Fig 1.
Conditional independence graph of a 6-neighbour conditional MRF with highlighted edges of the vertex corresponding to Xi.
Fig 2.
Schematic diagram of the construction of the densities for each label.
The three labels are: ‘In focus’ tumour cells with a mixture of ‘out of focus’ CAFs and ‘background’ in the other dimension (red), ‘in focus’ CAFs with a mixture of ‘out of focus’ tumour cells and ‘background’ in the other dimension (green) and a mixture of ‘out of focus’ and ‘background’ in both dimensions (dashed).
Fig 3.
Overview of our 3D segmentation method.
Confocal microscopy is used to image 3D co-culture models resulting in a 3D stack of images. Our 3D segmentation method is applied to the 3D stack of images resulting in 3D segmentation output.
Fig 4.
Example 3D segmentation output.
(a) Maximum intensity projection of a representative 3D stack. (b)-(d) Different viewpoints on the corresponding 3D segmentation output using our MRF based method. The blue arrow indicates where the CAFs appear to be inside the tumour organoid in the maximum intensity projection but can be seen to be outside in the 3D segmentation output. See S1 Video for a video of the 3D segmentation output.
Fig 5.
Quantification of tumour-stroma contact in the FAK image data.
(a)-(b) Scatter plots of the total volume and total surface area (in pixels) of the segmented ‘tumour cells’ (red) and ‘CAFs’ (green) regions. (c) Scatter plot of the total contact (in pixels) between the segmented ‘tumour cells’ and ‘CAFs’ regions.
Fig 6.
Utility of the local entropy filter.
(a) Maximum intensity projection of an example 3D stack. (b) The corresponding local entropy filtered image. The blue arrow indicates where a weakly fluorescent tumour organoid and CAF structure is more clearly distinguished in the local entropy filtered image.
Fig 7.
Comparison of 3D segmentation output with and without the local entropy filter.
(a)-(b) 3D segmentation output using the ‘intOtsu’ method on the original intensity images. (c)-(d) 3D segmentation output using the ‘entOtsu’ method, which includes using the local entropy filter. The blue arrow indicates where a tumour organoid and CAF structure appears to be segmented more accurately by the ‘entOtsu’ method. The magenta arrow indicates where the ‘entOtsu’ method appears to have segmented a different CAF structure less accurately.
Fig 8.
Maximum intensity projections, manual segmentations and the output for all segmentation methods on the IF image data.
Fig 9.
Maximum intensity projections, manual segmentations and the output for all segmentation methods on the LIVE image data.
Table 1.
Mean (and median) macro F1-scores of the segmentation methods for the IF and LIVE image data.
Fig 10.
Box and line plots of the F1-scores for the IF and LIVE image data.
Fig 11.
Pairwise comparisons of the F1-scores for the IF and LIVE image data.
The dotted lines correspond to equal F1-score and the p-values correspond to Wilcoxon signed-rank tests that there is no difference between the paired F1-scores. Note that for the IF image data, the p-values are all equal because the MRF F1-score is always higher (all points are below the dotted line). For the comparison with the ‘intOstu’ method for the LIVE image data, the MRF F1-score is also always higher but the p-value is lower here because there are more data points.
Fig 12.
Comparison of 3D segmentation output with and without the ‘neighbour’ information.
(a)-(b) 3D segmentation output using the ‘mixtures’ method, which is equivalent to our MRF based method with λ0 = λ1 = 0. (c)-(d) 3D segmentation output using our MRF based method with λ0 = mini, l ui;l, λ1 = maxi, l ui;l − λ0 and . The blue and magenta arrows indicate areas where the MRF method produces a smoother segmentation. See S2 Video for a video of the 3D segmentation output.