## 2 Data  
Two types of data were considered: real volume and synthetic volume used in Monte Carlo test. Exemplary real volume was tested in this paper for illustrative purposes (Figure 1).  
Proper 3D view with enhanced contrast and color allows visual inspection of parathyroid glands and some details of the structures are visible, including local maxima [27]. Maximal Intensity Projection (MIP) is used for the visualization of SPECT [45; 46; 47]. This solution indicates details such as local maxima of SPECT that are not visible for Average or Composite Intensity Projections [47] and removes artifacts from distant regions not related to parathyroid glands by the application of spherical region of interest [27]. Additional threshold for removal voxels with values below specified value improves visibility of region with parathyroid glands (Figure 1 right) [27]. This volume has complex structure and shows the importance of multiparameter mixtures for analysis.  
Automated analysis is required for the estimation of parameters because the selection of 3D view parameter is not sufficient and is a time-consuming task. It could lead to human operator induced error, therefore automated volume analysis is very important for achieving reliability.  
Synthetic volumes that are generated from the model are used in this work for the evaluation of the estimation algorithm and allow testing and validation of estimated properties for different algorithms [31]. The assumed volume is \(32\times 32\times 32\) voxels (cells) in size and was selected based on observation of real SPECT volumes. Such size (power of two) is also important for code and memory accesses optimization. The estimation of parameters for three additive distributions (components) was tested and it was assumed that number of distributions was known. The Monte Carlo approach was used for the testing of performance using random number generators. There were 15,000 test cases for global best, ring, and random neighborhood topologies each. There were 32 particles and 500 iterations steps of PSO that were selected arbitrarily after pretests.  
Synthetic volumes allow testing of the estimation algorithm quality. Noiseless volume is smooth and depends on filtering algorithms and parameters during volume reconstruction. Adding noise to synthetic volume allows testing the algorithm with higher independence on the selection of filtering algorithms and filtering parameters used in volume reconstruction (acquisition) process. Low-pass filtering smooths volume, reduces contrast, and blurs edges. Adding noise to synthetic volume allows extending testing boundaries of the tested algorithm. It improves the testing reliability, because it reduces dependence on the filter settings.  
Separation of left and right parathyroid glands is usually straightforward. The problem is the overlapping of multiple structures in SPECT images for left or right side. The model-based approach allows algorithm testing using smooth (ideal, without noise) volumes as well as noised volumes, such as in the examples shown in Figure 2. Noised volumes are achieved using additive Gaussian noise with mean zero and unit standard deviation. Testing separation algorithms with noises even higher then observed typically allows determination of properties and comparison of further selections in CADx applications.  
Figure 1: Fusion coronal image of Single-Photon Emission Computed Tomography combined with Computed Tomography (SPECT/CT)—a lesion with slightly increased uptake in a lower left pole of thyroid gland corresponds with abnormal parathyroid gland (**left**). 3D view of parathyroid glands (**right**, SPECT only).  
Figure 2: Exemplary slices from synthetic volume (there are three overlapping additive components).