Evolutionary Multi-Objective Optimization of Trace Transform for Invariant Feature Extraction

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2 Evolutionary Multi-Objective Optimization of Trace Transform for Invariant Feature Extraction Wissam A. Albukhanajer, Yaochu Jin, Johann Briffa and Godfried Williams Nature Inspired Computing and Engineering Department of Computing University of Surrey United Kingdom 11 th June 2012

3 In this talk: Introduction : Research Topic & Challenges Objectives Invariant Feature Extraction Related Work Moment Invariants Radon Transform Trace Transform Evolutionary Trace Transform (ETT) Multi-Objective Optimization Non-dominated Sorting Genetic Algorithm NSGA-II Experimental Results Conclusion and Future Work

4 Introduction Image Copyright Infringement by Visitors of Museums If an object or paintings is in copyright, then a digital image of that object is an infringement of copyright. Wissam A. Albukhanajer Source Victoria & Albert Museum UK, 2010

5 Introduction Research Challenges Volume of images to be processed: 4 billion images as of October billion images as of September billion images as of January 2011 [10] Robustness to general deformations. Ex: Image taken from different angles, distances and lighting conditions) [10] Facebook Statistics

6 Introduction Objectives To develop robust yet computationally efficient feature extraction algorithms for identifying copyrighted digital images.

7 Introduction Invariant Feature Extraction The Rotation, Scale and Translation (RST) Invariants A A B B

8 Related Work Moment Invariants Moments are an expression of the image function f(x,y) as a polynomial basis [2]. m µ pq pq = = Where M M N x= 1 y= 1 N x= 1 y= 1 m x = m ( x x) x p y q and f ( x, y) p ( y y) m y = m q f ( x, y) are the centre of gravity coordinates. Moments have a drawback that it is sensitive to noise. Calculating high order moments requires substantial computational efforts [2] M. Hu, "Visual pattern recognition by moment invariants," IRE Transactions on Information Theory, vol. 8, pp , 1962.

9 Related Work Radon Transform is a useful tool in computed tomography medical imaging (CT scanner). Johann Radon first introduced the transform in 1917 [11]. R{ f ( x, y)} = f ( x, y) δ ( ρ x cosθ y sinθ ) dxdy Robust to noise. Calculating a line sum on image pixels at different angles. Additional effort to achieve general invariants (ex: Singular Value Decomposition SVD) An Image and its Radon transform as a function of (rho, ϴ) [11] S. R. Deans, The Radon Transform and some of its Applications. Krieger Publishing Company, 1983.

10 Related Work The Trace Transform (TT) Inspired by Radon transform, proposed by Kadyrov and Petrou [1] Trace Transform is a generalisation of Radon Transform. The functional calculated on the image pixels is not necessary the integral. [1] A. Kadyrov and M. Petrou, "The Trace transform and its applications," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, pp , 2001.

11 The Trace Transform (TT) (Cont.) (p) Different Trace Transforms can be produced Using different trace functionals: (a) (b) Angle (ϴ) (p) (p) (c) Angle (ϴ) (d) Angle (ϴ) A butterfly image (a) and its Trace transforms using different Trace functionals: (b) Gradient, (c) Integral and (d) Standard deviation.

12 The Trace Transform (TT) (Cont.) Triple Feature: Triple feature can be constructed by applying another two functionals: Diametric functional D applied to the Trace Matrix to produce a vector of length (ϴ). Circus functional C is applied to the diametric vector to produce a real number to describe the image = C { D [ T[ f ] ] }

13 The Trace Transform (TT) (Cont.) Triple feature construction procedure: Trace Algorithm. Triple feature from an Image.

14 The Trace Transform (TT) (Cont.) Trace diametric function: Two different images and their corresponding diametric functions. The solid line in the plot represents diametric of the original image and dotted line represents a rotation in the original image by 90 degrees.

