Figure 1.
Illustration of generic co-localisation.
(A) the red object (top) and green object (bottom) are overlapped and co-localised at focal plane 2, (B) the red (top) object and green object (bottom) are not co-localised, however many co-localisation measurements would incorrectly recognise these as co-localisation.
Figure 2.
Illustration of the template stack consisting of 15 frames 256×256 pixel images.
The template focal plane I is plane number 8, which is in the middle of all focal planes.
Figure 3.
. Only the 5th frames from the top of each stack (15 frames in total) images are shown for illustration purposes. Each image has the size of 256×256 pixels.
Figure 4.
. Only the overlaid red-green colour images are shown here. Each row represents the first nine frames of a test set. As all 16 dots in a frame are identical, to save space, only one dot (20×20 pixels) is shown. For test case 10 to test case 19, the first nine frames are the same.
Figure 5.
Three examples of murine organotypic brain slice cultures.
(A) Control OSC, (B) Demyelination, (C) Remyelination. *All these figures are single focal planes taken from a set of 5 control, 5 demyelination and 7 remyelination stacks. MBP (Myelin) is shown in green and N200 (Axons) is in red.
Figure 6.
Comparison of CICα measurement and Manders'
using examples from murine organotypic brain slice cultures. (A) An example of a focal plane from murine OSC at 40× magnification, showing CICα = 0% using our method, (B) side view of the z-stack (view in the x and z plane) for Figure A, (C) view in the y and z plane for Figure A, (D) The same example image as Figure A showing the result using Manders' method, where the white region indicates co-localisation, (E) side view of the z-stack for Figure D, (F) bottom view of the z-stack for Figure D.
Figure 7.
Performance evaluations of CBCα and CICα with other 7 popular co-localisation measurements from murine organotypic brain slice cultures.
Co-localisation measurements are evaluated for control, demyelinated and remyelinated samples. Error bars represent SEM. (A) Performance comparison between CBCα and CICα, (B) Performance comparison between CBCα and overlap coefficient k1, (C) Performance comparison among Pearson's Coefficient (PC), Pearson's coefficient using Costes' automatic thresholding (PCC) and the maximum cross-correlation coefficient (CCF), (D) Performance comparison among CBCα, Manders' co-localisation coefficient (M1), Manders' co-localisation coefficient with Costes' automatic thresholding () and Manders' co-localisation coefficient with Otsu automatic thresholding (
). *The measurements presented in Figure A, B and D multiplied by 100% to be comparable with CBCα.
Table 1.
List of evaluation results for the 10 test cases from set .
Figure 8.
Performance comparison between CBCα and Manders' method shows that our co-localisation measurement is a lot closer to the ground truth value than measurements obtained using Manders' method with Otsu's thresholding method.
(A) Co-localisation measurements of CBCα(k) (blue dots) and Manders' (red star) for all non-empty frames in test cases 8–10 is plotted. The range of ground truth is shown in the gray box with its centre Vt shown in a green triangle. The CBCα value, which is also the geometric centre of CBCα(k), is shown by the large blue dot, and the value of
, which is the geometric centre of
, is shown by the large red star. Results show that the distance between
and Vt, dM = 23.06 is considerably larger than the distance between CBCα and Vt, dCBC = 1.68, which suggests greater accuracy of our method in comparison with Manders' method, (B) two sample t-test results show that the individual distances dCBC(k) (between CBCα(k) and Vt) are significantly smaller than the distances dM(k) (between
and Vt). *The y-axis in Figure B indicates dCBC(k) and dM(k), which is measured using the percentage of co-localisation.
Figure 9.
Illustration of identifying cross-over situations using our proposed method in comparison with Manders' co-localisation coefficient masks.
The overlaid masks are shown in Figure A–D, where the white regions are the co-localised regions. (A) Results using our method from frame 6 of test case 8 in , (B) Manders' co-localisation coefficient mask using frame 6 of test case 8 in
, (C) Results using our method from frame 8 of test case 8 in
, (D) Manders' co-localisation coefficient mask using frame 8 of test case 8 in
, (E) the plot of image intensity at a pixel pointed by the blur arrow in Figure A using a nine frame neighbourhood using our method, (F) the plot of image intensity at a pixel pointed by the blur arrow in Figure C using a nine frame neighbourhood using our method. Figure A and C represent different degree of blur.
Figure 10.
Individual frame CIC and CBC scores for three test cases from
. (A) CICα(k) and CICβ(k) for all the frames k = 1,2,…,15 from test case 3, (B) CICα(k) and CICβ(k) for all 15 frames from test case 4, (C) CICα(k) and CICβ(k) for all 15 frames from test case 9, (D) CBCα(k) and CBCβ(k) for all 15 frames from test case 3, (E) CBCα(k) and CBCβ(k) for all 15 frames from test case 4, (F) CBCα(k) and CBCβ(k) for all 15 frames from test case 9.
Table 2.
List of evaluation results for the 19 test cases from set .
Figure 11.
Co-localisation test results using frame 5 from test cases
as an examples. As all dots per focal plane represent the same results, only one dot is shown here in Figure A. (A) Test results using our method in comparison with Manders' co-localisation coefficient overlaid masks. (B)–(I) pixel similarity plots at the pixel indicated with arrows. *In Figure A, column ‘Overlaid’ indicates the unprocessed overlaid colour channel Cα and Cβ. Column ‘Binary’ shows the binary mask where white indicates the region of co-localisation. Column ‘Super-imposed’ shows the superimposition of column ‘Binary’ on top of column ‘Overlaid’, whereas column ‘Manders'’ is the overlaid mask from Manders' co-localisation coefficient measurements. In Figure (B)–(I), Figure B represents a good co-localised case, whereas Figure (C)–(H) are all not co-localised because they do not satisfy the ASCI similarity measurements, whereas Figure (I) is not co-localised because the image intensity values for both colour channels are below the Otsu's threshold. Test cases 7–19 are not shown here as their binary masks are completely black using our method as in case 6, indicating 0% co-localisation.
Figure 12.
Plots of an edge and centre point of a dot from frame 5 for the first six test cases in
. Signal 1 is the image intensity values for a nine frame neighbourhood from colour channel Cα, whereas Signal 2 stands for Cβ. For both Signal 1 and 2, linear interpolation is applied to generate more data points.