Figure 1

(a) Experimental HAADF STEM image of a Pb nanoparticle embedded in crystalline Si. (b) Refined model. (c) Histogram of scattered intensities of the Pb columns. The black solid curve shows the estimated mixture model; the individual components are shown as red dashed curves. (d) The integrated classification likelihood criterion evaluated as a function of the number of Gaussian components in a mixture model. (e) Number of Pb atoms per column.Reuse & Permissions

Figure 2

(a) Histogram of simulated intensities together with the underlying known Gaussian mixture model that has been used to generate these intensities. In this simulation, the input mixture model corresponds to the estimated mixture model shown in Fig. 1c. The 25 true values for the mean intensities of each component are indicated by means of black dots. (b) The integrated classification likelihood criterion evaluated as a function of the number of Gaussian components in a mixture model. A clear minimum is revealed at 25 corresponding to the correct number of components. (c) Comparison of the input mean values for the simulation [corresponding to the black dots in (a)] together with the estimated parameters in red.Reuse & Permissions

Figure 3

(a) Histogram of simulated intensities together with the underlying known Gaussian mixture model that has been used to generate these intensities. The 47 true values for the mean intensities of each component are indicated by means of black dots. (b) The integrated classification likelihood criterion evaluated as a function of the number of Gaussian components in a mixture model. A clear minimum is revealed at 47 corresponding to the correct number of components. (c) Comparison of the input mean values for the simulation [corresponding to the black dots in (a)] together with the estimated parameters in red.Reuse & Permissions

Figure 4

(a) Histogram of simulated intensities together with the underlying known Gaussian mixture model that has been used to generate these intensities. The 25 true values for the mean intensities of each component are indicated by means of black dots. Here a nonlinear increase of the intensities with increasing number of atoms has been assumed. (b) The integrated classification likelihood criterion evaluated as a function of the number of Gaussian components in a mixture model. A clear minimum is revealed at 25 corresponding to the correct number of components. (c) Comparison of the input mean values for the simulation [corresponding to the black dots in (a)] together with the estimated parameters in red.Reuse & Permissions

Figure 5

(a) Histogram of simulated intensities together with the underlying known Gaussian mixture model that has been used to generate these intensities. The 25 true values for the mean intensities of each component are indicated by means of black dots. In this simulation, it is assumed that the intensities reach a plateau at a thickness of 10 atoms. (b) The integrated classification likelihood criterion evaluated as a function of the number of Gaussian components in a mixture model. A clear minimum is revealed at 10 corresponding to an underestimation of the number of components. (c) Comparison of the input mean values for the simulation [corresponding to the black dots in (a)] together with the estimated parameters in red.Reuse & Permissions

Figure 6

(a)–(c) Sequence of HAADF STEM images of a Ge cluster. (d)–(f) Refined models together with the counting results in which green, red, and blue dots correspond to one atom, two atoms, and three atoms, respectively. (g) Histogram of scattered intensities of the Ge atoms. The black solid curve shows the estimated mixture model; the individual components are shown as red dashed curves.Reuse & Permissions

Figure 7

(a) HAADF STEM image of a Au nanorod. (b) The integrated classification likelihood criterion evaluated as a function of the number of Gaussian components in a mixture model. (c) Histogram of scattered intensities of the Au columns together with the estimated mixture model and its individual components. The component for which $g$ equals 29 is shown in color. Columns whose intensities belong to the central blue part will be assigned 29 atoms. Columns whose intensities belong to the outermost red part will be assigned 28 or 30 atoms. (d) Number of Au atoms per column. (e) Comparison of experimental and simulated scattered intensities together with 90$\%$ tolerance intervals.Reuse & Permissions