# Synthetic Data Generation for the Development of 2D Gel Electrophoresis Protein Spot Models
## 3 Results and Discussion
Model performance is compared by normalized sum of squared error (NSSE) (lower is better). Models “M2G”–”MSAS” are the baselines, and “AE+B” and “AE–B” are the developed autoencoder-based spot models. Experimental cases: “=1 spot”/“>1 spot”——one or more spots in the input image; “+Mask”/“–Mask”——spot mask is provided or not (mask is used by the baseline algorithms); “+Noise”/“+Bckg”—input images may be corrupted by Gaussian noise or by slowly varying background. Please refer to the text of Section 3 for more details on the models and for the description of the experimental case notation used in the legend. The results of the spot parameter estimation experiments are presented in (Figure 9). This experiment is performed using the synthetic images only due to the fact that the ground-truth parameters of the real spots are unknown. The experimental cases are the same as in the reconstruction of the synthetic images: \"=1 spot\" or \">1 spot\"; \"+Mask\" or \"\(-\)Mask\"; and \"+Noise\", \"+Bckg\", or neither. Spot parameters can be computed in two ways: from the reconstructed spot or predicted from the bottleneck features of the AE. Both solutions are implemented and experimentally compared. Algorithms \"AE+B\"r\" and \"AE-B\"r\" compute the spot's parameters from the reconstructed spot. Algorithms \"AE+B\"p\" and \"AE-B\"p\" predict the spot's parameters from the AE's bottleneck features. The following is a list of the protein spot baseline models evaluated and compared during the experiments [42; 45; 46; 63]:  
* Two-way adapting (anisotropic) 2D Gaussian model (M2G);  
Figure 9: Results of protein spot key parameter estimation: peak intensity (**a**) and integrated spot intensity (volume) (**b**). Model performance is compared by normalized mean of squared error (NSSE) (lower is better). Models “M2G”–“MSAS” are the baselines, and “AE+B”r”, “AE\(-\)B”r”, “AE+B”p”, and “AE\(-\)B”p” are the developed autoencoder-based spot models. Experimental cases: “=1 spot”/”>1 spot”——one or more spots in the input image; “+Mask”/”—Mask”—spot mask is provided or not (mask is used by the baseline algorithms); “+Noise”/”+Bckg”—input images may be corrupted by Gaussian noise or by slowly varying background. Please refer to the text of Section 3 for more details on the models and for the description of the experimental case notation used in the legend. * The diffusion model (MD);
* Three Gaussian functions model (M3G);
* Four Gaussian functions model (M4G);
* Four Gaussian functions with flat top model (M4 GFT);
* Simple \(\Pi\)-shaped model (MP);
* \(\Pi\)-shape model with flat top (MPft);
* Two-way symmetric bell-shaped model (MBS);
* Asymmetric bell-shaped model (MBAS);
* Two-way symmetric sigmoid-based model (MSS);
* Asymmetric sigmoid-based model (MSAS). The following is a list of the new spot reconstruction algorithm variants or the separate outputs of the same algorithm that were included in the evaluation results (graphs):  
* \"AE+B\"--spot reconstructed by the autoencoder with the constant background remaining;
* \"AE-B\"--spot reconstructed by the autoencoder without background;
* \"AE+B\"--spot parameters computed from the reconstructed spot, and background is not removed during reconstruction;
* \"AE-B\"--spot parameters computed from the reconstructed spot, and background is removed during reconstruction;
* \"AE+B\"--spot parameters predicted from the AE's bottleneck features, and AE is trained to reconstruct the spot leaving the background;
* \"AE-B\"--spot parameters predicted from the AE's bottleneck features, and AE is trained to reconstruct the spot without background. To summarize the results of all the experiments, the developed spot reconstruction algorithm trained using only synthetic data outperforms all the baseline algorithms in all experiments based on synthetic and real data. Lower performance gains are achieved when the experimental data includes the least noise. When additional noise is introduced, the new algorithm performs better with a larger margin, and this tendency holds in all cases.