Outline

1. Enhanced Generic Fourier Descriptor for Object-Based Image RetrievalDengsheng Zhang, Guojun LuGippsland School of Comp. & Info TechMonash UniversityChurchill, VIC 3842Australiadengsheng.zhang@infotech.monash.edu.auhttp://www.gscit.monash.edu.au/~dengs/

2. Outline • Motivations • Generic Fourier Descriptor (GFD) • Problem • Enhanced Generic Fourier Descriptor (EGFD) • Experimental Results • Conclusions

3. Motivations • Content-based Image Retrieval • Shape is an important image feature along with color and texture • Effective and Efficient Shape Descriptor • good retrieval accuracy, compact features, general application, low computation complexity, robust retrieval performance and hierarchical coarse to fine representation • Affined Shape Retrieval • Affined shapes are common in nature due to objects being viewed from different angles and objects being stretched, skewed.

4. Affine Distorted Shapes Are Common

5. Generic Fourier Descriptor • Polar Transform • For an input image f(x, y), it is first transformed into polar image f(r,  ):

6. Generic Fourier Descriptor-II • Polar Raster Sampling Polar Grid Polar image Polar raster sampled image in Cartesian space

7. Generic Fourier Descriptor-III • 2-D Fourier transform on polar raster sampled image f(r,  ): where 0r<R and i = i(2/T) (0i<T); 0<R, 0<T. R and T are the radial frequency resolution and angular frequency resolution respectively. • The normalized Fourier coefficients are the GFD.

8. Problem • Generally, GFD has good performance on generic shapes. Its overall retrieval precision after full recall is 98.6% for rotated shapes, 90.5% for scaled shapes, 74.1% for perspective transformed shapes and 80.5% for generally distorted shapes. • Compared with rotation and scaling invariance test, the retrieval performance on perspective transform and generally distorted shapes are significantly lower. • The problem is caused by the polar raster sampling method.

9. Under-sampling Problem Only half the sampled positions contain shape information Virtually all the sampled positions contain shape information

10. Enhanced GFD • Normalization • Find major axis • Rotation normalization so that major axis of the shape is horizontal • Scaling normalization so that the ecentricity of the shape is 1.

11. Enhanced GFD-II • Optimized Major Axis Algorithm (MAA) • Find the boundary point pairs in a number of directions (e.g. 360). • Find the two points p1, p2 with the furthest distance in the found boundary points, then p1p2 is the major axis. • The computation of MAA is O(N) rather than O(N2).

12. Enhanced GFD-III • Normalization Result:

13. Enhanced GFD-IV • Applying GFD transform on the rotation and scaling normalized image. • The normalized transform coefficients are the enhanced GFD (EGFD).

14. Experiment • Dataset • Two datasets from MPEG-7 region shape database CE-2 are used. (CE-2 has been organized by MPEG-7 into six datasets to test a shape descriptor’s behaviors under different distortions) • Set A4 consists of 3101 from the whole database, it is for test of robustness to perspective transform. 330 shapes in Set A4 have been organized into 30 groups (11 similar shapes in each group) which are used as queries. • The whole database consists of 3621 shapes, 651 shapes have been organized into 31 groups (21 similar shapes in each group) which are used as queries. • Indexing and automatic retrieval

15. Performance Measurement • Recall vs Precision

16. Results • Recall-Precision of EGFD on perspective shapes. • Compared with GFD, the improvement on Set A4 is 15.4%, the overall precision is increased from 74.1% to 89.5%.

17. Results • Recall-Precision of EGFD on Generally Distorted Shapes • Compared with GFD, the improvement on CE-2 is 12%, the overall precision is increased from 80.5% to 92.5%.

18. Results GFD EGFD ZMD

19. Results GFD EGFD ZMD

20. Application of EGFD • The application of the enhancement process is database/ application dependent. • If the database has abundant perspective shapes, this technique can be very effective in retrieving similar shapes. • If the database does not have perspective shapes, or the user wants finer distinction between similar shapes, the enhanced process may not be desirable. For example, if the user wants to distinguish between rectangles and squares, or to distinguish between ellipses and circles, the enhanced GFD can fail, because it normalizes all the shapes into same eccentricity (=1). • In general applications, the enhancement is a useful option to the retrieval system rather than the replacement of GFD.

21. Conclusions • The proposed EGFD improves GFD significantly. It improves GFD’s relatively lower retrieval performance on severely skewed and stretched shapes. It also improves GFD’s robustness to general shape distortions. • A shape normalization method is presented. The shape normalization method can be exploited for general shape representation purposes. • An optimized major axis algorithm (MAA) is proposed. MA is a common normalization mechanism in shape modeling and representation. Common MAA is only for finding MA of contour shape. The proposed optimized MAA can be used for finding MA of generic shapes.