# Learning to Segment Blob-like Objects by Image-Level Counting
## 4 Experiments and Results
### Architectures, Training, and Evaluation Settings
#### 4.2.2 Synthetic Data Generation  
In addition to the evaluation of the training approaches on natural data, we used a method to generate synthetic data to avoid the limiting characteristics of natural data in a separate evaluation. In this way, it is possible to generate any number of objects in an image and to ensure consistent annotations for each example. In contrast, manually generated annotations are always subject to errors, such as missing, inaccurate, or inconsistently marked regions.  
To make a synthetic image \(\mathbf{I}_{j}\) similar to the natural ones described in Section 4.2.1, we used a background of random noise by sampling values from a uniform distribution between 0 and \(r_{\text{max}}\) for each pixel and added a set of \(n_{j}\) ellipses with intensities \(k_{j,1},..,k_{j,n_{j}}\), centers at \(p_{j,1},..,p_{j,n_{j}}\), rotations \(\varphi_{j,1},..,\varphi_{j,n_{j}}\), and bounding box side lengths \((s_{j,1,x},\,s_{j,1y}),..,(s_{j,n_{j},x},\,s_{j,n_{j},y})\) with \(s_{\text{min}}\leq s_{j,u,v}\leq s_{\text{max}}\), \(1\leq u\leq n_{j}\), \(v\in\{x,y\}\). The resulting images were overlaid with wave patterns to simulate image artifacts. For this purpose,we used a method presented in previous work [40] that creates a given number \(w_{j}\) of sinus waves with center positions \(c_{j,1}^{(w)},..,c_{j,w_{j}}^{(w)}\) and intensities \(l_{j,1}^{(w)},..,l_{j,w_{j}}^{(w)}\). To create imperfections similar to those in natural images, the method uses an additional fading center point \(c_{j,q}^{(t)}\) and a fading rate \(\beta_{j,q}\) for each wave \(q\), which makes the wave intensity decrease with increasing distance to \(c_{j,q}^{(0)}\). This allows for different combinations of wave intensities to be visible at different positions. With a probability of \(\gamma\), no waves were added to the image at all. Each parameter was randomly selected from a predefined interval, which is given in Table 1. Example images generated with this method are shown in Figure 6.  
\begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Interval** & **Description** \\ \hline \(n_{j}\) & \([0,50]\) & number of ellipses \\ \(f_{\text{max}}\) & \([1,1]\) & noise intensity \\ \(k_{j,i}\) & \([0.5,1]\) & ellipse intensity \\ \(s_{j,u,v}\) & \([6,18]\) & bounding box side lengths \\ \(l_{j,i}^{(w)}\) & \([0.75,1]\) & wave intensity \\ \(\gamma\) & \([0.5,0.5]\) & waves probability \\ \(w_{j}\) & \([0,5]\) & number of waves \\ \(\beta_{j,q}\) & \([0,1]\) & wave fading rate \\ \hline \end{tabular}
\end{table}
Table 1: Parameter intervals for the generation of a synthetic image \(\mathbf{I}_{j}\). The images produced with these parameters were scaled to a fixed interval after their generation.  
Figure 5: Examples of surface plasmon resonance effect (SPR) [39] images recorded with the plasmon-assisted microscopy of nano-objects (PAMONO) sensor [9]. All images contain artifacts of rather low intensities. The upper row shows signals from 1, 3, and 7 annotated particles (from left to right), which can be seen as bright spots of different intensities. Around some of the particles, typical SPR wave patterns are visible. The lower row shows images without particles.  
Figure 6: Examples of synthetically generated images. The images in the upper row contain elliptical objects of different sizes, circularities, and intensities on a random noise background overlaid with random waves. The images in the lower row were generated in the same way, but contain no objects.