15 The Trace Transform (TT) (Cont.) Trace functionals: Table I. Some Trace functionals:

16 The Trace Transform (TT) (Cont.) Which Trace Functional is used? Traditionally, triple features are constructed by a combination of the three functionals: Trace (T), Diametric (D) and Circus (C) Which Functional combination is used? Currently, Trace (T), Diametric (D) and Circus (C) are picked at random

17 Evolutionary Trace Transform (ETT) [12] Multi-Objective Optimisation (MOO) For Multi-Objective optimization, more than one objectives that reflect the model complexity should be considered [13]. In this work, we form two objectives: 1. Minimize the within-class feature variance (S w ) 2. Maximize the between-class feature scatter (S b ) [12] W. A. Albukhanajer, Y. Jin, J. Briffa and G. Williams Evolutionary Multi-Objective Optimization of Trace Transform for Invariant Feature Extraction IEEE Congress on Evolutionary Computation CEC, Brisbane, Australia, June 10-15, [13] Y. Jin and B. Sendhoff, "Pareto-Based Multiobjective Machine Learning: An Overview and Case Studies," Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on, vol. 38, pp , 2008.

18 Evolutionary Trace Transform (ETT) (Cont.) Single and Multi-Objective Optimisation (MOO) Single and Multi-Objective Optimisation.

19 Evolutionary Trace Transform (ETT) (Cont.) Multi-Objective Optimisation (MOO) The Objectives are to minimize the following: where: S S b w = = C k k = 1 j= 1 C k = 1 N ( µ µ ) k ( x k j µ ) 2 ε : is a small quantity to avoid division by zero. k : Number of samples in class k : Number of classes : Mean of class k :The sample of class k Mean of all classes

20 The Non Dominated Sorting Genetic Algorithm NSGA-II [14]: NSGA-II [14] K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGA-II," Evolutionary Computation, IEEE Transactions on, vol. 6, pp , 2002.

21 NSGA-II: Pareto-Optimality Solution 1 dominates 2&3 Pareto rank assignment - NSGA-II

22 NSGA-II: Crowding Distance 4 3 f f1 Crowding distance NSGA-II

23 Experimental Results Optimal Front Front 1 Front 2 Front 3 Table II Parameter set-up f f 1 Three non-dominated fronts near the optimal front

24 Experimental Results (Cont.) Pareto-Optimal Front Non-dominated solutions obtained by NSGA-II

25 Fish Images Database Fish database. Each image subjected to random RST deformation [1].

26 Experimental Results (Cont.) Feature Samples by a traditional TT [1] 2D features for 5 fish image classes, each with random RST from traditional TT. [1] A. Kadyrov and M. Petrou, "The Trace transform and its applications," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, pp , 2001.

27 Experimental Results (Cont.) Comparison between traditional TT[1] and ETT 2D features for 5 fish image classes, each with random RST. a) traditional TT and b) ETT. [1] A. Kadyrov and M. Petrou, "The Trace transform and its applications," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, pp , 2001.

28 Experimental Results (Cont.) Invariant Features: Fish Images (5 Classes) ETT Table III. Triple features - ETT:

29 Experimental Results (Cont.) S w /S b Ratio ( Traditional TT vs. ETT) Table IV. S w /S b Ratio ( Traditional TT vs. ETT)

30 Sample images - Iraq Museum Sample images Iraq Museum.

31 Robustness to Rotation (ETT) Table V. Robustness to Rotation - ETT:

32 Robustness to Rotation (ETT vs. traditional TT) Robustness to Rotation. Traditional TT vs. ETT

33 Robustness to Gaussian Noise Images with Gaussian noise.

34 Robustness to Noise (ETT vs. traditional TT) Robustness to Noise. Traditional TT vs. ETT

35 Robustness to Flips (traditional TT vs. ETT) Table VI. Robustness to flips Traditional TT vs. ETT

36 Conclusion ETT shows better performance than traditional TT. ETT requires less computation efforts than the traditional TT because features are not normalized and trace images on 180 o only. ETT shows excellent robustness to RST and flips.

37 Future Work Complexity and Robustness Analysis of the ETT Design of novel ETT structure Develop an efficient classifiers Extend the algorithm to 3D recognition

38 Q&A Thank you Wissam A. Albukhanajer Nature Inspired Computing and Engineering T: F: Department of Computing Faculty of Engineering & Physical Sciences University of Surrey Guildford, UK. GU2 7XH Wissam A. Albukhanajer 11 th June 2012