Table 1.

Mean absolute error and standard deviation between the estimated and ground-truth normal-mode amplitudes along with the angular and shift distances obtained with HEMNMA-3D and “Discrete” synthetic dataset, using an atomic structure (Atomic) and simulated EM map (Volume) as input references.

Experiment		Mode 7		Mode 8		Mode 9		Angular (deg)		Shifting (vox)		p-Value	Samples
Ref	Dataset	Mean	Std	Mean	Std	Mean	Std	Mean	Std	Mean	Std
Atomic	“Discrete”	16.51	11.87	10.91	7.64	10.70	6.66	1.33	0.77	0.19	0.09	p > 0.01	871/900
Volume	“Discrete”	17.70	13.26	11.90	10.13	12.29	8.03	1.33	0.81	0.21	0.10	p > 0.01	870/900

The data points below the p-value of 0.01 were excluded from the error evaluation based on the Mahalanobis distance measure (few data points differing significantly from the remaining observations, which would not be selected in real-case experiments as being too isolated and far from other points). The number of points used for the error computation is shown in the last column of the table (column Samples) and the region with the kept points (p-value > 0.01) is shown in Figure 6.