1. 1 Diffusion Distance for Histogram Comparison, CVPR06. Haibin Ling, Kazunori Okada Group Meeting Presented by Wyman 3/14/2006

2. 2 Introduction This paper proposed: –A new dissimilarity measure between histogram-based descriptors called diffusion distance (SIFT, GLOH, Shape Context, Spin Image) It performs better in both accuracy and efficiency than other distance measures in shape matching and interest point matching It may be useful to other histogram comparison problems

3. 3 Background Given one image of an object, how do we find all of its remaining images in a database? Articulated shape database Difficulties: Shapes look similar, but are articulated Solutions: Use histogram- based shape descriptor, such as Shape context

4. 4 Background – Shape Context Key idea: Represent an image in terms of descriptors at certain locations that describe the edges relative to those locations Shape context of a point is the histogram of the relative positions of all other points in the image. Use bins that are uniform in log-polar space to emphasize close- by, local structure. PAMI 2002

5. 5 Background – Shape Context Original method use the chi-square test statistic to compare two histograms: Some problems arose due to this distance metric! Bin-to-bin distances between histograms/descriptors

6. 6 Background – Shape Context Problems: –Sensitive to quantization effects –Sensitive to distortion problems due to deformation, illumination change and noise

7. 7 Background – Shape Context Solutions: –Use cross-bin distance metric such as the Earth Mover’s Distance (EMD) It allows bins at different locations to be partially matched It solves quantization effect Very slow!

8. 8 Modeling Histogram Difference with a Heat Diffusion Process First consider 1D distributions h 1 (x) and h 2 (x) Their difference d(x) = h 1 (x) - h 2 (x) Bin-by-bin distance can be obtained by putting a metric (e.g. L2 norm) on d(x), but we do not do so! Treat the difference as an initial value (at time t = 0) of an isolated temperature field T(x,t), i.e. T(x,0) = d(x)

9. 9 Heat Diffusion Equation As time goes by, d(x) vanishes everywhere!

10. 10 The distance A distance between the histograms is defined as:

11. 11 Example

12. 12 Example From the result, we see that K are monotonically increasing with delta, thus K measures the degree of deformation between two histograms

13. 13 Better than EMD EMDDiffusion Dist. EMD = minimal amount of work that needs to be done to transform one distribution into the other The same for both differences! Smaller distance for d 12

14. 14 Diffusion distance Now consider 2D histograms Interpretation: Summing the value in each layer of difference’s pyramid (with exponentially decreasing size)

15. 15 Experiment 1 Shape Matching with Shape Context

16. 16 Experiment 2 Image Feature Matching –SIFT and Spin Image are also histogram-based descriptors –SIFT and Spin Image are originally designed to use L2 norm as the distance metric

17. 17 Experiment 2

18. 18 Experiment 2 Running time is low!

19. 19 Q & A Thank you!