1. Ashish Uthama http://bisicl.ece.ubc.ca/ EOS 513 Term Paper Presentation Ashish Uthama Biomedical Signal and Image Computing Lab Department of Electrical and Computer Engineering University of British Columbia G. Chen and T.D. Bui "Invariant Fourier-wavelet descriptor for pattern recognition," Pattern Recognition, vol. 32, pp. 1083-1088

2. Ashish Uthama http://bisicl.ece.ubc.ca/ The problem … Pattern recognition: Classifying an object into predetermined categories Applications:  Written character recognition  Object identification for unmanned vehicles  Content based image retrieval ……

3. Ashish Uthama http://bisicl.ece.ubc.ca/ What’s in it for me? My problem: Try to find if there is a significant difference two groups of 3 dimensional distributions. Quantify this difference. Similarities between the problem domains:  Sparse representation of the object  Sparse enough to significantly speed up the computations  Complete enough to discriminate between important differences  Use this representation to classify (differentiate)

4. Ashish Uthama http://bisicl.ece.ubc.ca/ Solution requirements … Translation and scale invariant representation Rotation invariant representation Noise resistant

5. Ashish Uthama http://bisicl.ece.ubc.ca/ Translation invariance Achieved by changing the origin to the centroid (Centre of gravity/mass ) of the image

6. Ashish Uthama http://bisicl.ece.ubc.ca/ Achieved by normalizing in the polar coordinate system ‘N’ concentric circles (radius = d*i/N) Scale invariance

7. Ashish Uthama http://bisicl.ece.ubc.ca/ Rotational invariance Analyzing the data along polar angle axis Rotation results in circular shift of signals along this axis 1-D Fourier transform results in features that are invariant under rotations

8. Ashish Uthama http://bisicl.ece.ubc.ca/ Feature extraction Apply wavelet transform along the radial direction (after 1-D Fourier) Multiresolution representation Haar, Daubechies-4, Coiflet-3 and Symmlet-8 basis tried with no much difference in performance Coarse coefficients aggregate at the center

9. Ashish Uthama http://bisicl.ece.ubc.ca/ Classification Number of coefficients are small in coarse scale and increase with scale Use the wavelet coefficients to locate a match progressively At each scale:  If only one match found : STOP (object classified)  If none match : STOP (object can not be classified)  If more than one match: Repeat at next scale Efficient, Reduces number of entries to search

10. Ashish Uthama http://bisicl.ece.ubc.ca/ Images from the paper

11. Ashish Uthama http://bisicl.ece.ubc.ca/ Results Table shows the performance of this approach using Haar wavelet basis.

12. Ashish Uthama http://bisicl.ece.ubc.ca/ Critique Image parameters and algorithm parameters (N, angular resolution, database size/content) not mentioned in the results Performance under noise not evaluated (Effects all steps) Effect of Quantization/ Re-sampling (while converting to polar) errors not clear Details of comparing coefficients not presented (Distance between coefficients?) Handling of different number of samples along the angular direction not clarified

13. Ashish Uthama http://bisicl.ece.ubc.ca/ Critique Novel, simple and intuitive! Invariance of extracted features seems plausible (as demonstrated) Computations/Comparisons for classification reduced Easily extensible to 3D!

14. Ashish Uthama http://bisicl.ece.ubc.ca/ Questions … Comments … ?