## Materials and Methods
### Reconstruction Procedure
#### 2.2.3 Challenges and Automation of Laser Point Detection  
Until now [21], all relevant laser points in the initial frame had to be selected individually and the relative position with respect to its next neighbors had to be registered in a subsequent step. This procedure is very time-consuming and hardly effective. Now, we developed a semi-automatic approach to determine the laser points in the initial frame and its assignment to the respective grid positions. A flowchart of the presented algorithm is shown in Figure 10. Based on a region of interest that can be chosen by the user, the algorithm provides two different methods and suggests six different initial grids. The first method as already used in the previous tracking algorithm [21], applies a top-hat filter, which compensates for uneven illumination of the darker background in the case of bright features. The second method is based on the \"Difference of Gaussians\" (DoG-filter) [31]. By the subtraction of a blurred version (Gaussian filter) of the image from a less blurred version, distinct features like the laser points are enhanced in the resulting difference image. In both cases, the binarization of the images is calculated with a dynamical threshold using again [PERSON]'s method [29]. Small objects below average are discarded since they likely represent reflections on the mucosal vocal fold tissue. The center of mass is determined on the remaining objects and very close points are merged. In a post-selection step, the detected points are checked for regularity using triangulation. All neighboring laser points are linked by triangles and points with strongly deviating angles are eliminated. The relative grid position of each laser point is automatically concluded from the geometrical orientation to its neighbors as described by [32]. Potentially required corrections in the laser point detection (adding, moving, deleting laser points) and the grid alignment can be done manually, which is supported by a graphical user interface. However, the global grid position, which is crucial to correctly assign the corresponding homography from the calibration procedure to every individual laser point, still has to be determined by an experienced operator. This inherent difficulty of the reconstruction algorithm will be addressed in detail in Section 4. The major challenge in tracking the laser points from frame to frame is the disappearing and reappearing of the points, which occurs only partly periodical. On the one hand, the disappearing results from the opening and closing of the glottis. The laser points within the glottis hit the tissue surface considerably deeper than the vocal folds in the subglottal area and are therefore typically not visible in the recordings. The laser points then reappear during the closing process, in which case the reassignment to the correct grid position must be guaranteed. Earlier versions of the tracking algorithm already \"freezed\" the laser points that lie within the glottis and suspended the tracking. However, the corresponding \"unfreeze\" action, when the points reappear and lie outside the glottis contour, had to be initiated manually. In addition to that, a combination with suboptimal glottis  
Figure 10: Flowchart of the initial grid detection. White corners indicate new processing steps and red corners indicate a necessary or optional user interaction. contours frequently led to a \"flight\" of the laser points from the glottis contour due to the gradual grayscale distribution at the vocal fold edge. On the other hand, laser points may also be overlapped by reflections on the mucosal surface of the vocal folds. In this case, the tracking algorithm repeatedly followed the typically brighter reflections instead of the laser points if not prevented by the operator. An improved and robust tracking algorithm, which is equally efficient around the glottis and in case of reflections, requires less interaction from the user and makes the reconstruction process more effective.