## 3 Glottal Gap Segmentation and Facilitative Playbacks
### Facilitative Playbacks Representation
#### 3.3.2 Global-Dynamics Facilitative Playbacks
Alternatively, reference [123] use phase space reconstruction and correlation dimension over the glottal area time series (GAW) to investigate the dynamic characteristics of the vocal folds. In [124], PVG and GAW were combined to construct a 3D representation named Phonovibrographic Wavegram (PVG-wavegram). This playback let visualize the intra- and inter-cycle characteristics of vocal fold vibrations within a single three-dimensional scalar volume field for long phonation sequences. One of the latest FP proposed in the literature is Glottocorrelogram (GCG). This representation allows to visualize the correlation coefficients obtained from the glottovibrogram presenting phase and frequency variations among the vocal folds edges. Only a few FP do not depend on a segmentation approach. Reference [125] proposed a method for extracting spatial features based on pixel-wise Fourier analysis of a time-varying brightness curve for each pixel across images. They named this FP Laryngotopography (LGT). LGT let to display spatial information related to natural frequencies of a portion of a larynx, amplitude of vibration, and propagation speed of MW. In [126] Principal Component Analysis (PCA) was applied to the pixel intensity of the high-speed sequence, and the first two PCA coefficients were visualized. The Glottaltopogram (GTG) method reveals the overall spatial synchronization pattern of the vocal folds vibrations for the entire laryngeal area, rather than focusing on a specific location or frequency. Despite full spatial resolution is maintained, the time information is not preserved. Since the purpose of HSV analysis is to characterize the motion of the vocal folds by identifying their movements from one frame to the followings, the authors in [127] used Optical Flow (OF) computation to track the vocal folds solely based on its motion, with no need of additional segmentation techniques. OF aims at understanding and interpreting the dynamical behavior of moving objects  
Figure 14: Schematic representation of the GVG playback. (1) Segmentation; (2) Resampling of the extracted vocal folds edges; (3) Computation of vocal fold deflections \(\delta_{GVG}(pc,t_{k})\); (4) \(I_{GVG}(x,y)\) representing an HSV with five glottal cycles. a low-level by the estimation of a displacement vector for each pixel in the image, creating a dense motion field \(\mathbf{\mathcal{W}}(\mathbf{x},t_{k})\) (Equation (6)) [69]. The direction of the motion field is expected to be inwards in the closing phase and outwards during the glottal opening. The authors implemented two global FP from \(\mathbf{\mathcal{W}}(\mathbf{x},t_{k})\) named as Optical Flow Glottovibrogram (OFGVG) and Optical Flow Kymogram (OFKG). OFGVG is derived from GVG and represents the velocity of glottal movement per cycle. It is obtained by averaging each row of the \(u(\mathbf{x})\) component of the flow, and represents it as a column vector. The OFGVG complements the spatio-temporal information provided by the common techniques (GVG, PVG) by adding velocity information for each displacement of the vocal folds. On the other hand, GOFW is a 1D representation that is based on GAW, but here the total magnitude of the velocity is computed over a ROI for each instant of time. GOFW represents the change of velocity along time at the same instant in which it is quantified the total velocity variation. Both FP have the same limitation existing in GVG and GAW, since they are not suitable to analyze symmetry between the vocal folds. A summary of the main studies carried out to synthesize the vocal folds vibratory patterns is presented in Table 4.