1. Estimating the tumor-breast volume ratio from mammograms Jorge Rodríguez*, Pedro Linares*, Eduardo Urra*, Daniella Laya*, Felipe Saldivia , Aldo Reigosa  *Multidisciplinary Center of Visualization and Scientific Computing Faculty of Science and Technology – University of Carabobo  Biotechnological and Medical Research Center Faculty of Heath Sciences  Oncology Hospital “Miguel Pérez Carreño” January 2007

2. 2WSCG 07 Introduction One woman in eight either has or will develop breast cancer in her lifetime. Once a tumor has been detected we have to decide about the surgery. Breast conservation surgery (lumpectomy, quadrantectomy) must be applied when it is possible. One of the main factors to decide which type of surgery must be used (lumpectomy, quadrantectomy or total mastectomy) is the tumor-breast volume ratio

3. 3WSCG 07 Introduction Mammograms are among the best early detection methods A correct decision depends on the specialist's ability to imagine the 3D reconstruction from the mammograms This intuitive estimation means high probability of wrong decisions.

4. 4WSCG 07 The Problem ¿It would be possible to build a tool to compute the tumor-breast volume ratio from mammograms only?

5. 5WSCG 07 Our Proposal Segmentation and surface reconstrucion of the tumor and the breast from two orthogonal mammograms which allows the estimating of the tumor-breast volume ratio in order to provide a clinical support decision tool

6. 6WSCG 07 Overview 1.Digitalizing lateral and cranio-caudal mammograms. 2.Segmentation of the breast and tumor from digital mammograms. 3.Mapping the mammograms over 3D planes and establishing the spatial matching. between the projections. 4.Surface reconstruction of the tumor and breast. 5.Computing the breast-tumor volume ratio.

7. 7WSCG 07 Segmentation 1.Filter based strategies failed to segment the irregular and noisy tumor contour 2.A semiautomatic and interactive strategy was chosen in order to profit the specialist experience. 3.The “Intelligent Scissors” technique was implemented

8. 8WSCG 07 We will detect the best way between two point on the boundary. Segmentation with “intelligent scissors”

9. 9WSCG 07 ¿How to Chose the best path?

10. 10WSCG 07 The image is a discrete grid of pixels, so the contour is a piecewise of curves. Segmentation with “intelligent scissors”

11. 11WSCG 07 The best way is the set of pieces of curves which fit better the boundary. Segmentation with “intelligent scissors”

12. 12WSCG 07 The well fitted to the boundary is achieved by: 1.The gradient magnitude 2.The gradient Direction 3.The second derivative zero cross (Laplacian) Segmentation with “intelligent scissors”

13. 13WSCG 07 Let the image be a graph G=(V, E) where V is the set of pixels and there is and edge between two pixels when these pixels belong to the same 8- neighborhood. Also, each edge has a cost defined by a function which depends on the three previous components. Segmentation with “intelligent scissors”

14. 14WSCG 07 The local cost function L(p,q) from a pixel p to its 8- neighbor q, is defined as: L(p,q)=w Z ·f Z (q) + w G ·f G (q) + w D ·f D (p,q) Where, w Z, w G and w D are weights. The optimal cost is given by the minimum accumulated cost that results from adding the local costs in a path from the initial to the end pixel. Segmentación usando “intelligent scissors”

15. 15WSCG 07 Segmentation with “intelligent scissors”

16. 16WSCG 07 Mapping mammograms and 3D matching Mapping mammograms over the 3D planes Mapping contours over 3D planes Matching between mapped planes (interactive process)

17. 17WSCG 07 Surface Reconstruction Projecting curves over XY plane (breast base). Defining the semi-elliptical base of the breast. Swept the plane forward and repeat.

18. 18WSCG 07 Surface Reconstruction Once all the contours has been generated, a simple contour connection algorithm is applied. No branching is present, so the correspondence between adjacent contours is trivial. Tumor is overestimated using a bounding volume (box or sphere).

19. 19WSCG 07 Computing the volume ratio Breast Volume =  A i *step A i : Ellipse i Area Step: Step between adjacent ellipses Tumor volume < Bounding volume Volumetric Ratio = Tumor volume / Breast volume

20. 20WSCG 07 Results

21. 21WSCG 07 Results

22. 22WSCG 07 Results

23. 23WSCG 07 Results

24. 24WSCG 07 Results

25. 25WSCG 07 Conclusions and Future Work We have designed and implemented an useful software tool to estimate he breast-tumor volume ratio from two conventional mammograms The surface reconstruction of the breast has an acceptable appearance. Clinical validation of the software must be achieved in advance. Mammograms digitalizing device must be integrated to the application. The lateral-oblique mammograms must be incorporated to the software in order to achieve more accuracy reconstruction of the tumor and breast.

26. 26WSCG 07 Thanks!!!