Object Recognition using Particle Swarm Optimization on Fourier - - PowerPoint PPT Presentation

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Object Recognition using Particle Swarm Optimization

• n Fourier Descriptors

Muhammad Sarfraz Ali Taleb Ali Al-Awami

King Fahd University of Petroleum and Minerals KFUPM # 1510, Dhahran 31261, Saudi Arabia E-mail: sarfraz@kfupm.edu.sa

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Outline

• Introduction
• Statement of the Problem
• Methodology
• Solution (Algorithm)
• Experiments & Results
• Particle Swarm Optimization (PSO)
• Conclusion

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Introduction

Answer Database of Fourier Descriptors F-16 B-747 M-52 …… …... …… Classifier Contour shape Input shape

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Introduction

• Object recognition is the ultimate goal for many

image analysis and computer vision applications.

• Among the many cues proposed, such as color,

texture and others, shape is the most common and dominant feature

• Many Shape models have been studied whose

imaging conditions and object appearance are restricted or well controlled.

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Introduction

• The main difficulty lies in view variability

associated with the images of the given object.

• The previous work in view of invariant object

recognition can be classified into 3 approaches

– Using invariants – Part decomposition – Alignment

• Fourier Descriptors are popular invariants that

are invariant to 2D transformations.

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Statement of the problem

• To Recognize the Objects such as Airplanes

which are invariant to translation, rotation and scaling in 2-dimension.

• To recognize the objects in case of noise and
• cclusion.

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Methodology

• Getting Bitmap Image
• Removing Noise

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Methodology

• Extracting Outline

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Methodology : Fourier Descriptors

• Find the boundary of the image using the

algorithm

• Convert the x, y coordinates in the contour to a
• ne-dimensional vector by treating them as a

complex pair. That is: U(n) = X(n) + i * Y(n).

• Perform the Fast Fourier Transform on U and

take the absolute value to create a new vector A which is the magnitude of the coefficients.

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Methodology : Fourier Descriptors …..

• The Fourier

transform of a continuous function

• f a variable u is

given by the equation:

• When dealing with

discrete images the Discrete Fourier Transform (DFT) is used:

• The variable u is

complex, so by using the expansion: e[-j A] = cos (A) – j. sin (A) where A = 2πu/x and N is the number of equally spaced samples, one can have:

For Digital Images Using expansion

( ) ( )

2 j ux

F u f u e dx

π ∞ − −∞

= ∫

( ) ( )

2

1

1

j x

N N x

F u f u e N

π −

− =

⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ ∑

( ) ( ) ( ) ( )

( )

1

1 ) . cos .sin

N x

F u f x jy Ax j Ax N

− =

⎛ ⎞ = + − ⎜ ⎟ ⎝ ⎠ ∑

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Methodology : Fourier Descriptors ……

• The simple geometric transformations of the

Fourier transforms

• Translation: u(n)+t a(k)+tδ(k)
• Rotation : u(n)ejθ a(k)ejθ
• Scaling: su(n) sa(k)
• Starting point: u(n-t) a(k) ej2∏tk/N

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Methodology : Fourier Descriptors ……

The Fourier transform:

The magnitude is independent of the phase, and so unaffected by rotation. The complex coefficients are called Fourier descriptors (FD)

• f the boundary.

The magnitude completely defines the shape (according to Zahn and Roskies).

( ) ( )

1

2

1 N N x

x j

e u f N u F

π −

∑

− =

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ =

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Methodology : Fourier Descriptors ……

• Throw away A(0) since it is the DC component; that is, it

represents only the translation of the contour.

• Truncate A(>6) since higher frequency components don't

add much to the shape.

• Normalize the remaining magnitudes by dividing each

element of A by A(0).

• Reason: when a shape is scaled by a constant factor

(alpha), the magnitude of each of the coefficients in the resulting FFT is also multiplied by alpha.

• To remove alpha from the equation, we simply divide by

a number, A(0), which is known to be a product of alpha.

• The FD of the test object is compared with each object
• f the training set
• The object with the least Euclidean distance in the

training set will be the recognized object.

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Methodology : Similarity Measures

• If two shapes, A and B, produce a

set of values represented by a(i) and b(i) then the distance between them can be given as c(i) = a(i) – b(i).

• If a(i) and b(i) are identical then c(i)

will be zero.

• If they are different then the

magnitudes of the components in c(i) will give a reasonable measure

• f the difference.

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Methodology : Similarity Measures

• Euclidean Distance (ED)
• Percentage Error (PE)

( ) ( )

∑

= n i

i b i c

1

( )

∑

= n i

i c

1 2

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Solution

ALGORITHM

• Clean up the image of noise by using a

median filter and then removing all but the

• largest of the objects in the scene.
• Find the boundary of the image.
• Convert the x, y coordinates in the

contour to a one-dimensional vector by treating them as a complex pair. That is: U(n) = X(n) + i * Y(n).

