K Means Clustering Using Localized Histogram Analysis and Multiple Assignment. Michael Bryson 4/18/2007

Transcription

1 1 K Means Clustering Using Localized Histogram Analysis and Multiple Assignment Michael Bryson 4/18/2007

2 2 Outline Introduction Redefining Distance Preliminary Results Multiple Assignment Discussion

3 3 Introduction Introduction What is clustering? Why cluster medical images? What is K Means clustering? How is distance defined? Redefining Distance Preliminary Results Multiple Assignment Discussion

4 4 What is clustering? Clustering is a form of segmentation, where small units are grouped into larger groups to create distinct regions.

5 5 Why cluster medical images? Many applications of general image segmentation to medical images: Locate tumors and other pathologies Measure tissue volumes Computer guided surgery Diagnosis Treatment planning Study of anatomical structure Pseudo colorization

6 6 What is K Means Clustering? K means clustering iteratively assigning each pixel to the cluster with the 'closest' center. Choose a K (number of clusters) Generate K random centers (or choose them heuristically) Assign each pixel to the 'closest' cluster center Calculate new centers Repeat until convergence

7 7 What is K Means Clustering? means_algorithm

8 8 What is K Means Clustering? means_algorithm

9 9 What is K Means Clustering? means_algorithm

10 10 What is K Means Clustering? means_algorithm

11 11 How is distance defined? In order to determine which center is closest to each pixel, distance must first be defined. Two simple distances are Geometric distance and difference between intensities. These two metrics have limited effectiveness in medical images. x x c 2 y y c 2 F x, y C i

12 12 Redefining Distance Introduction Redefining Distance Intensity Difference Problems Averaging? Local Histograms Preliminary Results Multiple Assignment Discussion

13 13 Intensity Difference Problems F x, y C i

14 Intensity Difference Problems 14

15 15 Averaging? Using the average of a pixel's neighborhood could help this problem, but could still have large ambiguities.

16 16 Local Histograms The histogram of the neighborhood surrounding a pixel should provide a 'fingerprint' identifying its region. Sample Histograms Row 4 6 Row Row 2 0 Column B Column E Column H Column K Column N Column Q

17 17 Local Histograms The distance between two histograms is calculated as the RMSD between each pair of bins. i H 1 i H 2 i 2

18 18 Local Histograms This algorithm adds two new parameters: K: number of clusters Bin Size: size of each bin for calculating histograms (assumed to be uniform) Neighborhood Size: the number of surrounding pixels to consider for the calculation of each histogram

19 19 Preliminary Results Introduction Redefining Distance Preliminary Results Intensity Based Results Histogram Based Results Multiple Assignment Discussion

20 Intensity Based K Means (1) 20

21 Intensity Based K Means (2) 21

22 Intensity Based K Means (3) 22

23 Intensity Based K Means (4) 23

24 Intensity Based K Means (5) 24

25 Intensity Based K Means (6) 25

26 Histogram Based Distance (1) 26

27 Histogram Based Distance (2) 27

28 Histogram Based Distance (3) 28

29 Histogram Based Distance (4) 29

30 Histogram Based Distance (5) 30

31 Histogram Based Distance (6) 31

32 Comparison 32

33 33 Histogram Based Distance Sensitive to Initial Centers

34 34 Multiple Assignment Introduction Redefining Distance Preliminary Results Multiple Assignment Discussion

35 35 Multiple Assignment What should 3 clusters look like in this picture? 4? 5?

36 36 Multiple Assignment Consider the following list of distances for a hypothetical pixel to five centers: What would happen if this pixel was assigned (equally) to both clusters 1 and 2?

37 37 Multiple Assignment This could lead to overlapping clusters, and clusters within other clusters. Assignment to multiple clusters might cause issues with convergence. A simple solution to guarantee convergence is to use a 'cooling' function.

38 38 Discussion The methods presented are general, and can be applied to a wide range of medical images. No high level information such as shape models are used. Using histogram based K Means has better performance then single intensity based clustering, but is still not perfect.

39 Questions, Comments, 39 Suggestions?