A Segmentation Algorithm Using Dyadic Wavelet Transform and the Discrete Dynamic Contour

1. A Segmentation Algorithm Using Dyadic Wavelet Transform and the Discrete Dynamic Contour Bernard Chiu University of Waterloo

2. Agenda • Introduction and Problem Definition • Proposed Solution • Dyadic Wavelet Transform • Discrete Dynamic Contour (DDC) Model • Conclusion

3. Introduction and Problem Definition • This segmentation algorithm is developed for detecting the prostate boundary in 2D ultrasound images. • Prostate segmentation is a required step in determining the volume of a prostate. • The radiologists manually segment at least a hundred cross-sectional ultrasound images before they can obtain an accurate estimate of the prostate volume  Too time-consuming!

4. Introduction and Problem Definition • To reduce the time required for prostate segmentation, a computerized method has to be developed. • The quality of the ultrasound images make it a very difficult task, because of the presence of false edges.

5. Proposed Solution

6. The Dyadic Wavelet Transform

7. The Dyadic Wavelet Transform

8. The Dyadic Wavelet Transform

9. The Fast Discrete Dyadic Wavelet Transform

10. The Fast Discrete Dyadic Wavelet Transform

11. The Fast Discrete Dyadic Wavelet Transform

12. Example: The scale-24 gradient modulus calculated for a typical ultrasound prostate image

13. The DDC Model • Motivation for introducing the DDC model • Terminology • Initialization • Internal and External Forces • Dynamics • Resampling

14. Motivation for introducing the DDC Model • After obtaining the gradient modulus using the fast dyadic wavelet transform, one needs to estimate the location of the edge. • In Mallat’s multiscale edge detection algorithm, edge are defined by joining the local maxima points of the gradient. Unfortunately, it is almost impossible to get a closed contour using this method. • The DDC model can be used to solve this problem since it is always closed.

15. Terminology

16. Terminology Define curvature, tangent and radial vector

17. Initialization • The spline interpolation techniques are used to define the initial contour.

18. Internal and External Forces • The purpose of internal forces is to minimize the curvature of the contour, so that the general shape of the segment is not distorted by small/irregular features. • User defines an energy function, Eim, that relates to some kind of image feature.

19. Contour Dynamics • Total force • Calculate position, velocity and acceleration

20. Resampling

21. Evaluation Criteria – Distance-Based Metric

22. Evaluation Criteria – Distance-Based Metric

23. Results

24. Conclusion • Proposed a new algorithm that • uses the gradient modulus of the image obtained using dyadic wavelet transform, and • defines the edge using the DDC model, which is driven by an external energy field proportional to the gradient modulus. • This algorithm always gives a closed segment, which cannot be obtained by using Mallat’s multiscale edge detection algorithm. • The proposed algorithm requires a radiologist to enter four initial points, rather than 30-40 points required to define the prostate boundary. • Our algorithm is obviously not perfect. In particular, the performance of the DDC model is sensitive to the initial contour. Fortunately, in most cases, the initialization method introduced approximates the actual boundary with reasonable accuracy.