# Wavelia Breast Imaging: The Optical Breast Contour Detection Subsystem
## Appendix B Generation of the Input Point Cloud for the 3D Breast Surface Reconstruction Method
### Ring Removal and Verification  
As mentioned in the introduction, the opening of the examination table of the Wavelia OBCD subsystem is fitted with a plastic ring. The ring removal procedure consists in identifying the points of the working point cloud corresponding to the ring and setting to zero their z coordinate values. To do this, a disk section of points corresponding to the flat surface of the ring is selected, then those points are fitted to a plane. The signed distance to this plane is used as a criterion for the removal of points (positive distance for points above the plane and negative distance for points below the plane). To apply the point removing criterion, a parameter is defined:  
* _inner radius (InRad)_: this parameter is defined as the physical radius of the ring minus an estimate of the expected variation due to reflections on the vertical wall of the ring during the OBCD scan of the breast.  
The removing criterion is applied to the points with Euclidean distance to the xy plane greater than _InRad (see inner radius_ in Figure A6a). The complete ring removal procedure, as applied to a test breast phantom, is shown in Figure A6b.  
The new point cloud, as obtained after ring removal, is named \(Pc_{B}\).  
Some points corresponding to the ring may still remain. To verify this, the following parameters are used:  
* _ring height_: it is the physical height of the ring, including an estimate of the noise along the z axis on the flat ring section (see Figure A6b) during the OBCD scan;
* _mesh resolution (Dxy)_: it corresponds to the desired resolution on the xy plane for the 3D breast reconstructed mesh;
* _remaining reference factor_: it is a factor in the range [0-1], defining whether processing to remove remaining ring points is required, or not. This factor has been determined empirically, based on observations from a series of available scan data, involving both human and phantom breasts.  
The points are selected with an absolute z coordinate value lower than _ring height_. A rectangular flat grid is generated with a resolution corresponding to _Dxy_ by using the minimum and maximum values for the x and y coordinates of the selected points. The z coordinate values of this flat grid are zero. Then a disk section is defined on that grid between radii _InRad_ and _InRad_ - _2-Dxy_. Then, the selected points on the flat grid are projected, and the points of the grid which correspond to the disk section where at least one projected point is present are set to 1. The other points, which do not correspond to the disk section, are set to 0 (see illustration in Figure A7).  
The remaining ring factor is computed by dividing the number of points equal to 1 present within the disk section on the flat grid (white points in the right-hand images in Figure A7) by the maximal number of points which may be present in the disk section. If this ratio is greater than _remaining reference factor_, a specific process to remove remaining ring points will be necessary to be applied. Otherwise, the regular process for artifact removal will be sufficient. Both processes are defined in Appendix C.1.