The document summarizes force field transforms, a technique for dimensionality reduction and feature extraction in images. It was developed by Dr. David Hurley in 2001 for use in ear biometrics. The technique models each pixel as a charged particle and calculates the force and energy fields. This maps the image to an energy surface highlighting ridges and wells for use as features. It offers improved edge detection over Sobel and was shown to achieve 99.2% accuracy in ear identification, outperforming other techniques. The document covers the mathematical models, implementations, applications in biometrics, advantages of being robust to distortion, and contributions of related ear biometric research.

1. FORCE FIELD TRANSFORMS
PRESENTED BY:
Adham Beyki
MS Kapoor
Shashank Dhariwal
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2. FORCE FIELD TRANSFORM
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INTRODUCTION
POINT OPERATORS
ELECTROSTATIC & PLANETARY FORCE FIELD
FORCE FIELD TRANSFORMS
MATHEMATICAL MODEL – Brute Force & FDA
IMPLEMENTATION – Brute Force Method
IMPLEMENTATION – Motion Blur
APPLICATION IN BIOMETRICS – Ear Detection
COMPARISON – Sobel Edge Detection
ADVANTAGES
DISADVANTAGES
CONTRIBUTIONS
REFERENCES
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3. INTRODUCTION
4 Ws
• Who
- Dr David Hurley (then a PhD student )
Dr Mark Nixon & Dr John Carter [1]
• When
- year 2001
• Where
- University of Southampton
• Why
- Objective was to reduce dimensionality of
pattern space yet maintain discriminatory power for
classification and invariant description in context of Ear
Biometrics.
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4. POINT & GROUP OPERATORS
• Point Operators : Basic operation in IP where each pixel value
is replaced with a new value obtained by
carrying out certain operations on the
previous pixel value.[2]
• Group Operators : Same as Point Operator but here the new
value of the pixel is determined by past
values of its neighbouring pixels. [2]
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5. POINT & GROUP OPERATORS
• Types of Point Operators [2]
1. Histogram Operations for Brightness/contrast control
2. Thresholding Operator for finding object of interest in an
image if its brightness level is known
• Types of Group Operators – used for filtering [2]
1. Template Convolution uses weighted coefficient template
2. Averaging Operator – equally weighted (1 or 1/9)
coefficient template
3. Gaussian Averaging Operator – template coefficient are
values set by Gaussian relationship
4. Median & Mode Operator – use statistical relationship
5. Anisotropic Diffusion – uses Heat Flow eq for calculating
the coefficients of the template.
6. Force Field Transform – ‘Today’s Topic of Discussion’!!!
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6. ELECTROSTATIC & PLANETARY
FORCE FIELD
Fig 1. Force Field of two charged bodies Fig 2. Gravitational Force resulting in orbits
Newton’ law of gravitation gives us equations for gravitational
potential energy E and force F.
E=
−𝐺 𝑚1 𝑀2
𝑟
F=
−𝐺 𝑚1 𝑀2
𝑟 𝑋 𝑟
(Inverse square law)
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7. FORCE FIELD TRANSFORM
(For Unit Test Pixel) [1]
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8. FORCE FIELD TRANSFORM
Fig 3. Original Image
Force Field
(Magnitude)
Fig 4. Array of
Test Pixels
Field lines, channels
and wells
Potential Ridges and wells are obtained by placing 50 test
pixels which generate field lines when iterated over time [3]
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9. FORCE FIELD TRANSFORM
There are two approaches to find the Force Field Transform
1. Brute Force – each pixel is transformed using the
defining equations for Force and energy.
2. Frequency Domain Analysis – the transformation is
carried out in freq. domain
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10. MATHEMATICAL MODEL – BRUTE FORCE
Here each pixel is transformed using the defining
equations for Force and energy. [1]
Or equivalently matrix multiplication as shown below
could be used
4X4 pixel image
where,
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11. MATHEMATICAL MODEL – FREQUENCY
DOMAIN ANALYSIS
Here a MxN pixel image is convolved with a Force Field
matrix for a unit pixel.[1]
The advantage of working in frequency domain is that
the computational time reduces from O (N^2) to O(N log N).
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12. FORCE FIELD TRANSFORM
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13. IMPLEMENTATION – BRUTE FORCE
Energy Surface
Original Image
(205X150)
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Force Field Transform (magnitude)

14. IMPLEMENTATION – MOTION BLUR
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Force Field Transform (magnitude)

15. IMPLEMENTATION – MOTION BLUR
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Energy Surface

16. APPLICATION - BIOMETRICS
• 3 Steps
1.
Find the transform
2.
Locate the Ridges and the wells
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3.
Match the wells with the data sets.

17. COMPARISONS (Edge Detection)
Force Field Transform
Sobel Edge Detection
• Textures are well detected.
• Gets more features & sharper edges.
• Can be made better with thresholding.
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18. ADVANTAGES
• Simplified implementation in time domain.
• Time complexity reduced considerably by working in freq.
domain (O(NlogN)).
• Impervious to distortion in image due to motion.
• Finds application in edge detection.
• Higher efficiency (99.2%) as compared to other techniques.
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19. DISADVANTAGES
• At times, transform generates only one ‘well’.
• High computational costs (O(N^2)) using direct method.
• Although it can be simply implemented in time domain, we
faced difficulties in implementing it in the frequency domain.
• Not widely applicable.
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20. CONTRIBUTIONS
• 1989 - Iannarelli :
 Took 12 measurements around the ear by placing a
transparent compass with 8 spokes.
 Two steps of registration.
• 1999 - Moreno et. al:
 Used various neural classifiers and combination techniques
 System efficiency: 93%
• 2000 - Hurley et. al:
 Used Force Field Transform feature extraction to map the ear to an
energy field which highlighted ‘potential wells’ and ‘channels’ as
features.
 System efficiency: 99.2%

21. CONTRIBUTIONS
• 2003 – Chang et. al:
 Used PCA for detection and found that there wasn’t much difference
in ear & face recognition.
 System efficiency: 90.9%
• 2007 - Sana et. al:
 Used Haar wavelet decomposition and the extracted wavelet
coefficients to represent the ear.
 Matched with ‘n’ trained images using Hamming distance.
 System efficiency: 98.4%
• 2010 - Nixon et. al:
 Technique describes how the transform is capable of highlighting
tubular structures and exploiting the elliptical shape of helix.
 System efficiency: 99.6%

22. REFERENCES
1.
2.
3.
4.
5.
PhD Thesis of David J Hurley, 2001, University of
Southampton.
Mark Nixon & Alberto Aguado, Feature Extraction & Image
Processing, Second Edition, Elsevier Ltd, 2008.
D.J. Hurley, M.S. Nixon, J.N. Carter, Force field energy
functionals for image feature extraction, Proceedings of
the Tenth British Machine Vision Conference BMVC99,
2(1999) 604-613.
Ruma Purkait, Ear Biometric: An Aid to Personal
Identification, Anthropologist Special Volume No. 3: 215218 (2007).
D. J. Hurley, B. Arbab-Zavar, and M. S. Nixon, The Ear as a
Biometric, EURASIP (2007).
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