Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction

Transcription

1 Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction Wissam A. Albukhanajer, Yaochu Jin and Johann A. Briffa Wissam A. Albukhanajer (student) E: T: +44(0) CEC 2015, Sendai, Japan SS37: Evolutionary Feature Selection and Construction & SS13: Evolutionary Computer Vision Nature Inspired Computing and Engineering Department of Computing Faculty of Engineering and Physical Sciences University of Surrey United Kingdom GU2 7XH May 28 Thursday, 2015

2 In this Talk Introduction Traditional Trace Transform. Triple Features. Evolutionary Trace Transform. Computational Complexity of the Trace Transform Multi-Objective Parameters Tuning Two-Objective Optimisation Three-Objective Optimisation Experimental Results Selection of Knee Point Solutions Performance Analysis Complexity Analysis Summary and Conclusion 2

3 Introduction Traditional Trace Transform (TT): Inspired by Radon transform, proposed by Kadyrov and Petrou [15] Trace Transform is a generalisation of Radon Transform. The functional calculated on the image pixels is not necessary the integral. Different Trace Transforms can be produced Using different Trace functionals T. An image The Trace matrix [15] A. Kadyrov and M. Petrou, "The Trace transform and its applications," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, pp ,

4 Introduction Traditional Trace Transform (TT) (cont.) Triple feature construction : 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 called Triple Feature. Schematic diagram of Triple feature construction. 4

5 Introduction Evolutionary Trace Transform: Using NSGA-II [17] based Multi-objective optimisation (MOO) to search the best combinations of Triple features functionals The two objectives are: 1. Minimize the within-class feature variance (S w ) 2. Maximize the between-class feature scatter (S b ) where K is the number of classes, C k is the number of samples in class k, μ k is the mean of class k of Ξ Triple features, Ξ jk is the j th Triple features of class k, and μ Ξ is mean of all classes of Ξ Triple features. NSGA-II is implemented using SHARK Machine Learning Library[16] [16] Christian Igel, Verena Heidrich-Meisner, and Tobias Glasmachers. Shark. Journal of Machine Learning Research 9, pp , [17] 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 ,

6 Introduction Evolutionary Trace Transform in the Presence of Noise (ETTN) In the evolutionary set up, sample images include three different classes, each containing five different types of changes. The major difference here is that Gaussian noise is added to the sample images apart from RST deformations: Sample 1 : A low-resolution image from (64 64) generated from a randomly chosen original image ( ); Sample 2 : Random rotation, scale and translation of Sample 1 with Gaussian noise (standard deviation=4); Sample 3 : Random rotation, scale and translation of Sample 1 with Gaussian noise (standard deviation=6); Sample 4 : Random rotation of Sample 1; Sample 5 : Random scale of Sample 1. Therefore, there are 15 images in ETTN (20 sample images in ETT). [145] L. Fei-Fei, R. Fergus, and P. Perona, \One-shot learning of object categories," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 4, pp , April

7 Computational Complexity Tuneable Parameters The Trace matrix of size n θ n ρ 7

8 Computational Complexity Traditional Trace Transform uses a thousand [87] (not optimised) features: n t = n ρ = n θ = 100, 0 θ 2π, and N T = N D = N C = 10 The largest number of sampling lines per rotation angle equals the number of pixels on the image diagonal, i.e., the maximum value of n ρ is equal to N 2 + N 2 = 2N with Δρ = 1. Randon Complexity (Big O): O(N 2 n θ ) The number of operations (in Big Theta notation) required to calculate a Triple feature is equal to: Θ(N T n t n ρ n θ ) for 0 θ π For n θ = 180, θ = 1: complexity equals to Θ(N 2 ) When considering Δθ, Δρ: Θ(N T N 2 /ΔθΔρ) [87] A. Kadyrov, A. Talepbour, and M. Petrou, \Texture Classification With Thousands of Features," in 13th British Machine Vision Conference. BMVC, 2-5 September , pp. 656{665. [190] S. Tabbone, L. Wendling, and J.-P. Salmon, \A new shape descriptor defined on the Radon transform," Computer Vision and Image Understanding, vol. 102, no. 1, pp.42-51,

