weights

WHAT THE SAMPLE SET HAS TO BE USED ?

HOW MUCH SAMPLES HAVE TO BE USED?

- HAND MADE BORDER WITH

REGULATED THICNESS (here is 2);

- LAPLAS, SOBEL, CANNY FILTERED

BORDERS ;

CLEAN_REC1 BORDER_REC1 NOISY_REC1

CLEAN_BAL1 BORDER_BAL1 NOISY_BAL1

- Rectangular, cycles …….? ;

- Mixed set of samples …..?

Experiments with supervised earning

NOISY_REC1 LF_CLEAN_REC1 BORDER_REC1

SAMPLES SET

NOISY_BAL1BORDER_BAL1

LF_CLEAN_BAL1

LAPLAS BORDERS

HAND MADE BORDERS

NOISY FRAMES

-5*5 neuron is learned with

different samples;

- neuron filter is tested with

noisy ”DOG AND BALL” ;

- low threshold is selected

by “hand” ;

NUMERICAL EXPERIMENTS - I

H51

0.155

0.067

0.07

0.086

0.136

0.07

9.212 103

0.169

0.013

0.059

0.084

0.17

0.376

0.155

0.091

0.075

6.329 103

0.175

6.182 103

0.065

0.139

0.079

0.083

0.077

0.152

H52

0.105

0.086

0.018

0.084

0.101

0.071

0.023

0.146

0.019

0.064

2.54 103

0.149

0.533

0.136

3.808 103

0.075

0.027

0.15

0.013

0.071

0.099

0.085

9.57 103

0.097

0.095

H51_CONST 4.991H52_CONST 2.265

NHL5_FIG_1C NHL5_FIG_2C NHL5_FIG_1N NHL5_FIG_2N

- HAND MADE BORDER WITH THICKNESS 2 WERE USED;

- REC and REC+BALL LEARNING SETS WERE USED;

- WEIGHT VECTOR TRANSFORMATION TO FILTER MASK :

TEST FIGURE (CLEAN AND NOISY) FILTERED WITH NEURON (TR min = 50)

CLEAN : H51 H52 NOISY: H51 H52

CONCLUSION: PERFOMANCE OF FILTER LEARNED WITH TWO SAMPLES IS BETTER.

NUMERICAL EXPERIMENTS - II

L51

4.399 103

0.151

0.245

0.153

2.188 103

0.156

0.293

0.169

0.337

0.142

0.251

0.16

0.824

0.132

0.287

0.152

0.314

0.167

0.325

0.148

0.011

0.152

0.273

0.152

0.017

L52

8.123 103

0.084

0.077

0.07

6.509 103

0.073

0.2

0.081

0.218

0.065

0.097

0.121

1.504

0.116

0.105

0.086

0.173

0.103

0.206

0.079

0.016

0.076

0.103

0.091

0.012

L51_CONST 0.091L52_CONST 0.135

- LAPLAS FILTERED BORDER WERE USED;

- REC and REC+BALL LEARNING SETS WERE USED;

- WEIGHT VECTOR TRANSFORMATION TO FILTER MASK :

TEST FIGURE (CLEAN AND NOISY) FILTERED WITH NEURON (TR min = 65)

NLL5_FIG_1C NLL5_FIG_2C NLL5_FIG_1N NLL5_FIG_2N

CLEAN : L51 L52 NOISY: L51 L52

CONCLUSION: IT IS POSSIBLE TO “STEAL” HEURISTIC ALGORITHM THROUGH LEARNING.

NUMERICAL EXPERIMENTS - III

H51

1.431 103

0.069

0.137

0.083

4.21 103

0.073

0.143

0.094

0.164

0.066

0.134

0.09

0.371

0.076

0.151

0.071

0.148

0.091

0.159

0.074

8.796 103

0.071

0.145

0.07

3.713 104

H52

6.134 103

0.051

0.034

0.052

0.012

0.036

0.117

0.044

0.128

0.037

0.051

0.034

0.541

0.036

0.054

0.041

0.107

0.04

0.13

0.041

4.03 103

0.043

0.038

0.047

9.927 103

H51_CONST 4.991H52_CONST 2.265

- HAND MADE BORDER WITH THICKNESS 1 WERE USED;

TEST FIGURE (CLEAN AND NOISY) FILTERED WITH NEURON

NHL5_FIG_2N

TRmin=40

NHL5_FIG_1N

TRmin=40

NHL5_FIG_2C

TRmin=30

CLEAN : H51

NOISY: H51 H52

CONCLUSION: MEAUSURE OF QUALITY OF FILTERING HAS TO BE INTRODUCED.

