# Multi-Channel Surface EMG Spatio-Temporal Image Enhancement Using Multi-Scale Hessian-Based Filters
## 3 Results and Discussions
The result of this analysis for an input SIR varying from 3 to 25 dB for the signal in Figure 4a is shown in Figure 5. It can be seen from the result that initially, at low-input SIR, the proposed filter is able to enhance the signal with less improvement in the output SIR; however, as the input noise level decreases, the performance of the proposed filter is better and the output SIR increases. The higher output SIR shows that this filter may be a better choice as a preprocessing step for EMG signal analysis. The results of the proposed filter for a multi-channel sEMG signal acquired from the external anal sphincter muscle acquired using an anal probe developed in the LISiN politecnico di Torino Italy [3] are shown in Figure 6. The signals were acquired from the EAS muscle of 478 pregnant women at clinical partners from five European Countries (Germany, Italy, Latvia, Slovenia, Ukraine). Each clinical partner obtained the approval from the local ethical committee. Each subject was informed about the study protocol and signed an informed consent prior to the experiment [27]. It can be seen in this example signal that the MUAP propagation pattern in the original signal is non-uniform at different locations due to varying size of the mucosa at different locations of the muscle [3]. The proposed filter has successfully enhanced the MUAP regions and the background noise is suppressed, as is evident from Figure 6c. The proposed multi-scale filter is finally evaluated as a pre-processing step for the segmentation of the MUAP propagation region. Graph cut segmentation as recommended in Reference [28] and discussed in detail in Reference [29] is applied to the enhanced image using the proposed filter. The proposed multi-scale filter is also compared with some of the line-like structure enhancement algorithms, namely Hermite Filter, Gabor filter, and Steerable filters. The results of these algorithms for a multi-channel sEMG of the right trapezius muscle are shown in Figure 7.  
Figure 5: The plot of the input to output SIR of the Hessian-based filter. Figure 6: (a) Multi-channel SD sEMG signal recorded from the EAS, (**b**) its interpolated spatio-temporal sEMG image, and (**c**) the output image using the multi-scale filter described in Equations (10)–(14). From the results of Figure 7, it can be summarized that the output of the proposed multi-scale filter is better because it enhanced both the bright and dark portions of MUAP and retained its negative and positive polarity. The Gabor filter added distortion to the image while other algorithms were unable to retain the same polarity of the EMG values, except the proposed filter. From Figure 7f, it is evident that the proposed filter enhanced both the dark and bright regions of the MUAP and suppressed the background pixels. This is because the second eigenvalues of the Hessian matrix for both the dark and bright MUAP regions are high, thus producing a higher filter output. In case of background, both the eigenvalues of Hessian are smaller, thus producing almost a zero-filter output. To analyze the results of the of the MUAP enhancement algorithms quantitatively, the enhanced image by each algorithm was segmented using the graph cut segmentation. True Positive (TP), True Negative (TN), False Positive (FP), and False Negative (FN) for computer-simulated sEMG signals were computed by labeling the pixels and counting the correctly labeled pixels. For these simulated  
Figure 7: (**a**) A multi-channel single differential sEMG signal recorded from the right upper trapezius muscle, (**b**) the spatio-temporal topographic image of the sEMG signal shown in (**a**), (**c**) the output of the Hermite filter, (**d**) output of the Gabor filter, (**e**) output of the steerable filter, and (**f**) the enhanced EMG image using the proposed multi-scale Hessian-based filter. signals, the skin layer thickness was 1 mm, fat layer thickness was 3 mm, conductivity ratio between skin and fat layers was 20, and conductivity ratio between fat and muscle layers was 0.5.