9 Multi-objective Trace Parameters Tuning Parameters Tuning Using Two-Objective Optimisation Two-objective minimisation with θ and ρ as extra parameters to be tuned in addition to the Trace functionals T, D, and C. Parameters Tuning Using Three-Objective Optimisation Time complexity is added as a third objective: Both integer and real coding for θ and ρ are considered. 9

10 Some Functionals 10

11 Multi-objective Trace Parameters Tuning Two-objective non-dominated fronts and a selection of solutions at the knee point Integer coding Search converges to value of 1 (better accuracy) Real coding 11

12 Multi-objective Trace Parameters Tuning Three-objective non-dominated fronts Integer coding Real coding 12

13 Experimental Results Two-Objective Parameters Tuning: RST with Gaussian Noise (COIL-20 database) Integer coding Real coding 13

14 Experimental Results Three-Objective Parameters Tuning: RST with Gaussian Noise (COIL-20 database) Integer coding Real coding 14

15 Experimental Results Average performance of three solutions of each method: 15

16 Experimental Results Time complexity of three solutions of each method: From Table VI, we can see there are three different T functionals in all Triple feature pairs, which are T1, T3 and T5. which are And which have a time complexity O(N). The run time in the three-objective case is smaller than the run time in the two-objective case due to the time complexity being added as a third objective in the three-objective case, which provides fastest features but a relatively low performance. 16

17 Summary and Conclusion This paper focused on the computational complexity in evolutionary Trace transform. There are five parameters were tuned, which are three functionals T, D, C, and θ and ρ. Multi-objective parameter tuning was presented for fine-tune Trace sampling parameters using both, integer and real coding. Both two-objective and three-objective evolutionary algorithms were used and compared. In the three-objective case, the time complexity was introduced as a third objective. Therefore, it has improved the computational complexity. On the other hand, it has impacted negatively on the accuracy. Without a constraint on the minimum acceptable level of accuracy, the resulting solutions would not be in a good performance. The integer coding scheme of the two-objective case was of the best overall performance and computational complexity compared to the original ETTN and the other multi-objective optimisation such as the real coding scheme. 17

18 Publications Journal Papers: W. A. Albukhanajer, J. A. Briffa, and Y. Jin, Evolutionary Multiobjective Feature Extraction in the Presence of Noise, IEEE Trans. on Cybernetics. Vol. PP, Issue September W. A. Albukhanajer, J. A. Briffa, and Y. Jin, Classifier Ensembles Using Pareto Optimal Image Features submitted, IEEE Transactions on Cybernetics. March Peer reviewed Conference Papers: W. A. Albukhanajer, Y. Jin, J. A. Briffa "Evolutionary Multi-Objective Feature Construction and Tuning for Invariant Image Analysis", submitted (January 2015), 2015 IEEE Congress on Evolutionary Computation (CEC), Sendai, Japan, May 25-28, W. A. Albukhanajer, Y. Jin, and J. A. Briffa, Neural Network Ensembles for Image Identification Using Pareto-optimal Features, WCCI2014 IEEE Congress on Evolutionary Computation (CEC), Beijing, China, 06-11, July Page(s): W. A. Albukhanajer, Y. Jin, J. Briffa and G. Williams Evolutionary Multi-Objective Optimization of Trace Transform for Invariant Feature Extraction, WCCI2012. IEEE Congress on Evolutionary Computation (CEC), Brisbane, Australia, June 10-15, Page(s): W. A. Albukhanajer, Y. Jin, J. Briffa and G. Williams A comparative study of multi-objective evolutionary trace transform methods for robust feature extraction, in Evolutionary Multi-Criterion Optimization, ser. Lecture Notes in Computer Science (LNCS), R. Purshouse, P. Fleming, C. Fonseca, S. Greco, and J. Shaw, Eds. Springer Berlin Heidelberg, 2013, vol. 7811, pp _43 18

19 Q&A Thank you Wissam A. Albukhanajer (student) E: T: +44(0) Prof. Yaochu Jin E: T: +44(0) , F: +44(0) Johann A. Briffa Nature Inspired Computing and Engineering Department of Computing Faculty of Engineering & Physical Sciences University of Surrey Guildford, UK. GU2 7XH 19