## 3 Glottal Gap Segmentation and Facilitative Playbacks
### Facilitative Playbacks Representation
#### 3.3.1 Local-Dynamics Facilitative Playbacks  
Local-dynamics FP analyzes the vocal folds behavior along one single line that is computed on a line perpendicular to the main glottal axis. In this category, the most used by clinicians and researchers are DKG, VKG and Vocal Folds Trajectories (VFT). They have been successfully applied to demonstrate the change of glottal dynamics in case of damaged tissues, such as lesions, scars, discoloration of the vocal folds and voice disorders [4; 7; 110; 111; 112; 113]. VKG and DKG provide a clear visualization of the glottal cycle opening and closing phases, of the MW traveling across the vocal folds upper surface, and of the displacement of the upper and lower margins of the vocal folds [114; 115; 110]. Given a video sequence \(I(\mathbf{x},t)\), let us denote a horizontal line at time \(t_{k}\) and position \(y_{j}\) as \(\mathbf{KG}(t_{k})\), where \(\mathbf{KG}(t_{k})\) is the row vector \([I(\mathbf{x}_{nj},t_{k})\ I(\mathbf{x}_{n-1j},t_{k})\ I(\mathbf{x}_{n-2j},t_ {k})\\ \cdots\ I(\mathbf{x}_{1j},t_{k})]\). Then, the kymographic matrix \(I_{DKG}(x,y)\) (or \(I_{DKG}^{R,G,B}(x,y)\) for color) is constructed with a set of \(N\) vectors \(\{\mathbf{KG}(t_{k})\in\mathbb{R}^{n},\ k=1,\cdots,N\}\), where each \(\mathbf{KG}(t_{k})\) is a column vector of \(I_{DKG}(x,y)\) (see Equation (1)). \[I_{DKG}(x,y)=\left( \begin{array}{cccc}\mathbf{KG}(t_{1})&\mathbf{KG}(t_{2}) &&\mathbf{KG}(t_{N})\\ \widehat{I(\mathbf{x}_{nj},t_{1})}&\widehat{I(\mathbf{x}_{nj},t_{2})}&\cdots &\widehat{I(\mathbf{x}_{nj},t_{N})}\\ I(\mathbf{x}_{n-1j},t_{1})&I(\mathbf{x}_{n-1j},t_{2})&\cdots&I(\mathbf{x}_{n-1 j},t_{N})\\ \vdots&\vdots&\ddots&\vdots\\ I(\mathbf{x}_{1j},t_{1})&I(\mathbf{x}_{1j},t_{2})&\cdots&I(\mathbf{x}_{1j},t_ {N})\\ \end{array} \right) \tag{1}\]  
In order to interpret the kymographic vibratory pattern, Figure 10 depicts the schematic view of DKG compared with the traditional displays of the vocal folds oscillations. The first row shows eight phases of a glottal cycle in the frontal section, starting with vocal folds opening and ending with a complete vocal folds closure. The second row presents the same eight phases as viewed from above  
Figure 9: Eight Facilitative Playbacks (FP) proposed in the literature. Vocal Folds Trajectories (VFT), High-Speed Digital Kymography (DKG), Glottal Area Waveform (GAW), Glottal Optical Flow Waveform (GOFW), High-Speed Digital Kymography (DKG), Glototovibrogram (GVG), Mucosal Wave Kymography (MKG), Optical Flow Kymogram (OFKG), Phonovibrogram (PVG), Glottaltopogram (GTG), illustrated on the same highspeed sequence. of the vocal folds using HSV. The third shows the DKG playback at a position \(y_{j}\). The kymographic image depicts two cycles of the vocal folds oscillation. The important features observed from the eight phases are: (1) lower margin of the vocal folds begins opening; (2) upper margin of the vocal folds starts to open; (3) lower and upper margins of the vocal folds are open; (4) lower margin of vocal folds is maximally open, upper margin of the vocal folds is still opens; (5) lower margin of the vocal folds closes and is visible; upper margin of glottis is maximally open; (6) lower and upper margins of the vocal folds close, MW propagates on the surface; (7) lower margin of the vocal folds is closed; and (8) upper margin of the vocal folds is closed. Besides the vocal folds, it is possible to observe the motion or none of the ventricular folds [116]. VFT (\(\delta^{IJ}_{seg}(pc,t)\)) synthesizes the HSV in a single image that describes the deflections of the vocal folds edges perpendicular to the glottal main axis [73]. Hence, the vocal folds edges (\(C^{l,r}(t)\)) have to be computed in advance. Later on, a trajectory line, \(\mathbf{L}(t_{k})\)), at time \(t_{k}\) that intersects perpendicularly with the glottal main axis (\(\mathbf{G}(t_{k})\)) in a predefined point \(\mathbf{g}_{pc}(t_{k})\) is defined.