Improving Retrieval Performance of Zernike Moment Descriptor on Affined Shapes Dengsheng Zhang, Guojun Lu Gippsland School of Comp. & Info Tech Monash University Churchill, VIC 3842 Australia dengsheng.zhang@infotech.monash.edu.au http://www.gscit.monash.edu.au/~dengs/

Outline Motivations Zernike Moment Descriptor (ZMD) Problem Improving ZMD Experimental Results Conclusions

Motivations Content-based Image Retrieval Image description is an important issue, which constitutes one of the key parts of MPEG-7. 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.

Affine Distorted Shapes Are Common

Zernike Moment Basically, ZMD is derived by applying Zernike moment transform on shape image in polar space.

Zernike Moment The first 36 Zernike moments of up to order 10 are shown in Table 1. Order (n) Zernike moment of order n with repetition m (Anm) Total number of moments up to order 10 A0, 0 36 1 A1, 1 2 A2, 0, A2, 2 3 A3, 1, A3, 3 4 A4, 0, A4, 2, A4, 4 5 A5, 1, A5, 3, A5, 5 6 A6, 0, A6, 2, A6, 4, A6, 6 7 A7, 1, A7, 3, A7, 5, A7, 7 8 A8, 0, A8, 2, A8, 4, A8, 6, A8, 8 9 A9, 1, A9, 3, A9, 5, A9, 7, A9, 9 10 A10, 0, A10, 2, A10, 4, A10, 6, A10, 8, A10, 10

Problem Generally, ZMD has good performance on generic shapes. Its overall retrieval precision after full recall is 97.6% for rotated shapes, 85.3% for scaled shapes, 99.3% for rotated and scaled shapes, 68.5.1% for perspective transformed shapes and 66.5% 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.

Only half the sampled positions contain Under-sampling Problem Skewed Only half the sampled positions contain shape information Non-distorted Virtually all the sampled positions contain shape information

Improving ZMD Normalization R S 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. R S

Improving ZMD 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).

Improving ZMD Normalization Result: Normalization Normalization

Improving ZMD Applying ZMD transform on the rotation and scaling normalized image. The normalized transform coefficients are the improved ZMD. Each shape in the database is indexed using the derived ZMD. The similarity between two shapes is measured by the Euclidean distance between their ZMDs.

Experiment Dataset Indexing and automatic retrieval 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

Performance Measurement Recall vs Precision For each query, the precision of the retrieval at each level of the recall is obtained. The result precision of retrieval is the average precision of all the query retrievals.  

Results Average Precision-Recall of the improved ZMD on perspective shapes. Compared with GFD, the improvement on Set A4 is 17.6%, the overall precision is increased from 68.5% to 86.1%.

Results Average Precision-Recall of EGFD on Generally Distorted Shapes Compared with GFD, the improvement on CE-2 is 22.5%, the overall precision is increased from 66.5% to 89%.

Results Improved ZMD ZMD Improved ZMD ZMD

Results Improved ZMD ZMD Improved ZMD ZMD

Application 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 improved ZMD 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.

Conclusions The proposed technique improves ZMD significantly. It improves ZMD’s relatively lower retrieval performance on severely skewed and stretched shapes. It also improves ZMD’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.