8(b), and the centroid of each damaged nuclei isolated using the region labeling technique. The above expressions were used to determine the centroid of the 3D islet volume shown in Fig. Intensities are assumed to be analogous to mass so that zero intensities represented zero mass. Where f( i, j, k) is the value of the 3D binary image (i.e., the intensity) at the point in the i th row, j th column and k th section of the 3D image i.e., at voxel ( i, j, k). (11) X c = Σ i Σ j Σ k i f ( i, j, k ) Σ i Σ j Σ k f ( i, j, k ) Y c = Σ i Σ j Σ k i f ( i, j, k ) Σ i Σ j Σ k f ( i, j, k ) Z c = Σ i Σ j Σ k i f ( i, j, k ) Σ i Σ j Σ k f ( i, j, k ) So it could be called “proximity weighted centroid.” The threshold value was determined by optimizing the mean error. The displayed results were actually not obtained with a pure weighted centroid approach, but by combining weighted centroid and introducing a lower RSSI threshold of −85 dBm such that only APs (here iBeacons) which have an RSSI value above this lower RSSI threshold are considered in the weighted centroid algorithm.
A quite likely explanation of that behavior is that the directional antenna pattern and the RF shading of the test persons body reduces weights of the “lower” transmitters, mainly IDs 1, 2, 7, 10, and 11. The obtained average deviation for this case is about 4.5 m, but as it can be seen, this is not equally distributed over the test area but more pronounced at the lower parts. 7, the test person always kept herself and the smartphone in a certain pose, that is, facing the top border with respect to the image. In the experiment run demonstrated at the right-hand side of Fig. Both shown graphs differ in pose of the test person: ( right) the test person rotated around herself while performing a measurement, ( left) the test person kept herself and the phone in a certain orientation, that is, facing the top border. The vectors starting at the test points indicate the calculated position. The size of the marked frame is about 28 × 11 m. The regular grid marked with squares indicates the real positions of measurements. Larger double squares on the borders indicate positions of radio transmitters (iBeacons). Results of two weighted centroid measurements recorded in a laboratory test setup.