FORCE FIELD TRANSFORMS

PRESENTED BY:Adham BeykiMS KapoorShashank Dhariwal 1

FORCE FIELD TRANSFORM

• 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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INTRODUCTION4 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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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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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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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 = F = (Inverse square law)

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FORCE FIELD TRANSFORM(For Unit Test Pixel) [1]

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FORCE FIELD TRANSFORM

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Fig 3. Original Image Force Field Fig 4. Array of Field lines, channels (Magnitude) Test Pixels and wells

Potential Ridges and wells are obtained by placing 50 test pixels which generate field lines when iterated over time [3]

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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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,10

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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FORCE FIELD TRANSFORM

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IMPLEMENTATION – BRUTE FORCE

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Energy Surface

Original Image (205X150)

Force Field Transform (magnitude)

IMPLEMENTATION – MOTION BLUR

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Force Field Transform (magnitude)

IMPLEMENTATION – MOTION BLUR

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Energy Surface

APPLICATION - BIOMETRICS

• 3 Steps 1. Find the transform

2. Locate the Ridges and the wells

3. Match the wells with the data sets.

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COMPARISONS (Edge Detection)

Force Field Transform Sobel Edge Detection

• Textures are well detected.• Gets more features & sharper edges.• Can be made better with thresholding. 17

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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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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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%

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%

REFERENCES

1. PhD Thesis of David J Hurley, 2001, University of Southampton.2. Mark Nixon & Alberto Aguado, Feature Extraction & Image Processing, Second Edition, Elsevier Ltd, 2008.3. 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) 604-613.4. Ruma Purkait, Ear Biometric: An Aid to Personal Identification, Anthropologist Special Volume No. 3: 215- 218 (2007).5. D. J. Hurley, B. Arbab-Zavar, and M. S. Nixon, The Ear as a Biometric, EURASIP (2007).

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