1. An Efficient and Robust Technique for Region Based Shape Representation and Retrieval
Dengsheng Zhang and Melissa Chen Yi Lim
Gippsland School of Information Technology, Monash University
Churchill, Victoria 3842, Australia

2. Outline Motivations Polar Raster Signature Experiments Results
Conclusions

3. Motivations—Shape Matrix
Conventional shape methods use grid sampling to acquire shape information.
The shape representation derived this way is usually not translation, rotation and scaling invariant. Extra normalization is therefore required.
Goshtasby proposes the use of shape matrix which is derived from a circular raster sampling technique

4. Motivations—Shape Matrix
Since shape matrix is a sparse sampling of shape, it is easily affected by noise.
Besides, shape matching using shape matrix is a two dimensional process which is too expensive.
Figure 1. A shape is overlaid with circular grid (left) and
its shape matrix (right)

5. Motivations—Area Ratio
Perui et al. propose a shape description based on the relative areas of the shape contained in concentric rings located in the shape centre of the mass
where A() is the area function. The shape descriptor is the feature vector of x = [x1, …xn]T.

6. Motivations—Area Ratio
Although the area ratio descriptor is more compact than the shape matrix, it ignores the shape distribution within the measured ring.
Consequently, it loses local information of a shape, and the two perceptually different shapes can be taken as the same under this descriptor.
Figure 2. The spike shape (left) and the dot shape (right) are regarded as same shape using AR, although they are very different.

7. Polar Raster Signature—Concepts
Considering the drawbacks of the above two methods, we propose a polar raster sampling signature technique which computes a signature function of the sampled points.
We overlay a polar raster grid over the shape image, and compute the number of shape pixels on each of the concentric circles and on each of the diameters of the polar sampling grid.
The number of pixels is a function of the radius and the angle, the function is called polar raster sampling signature, or PRS for short.
The proposed approach lines between the shape matrix and the area-ratio approaches.

8. Polar Raster Signature—implementations
The PRS signature function consists of two components: S(r) and S(), which are given by:
Where 0≤r≤R, 0≤≤; f(x, y) is the binary value of image pixel at (x, y), (xc, yc) is the centre of mass of the shape image; and (x) is the Dirac delta function

9. Polar Raster Signature—implementations
In our case, r is quantized by 32, and  is quantized by 30. An example shape and its first component of PRS signature are shown as following.
The matching between two sets of signatures is achieved using L2 distance.
Figure 3. A region shape (left) and its PRS component (right).

10. Polar Raster Signature—Invariance
Translation invariance. Due to the use of shape centroid as the origin, the PRS is translation invariant.
Rotation invariance. Due to the use of circular sampling, the PRS is rotation invariant.
Scaling invariance. The scaling invariance is achieved by normalize all shapes into the same size, which is 128x128. Before applying scaling, shapes are cropped out from the shape images to remove those blank surrounding.

11. Experiments—Setup
We test the retrieval performance of the proposed PRS using a standard shape database and measurement.
The retrieval performance of PRS is compared with the above mentioned area-ration (AR) method and two widely used shape descriptors in literature: geometric moment descriptor (GMD) and grid descriptor (GD).

12. Experiments— Performance Measurement

13. Experiments—Database
Data Set 1 – consists of 3,621 image shapes from the MPEG-7 shape database and is used test the scale and rotation invariance. There are 220 image shapes from set A1 and A2 which have been pre-classified into 20 groups
Data Set 2 – consists of 3621 shapes from the MPEG-7 shape database. There are 651 shapes from set A3 and A4 which have been pre-classified into 31 groups (21 similar shapes in each group). They are used to test arbitrary shape distortions

14. Results—Scaling & Rotation Test
Figure 4. Average retrieval performance on scaling and
rotation distortions using 220 queries.

15. Results—Arbitrary Distortion Test
Figure 5. Average retrieval performance on arbitrary distortions using 651 queries.

16. Results—Discussions
In the test of scaling and rotation invariance, the PR curve of PRS is always above the 3 other PR curves.
In the test of arbitrary distortions although PRS and AR have a relatively lower start, they pick up quickly. After 30% of recall, the two methods, especially PRS overtakes the GD significantly.
By analysing the PR curves of both the PRS and AR methods, it can be found that the shape and trend of the two PR curves are similar. Both have good behaviour and are quite stable.

17. Results—Computation Efficiency
Although PRS has higher feature extraction time than GMD,
due to the offline feature extraction, the computation time is acceptable.
The average PRS retrieval time is also acceptable although it is higher than GMD,
as it is only a very small fraction of a second.
Table 1: Time of feature extraction and retrieval of images database shapes
using two of our methods and two region-shape descriptors

18. Conclusions
An efficient and robust region based shape representation technique named PRS has been proposed.
It overcomes several drawbacks in existing techniques, like noise sensitivity, lost of local information and computation complexity.
Experimental results show that the proposed shape descriptor has promising performance compared with well known shape representation techniques.
In the future, various sampling rate at different sections of the radius should be studied to further improve the retrieval performance of PRS.
Dimension reduction method will also be studied, such as using PCA method.