1. Lijuan Zhao Advisors: Prof. Fatima Merchant Prof. Shishir Shah

2. Motivation Breast Reconstruction - Breast cancer treatments usually lead to complete or partial breast removal - Breast reconstruction surgery is used to rebuild lost or deformed tissue - Surgery is completed in a multi-step process lasting for 2-3 years - Currently there is no process to monitor or quantify changes occurring in breast morphology through the reconstruction process - This information is needed to better assess surgical outcome

3. Current Quantitative Parameters for Assessment of Breast Reconstruction Measurements of breast aesthetics - Volume, symmetry, proportion, projection, ptosis, etc. Current parameters provide a global assessment at a given time point No measure are available to correlate local morphological changes over time (a)(b) (c)(d) (e) (a) Volume (b) Symmetry (c) Proportion (d) Projection (e) Ptosis

4. Computational Challenge Visit 1Visit 2Visit 3 Retrieve breast data from 3D torso images Analyze breast changes for different visits for same patient

5. 3D Breast Imaging Example of 3D torso image Point cloud Triangular mesh surface 2D texture image mapped onto surface

6. Flow-chart of processing steps

7. Spatio-Temporal Correspondence Chest walls are not matched for different visits - Coordinate systems may not be same - Patient weight changes may occur - 3D correspondence is required

8. Mathematical Model for Spatio-temporal Correspondence Construct corresponding model - Choose some fiducial points - Connect them to form a geometry - Choose same points on different images - Construct the correspondence between torsos Experimental measurements: - Which fiducial points are suitable - Linear or non-linear relationships for distances between fiducial points in different images

9. Quantitative correlation of changes The transformations of breast data are deformable Using 3D group-wise point sets based non-rigid registration to analyze breast changes ‐ Propose new method with good cost function and optimization scheme Develop appropriate model to represent local topology of point sets Develop Similarity Metric for registration of temporal data sets Develop methods to quantify changes in breast morphology over time

10. Thank You! Questions?

11. Possible Approaches Robust point set registration using Gaussian mixture models ‐ Using Gaussian mixture models to represent point sets ‐ Divergence measure: L2 distance ‐ Deformation model: thin-plate splines (TPS)+ Gaussian radial basis functions (GRBF) ‐ PROS: efficient and robust ‐ CONS: but only works for pair-wise point set Group-wise point-set registration using a novel CDF-based Havrda-Charvat divergence ‐ Using Dirac mixture models to represent point sets ‐ Divergence measure: CDF-HC divergence ‐ Deformation model: thin-plate splines (TPS) ‐ PROS: efficient and simple to implement ‐ CONS: not robust for noise and outliers