Object Recognition using Particle Swarm Optimization on Fourier Descriptors

Transcription

1 Object Recognition using Particle Swarm Optimization on Fourier Descriptors Muhammad Sarfraz Ali Taleb Ali Al-Awami King Fahd University of Petroleum and Minerals KFUPM # 1510, Dhahran 31261, Saudi Arabia sarfraz@kfupm.edu.sa Slide 1

2 Outline Introduction Statement of the Problem Methodology Solution (Algorithm) Experiments & Results Particle Swarm Optimization (PSO) Conclusion Slide 2

3 Introduction Input shape F-16 B-747 M Database of Fourier Descriptors Contour shape Classifier Answer Slide 3

4 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. Slide 4

5 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. Slide 5

6 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 occlusion. Slide 6

7 Methodology Getting Bitmap Image Removing Noise Slide 7

8 Methodology Extracting Outline Slide 8

9 Methodology : Fourier Descriptors Find the boundary of the image using the algorithm 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 the coefficients. Slide 9

10 Methodology : Fourier Descriptors.. The Fourier transform of a continuous function of 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: j2 ( ) ( ) πux F u = f u e dx For Digital Images 1 = N N 1 ( ) ( ) F u x= 0 f u e Using expansion j2π x N 1 1 F u f x jy Ax j Ax N ( ) = ( + ).cos ) ( ).sin( ) x= 0 N ( ) Slide 10

11 Methodology : Fourier Descriptors The simple geometric transformations of the Fourier transforms -Translation: u(n)+t a(k)+tδ(k) -Rotation : u(n)e jθ a(k)e jθ -Scaling: su(n) sa(k) -Starting point: u(n-t) a(k) e j2 tk/n Slide 11

12 Methodology : Fourier Descriptors The Fourier transform: F 1 N N 1 x= 0 ( u) = f ( u) e j 2πx N The magnitude is independent of the phase, and so unaffected by rotation. The complex coefficients are called Fourier descriptors (FD) of the boundary. The magnitude completely defines the shape (according to Zahn and Roskies). Slide 12

13 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 of the training set The object with the least Euclidean distance in the training set will be the recognized object. Slide 13

14 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 of the difference. Slide 14

15 Methodology : Similarity Measures Euclidean Distance (ED) n c() i i= 1 2 Percentage Error (PE) n i= 1 c b () i () i Slide 15

16 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 Slide 16

17 Experiments & Results Fourier Descriptors under different transformations Slide 17

18 Experiments & Results 1a: Euclidean Measure Comparison of results for 100 model objects No. of FDs used 4 Transformations 71.67% Noise 75% Occlusion 5% Base Case % 93.75% 8.33% % 93.75% 20% T: Transformati ons % 93.33% 93.75% 93.75% 18.33% 23.33% N: Noise O: Occlusion 29 95% 93.75% 23.33% 40 95% 93.75% 23.33% Slide 18

19 Experiments & Results 1a: Euclidean Measure Using Euclidean distance Recognition Rate for Different Number of FDs Recognition Rateg Xmation Noise Occlusion No. of FDs Slide 19

20 Experiments & Results 1b: Percentage of Error Measure Comparison of results for 100 model objects No. of FDs used Transformations Noise Occlusion 4 70% 87.5% 8.33% Base Case 6 80% 81.25% 11.67% % 81.25% 13.33% T: Transformations N: Noise 16 75% 81.25% 8.33% O: Occlusion % 81.25% 6.67% % 81.25% 11.67% % 81.25% 11.33% Slide 20

21 Experiments & Results1b: Percentage of Error Measure Using Percentage of Errors Recognition Rate for Different Number of FDs Recognition Rate Xmation Noise Occlusion No. of FDs Slide 21

22 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 Slide 22

23 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. Slide 23

24 Particle Swarm Optimization (PSO) Experiment No Training set * X X X O X, O, N No. of FDs Consider ed Optimized Weights obtained *X = transformed objects, O = occluded objects, N = noisy objects Slide 24

25 Particle Swarm Optimization (PSO) Experiment No Training set * X X X O X, O, N No. of FDs Conside red No. of FDs Used Recog nit io n Ra te X N O 93.33% 93.75% 25% 95% 93.75% % % 90% 87.5% 20% 98.33% 87.5% 25% *X = transformed objects, O = occluded objects, N = noisy objects Slide 25

26 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 or 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 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. Slide 26

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