Learning asymmetry effect

- Learning asymmetry effect was discovered with SOFA-2009 model for the robot cruise neurocontroller ; - In sense of neuron edge detector effect results in the asymmetry of the weight values of the weights with the symmetry position ;

- Norm of the weight asymmetry can be introduced that can be used for estimation of quality of learning;

ONE SAMPLE LEARNING TWO SAMPLE LEARNING

H51

1.431 103

0.069

0.137

0.083

4.21 103

0.073

0.143

0.094

0.164

0.066

0.134

0.09

0.371

0.076

0.151

0.071

0.148

0.091

0.159

0.074

8.796 103

0.071

0.145

0.07

3.713 104

H52

6.134 103

0.051

0.034

0.052

0.012

0.036

0.117

0.044

0.128

0.037

0.051

0.034

0.541

0.036

0.054

0.041

0.107

0.04

0.13

0.041

4.03 103

0.043

0.038

0.047

9.927 103

H51_CONST 4.991H52_CONST 2.265

CONCLUSIONS : IT IS POSSIBLE TO CONTROL FILTER QUALITY WITH SOME ASSYMETRY NORM.

Modified One Step Learning Procedure - I

• The one possible way to solve asymmetry problem is using the description of the relation between the weights in explicit form;

• For learning asymmetry there are exist linear relation between the weights at the symmetry position in filter matrix;

• One step learning procedure on base of Lagrange multipliers provides possibility to take into account the existence of the linear relations for weights and avoid asymmetry effects also;

• This procedure was tested with SOFA-2009 model ;

Modified One Step Learning Procedure - II

• Learning asymmetry problem can be solved if one take into account the linear relations between weights

W(k,i) = W(m,n)

• In common way the set of this relations can be presented as Nsym symmetry conditions, expressed in matrix form

L W = b

• Lagrange multipliers method for one step learning procedure can be formulated as linear programming optimization problem:

min F(W) = (SW - F, SW – F) + (W,W) + Dμ (LW-b) W,Dμ

Modified One Step Learning Procedure - III

• Let us μ is the vector that is formed from Lagrange multipliers

μ = [μ1, μ2, ……. μ Nsym ]T

• For modified vectors and matrixes Wμ = [ W μ]T Fμ = [ F b]T

• Solution is a vector

Wμ= (SμTSμ+ Eμ)-1 SμT Fμ

E 0

0

0Eμ =S L

LT 0Sμ =

CONCLUSIONS : IT IS POSSIBLE TO PROVIDE SYMMETRY OF FILTER WITH THE

LAGRANGE MYLTIPLIERS METHOD AND THE SAME LEARNING

PROCEDURE.

MASTER_PIC

M_TEST_52H_30 M_TEST_52H_60 M_TEST_52L_30 M_TEST_52L_60

STANDART REAL IMAGE TEST

- NEURON FILTER 5*5 LEARNED WITH :

- TWO LAPLAS BORDERS SAMPLES;

- TWO HAND MADE BORDERS WITH THICNESS 2;

- LOW THRESHOLDS WAS 30 and 60 ;

CONCLUSION: FILTER PERFOMANCE IS EXELENT.

LEARNING WITH 2 HAND MADE BORDERS LEARNING WITH LAPLAS FILTERED BORDERS

CONCLUSIONS• PROPOSED APROACH IS EXTREMELY FLEXIBLE AND PROVIDES POSSIBILITY

TO GENERATE THROGHT LEARNING A VARIETY OF FILTERS : LINEAR,NONLINEAR, LOCAL, DISTRIBUTED AND SO ON;

• IT IS POSSIBLE TO USE AN VARIETY OF EXISTING FILTERS AS LEARNING SAMPLE SET;

• SOME WORK HAS TO BE DONE;

Supporting publications

1. Astapkovitch A.M. Learning Asymmetry Effect for the Neuron Net Control Systems. Proc. International

forum “Modern information society formation – problems, perspectives,innovation approaches ”, p.7-13,SUAI Saint-Petersburg,June 6-11, 2009

2. Astapkovitch A.M. Virtual mobile robot SOFA-2009 Proc. International forum “Information and communication technologies and higher education - priorities of

modern society development”, p.7-15,SUAI Saint-Petersburg, 20093. Astapkovitch A.M. Оne step learning procedure for neural net control system. Proc. International forum

“Information systems. Problems, perspectives , innovation approaches” , p.3-9,SUAI Saint-Petersburg, 20074. http://guap.ru > english version > student design center > student projects >

SOFA-2009 and publications

AND FAREWELLS

I LEAVED SUAI AND NOW IS WORKING FOR “LANIT-TERCOM” COMPANY THAT IS ROOTED TO STATE SAINT-PETERSBURG UNIVERSITY MATH-MECH FACULTY.

THANK FOR ALL PHOENIX-X STUDENT RESEARCH PROJECTS TEAMS OF DIFFERENT YEARS. AND I HOPE THAT YOU REMEMBER THE PHOENIX BIRD LEGEND.

Sincerely yours : tatalex2@gmail.com