• Perform the Fast Fourier Transform on U

and take the absolute value to create a new vector A which is the magnitude of

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Experiments & Results

Fourier Descriptors under different transformations

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Experiments & Results 1a: Euclidean Measure

• Comparison
• f results for

100 model

• bjects
• T:

Transformati

• ns
• N: Noise
• O: Occlusion

23.33% 93.75% 95% 40 23.33% 93.75% 95% 29 23.33% 93.75% 93.33% 22 18.33% 93.75% 90% 8 20% 93.75% 93.33% 11 8.33% 93.75% 83.33% 6 5% 75% 71.67% 4 Occlusion Noise Transformations

• No. of FDs

used

Base Case

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• Using Euclidean distance

Experiments & Results 1a: Euclidean Measure

Recognition Rate for Different Number of FDs

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57

• No. of FDs

Recognition Rateg Xmation Noise Occlusion

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Experiments & Results 1b: Percentage of Error Measure

• Comparison of

results for 100 model objects

• T: Transformations
• N: Noise
• O: Occlusion

Base Case

11.33% 81.25% 62.25% 40 11.67% 81.25% 68.33% 29 6.67% 81.25% 68.33% 22 8.33% 81.25% 75% 16 13.33% 81.25% 86.67% 9 11.67% 81.25% 80% 6 8.33% 87.5% 70% 4 Occlusion Noise Transformations

• No. of

FDs used

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• Using Percentage of Errors

Experiments & Results1b: Percentage of Error Measure

Recognition Rate for Different Number of FDs

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57

• No. of FDs

Recognition Rate Xmation Noise Occlusion

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Particle Swarm Optimization (PSO)

• J= - H + α sum(D)
• vid = w*vid + c1*rand( )*(pid-xid) +

c2*Rand( )*(pgd-xid)

• xid = xid + vid

pid = pbest

• pgd = gbest

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Particle Swarm Optimization (PSO)

• The PSO algorithm is described as follows:

– Define the problem space and set the boundaries, i.e. equality and inequality constraints. – Initialize an array of particles with random positions and their associated velocities inside the problem space. – Check if the current position is inside the problem space or not. If not, adjust the positions so as to be inside the problem space. – Evaluate the fitness value of each particle. – Compare the current fitness value with the particles’ previous best value (pbest[]). If the current fitness value is better, then assign the current fitness value to pbest[] and assign the current coordinates to pbestx[][d] coordinates. – Determine the current global minimum among particle’s best position. – If the current global minimum is better than gbest, then assign the current global minimum to gbest[] and assign the current coordinates to gbestx[][d] coordinates. – Change the velocities according to Eqns. (4) or (6). – Move each particle to the new position according to Eqn. (5) and return to Step 3. – Repeat Step 3- Step 9 until a stopping criteria is satisfied.

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Particle Swarm Optimization (PSO)

0.0143 0.0195 0.0138 0.1742 0.1083 0.3051 0.2216 0.1515 0.5409 0.2698 0.0002 0.0020 0.0009 0.0015 0.0001 0.0036 0.0005 0.0048 0.0041 0.0079 0.0296 0.0152 0.1033 0.4004 0.4368 0.5681 0.6245 0.9140 0.8876 0.2022 0.3879 0.4992 0.5281 0.0009 0.0035 0.0024 0.0328 0.0000 0.0156 0.0394 0.0651 0.0000 0.0000 0.0000 Optimized Weights

• btained

11 6 6 11 11

• No. of FDs

Consider ed X, O, N O X X X Training set* 5 4 3 2 1 Experiment No.

*X = transformed objects, O = occluded objects, N = noisy objects

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Particle Swarm Optimization (PSO)

*X = transformed objects, O = occluded objects, N = noisy objects 25% 20% 20% 23.33 25% O 87.5% 87.5% 87.5 93.75% 93.75% N 98.33% 90% 95% 95% 93.33% X Recog nit io n Ra te 10 6 6 11 7

• No. of FDs

Used 11 6 6 11 11

• No. of FDs

Conside red X, O, N O X X X Training set* 5 4 3 2 1 Experiment No.

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Conclusion

• Fourier descriptors were found to be able to recognize at a higher

rate if we use nine or more Fourier descriptors. This trend is seen to continue when the size of the database is increased from 15 to 45 to 60.

• Most cumulative combinations of Fourier descriptors are able to

recognize most of the images correctly for samples without noise

• r occlusion.
• It is noted that if an image is recognized, it is recognized by most

cumulative combinations of Fourier descriptors, and if it is not recognized, then it is not recognized by almost all cumulative combinations of Fourier descriptors.

• Noise (salt and pepper) with density of ten percent has a minimal

effect on the recognition ability of Fourier descriptors. When we use eight or more Fourier descriptors, the accuracy level does not drop if we add ten percent salt and pepper noise to the images.

• Occlusion brings down the recognition rate of Fourier descriptors

from 80-90 percent to around 20%.

• The Fourier descriptors show a steady increase in accuracy level

as the number of Fourier descriptors used increases. It then stabilizes at same level for nine to eleven descriptors.

• Using PSO to find the most suitable descriptors and to assign

weights for these descriptors improves dramatically the recognition rate using the least number of descriptors.

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