Additional file 1 of A model of the spatial tumour heterogeneity in colorectal adenocarcinoma tissue

File textFeat.xsl. Texture feature profiles for phenotypes found in the real data. Phenotypes are obtained based on the Haralick texture features shown in the table. For each feature the mean is shown in the first column and the standard deviation in the second column. (XLSX 17 kb

Correlation between the density maps and the ground truth with the associated <i>p-values</i> above each method for the H (left) and E (right) stains in all the three datasets.

<p>Indices a, b, c, d, and e of the x-axis show the correlation results of among all datasets for the Proposed method, Macenko <i>et al.</i> [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169875#pone.0169875.ref011" target="_blank">11</a>], Ruifrok and Johnston [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169875#pone.0169875.ref010" target="_blank">10</a>], BCD [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169875#pone.0169875.ref013" target="_blank">13</a>],and ICA [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169875#pone.0169875.ref012" target="_blank">12</a>], respectively Notice that most of the proposed methods perform similarly in estimating H satin (left). However, the weaker stain (E) is more challenging to estimate (right). Proposed method keeps its performance in estimating Eosin stain with mean significance of <i>p-value</i> < 0.05.</p

Estimation of Eosin channel for a sample image.

<p>Images a,b,c,d and e corresponds to the original image, Ruifrok and Johnston [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169875#pone.0169875.ref010" target="_blank">10</a>], Macenko <i>et al.</i> [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169875#pone.0169875.ref011" target="_blank">11</a>], BCD [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169875#pone.0169875.ref013" target="_blank">13</a>], respectively. We can notice in Ruifrok and Johnston method [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169875#pone.0169875.ref010" target="_blank">10</a>] that the pre-estimated mixing parameters is actually not reflecting the Eosin stain colour distribution in the original image. In Macenko <i>et al.</i> [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169875#pone.0169875.ref011" target="_blank">11</a>] method, the colour estimation is affected by the correlation between the two stain colours. In BCD method [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169875#pone.0169875.ref013" target="_blank">13</a>], the fine variation within the H stain is merged with the E due to the projection on the chromaticity plane. In the proposed method however, the variation of the stain colour distribution in the original image is perfectly reflected and H channel is smoothly separated.</p

Block diagram of the proposed method.

<p>Block diagram of the proposed method.</p

Bland Altman plot for the proposed method (left) and ICA [12] (right) for H and E stains using all datasets.

<p>Same randomly selected pixels are plotted from all three datasets by running the proposed method and ICA [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169875#pone.0169875.ref012" target="_blank">12</a>]. Median of agreement is -0.002 for the proposed method and -0.005 for [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169875#pone.0169875.ref012" target="_blank">12</a>]. Limits of agreements for the proposed method is [-0.48, 48] compared to [-0.79, 0.78] for ICA [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169875#pone.0169875.ref012" target="_blank">12</a>].</p

Euclidean Distance between the estimated stain matrix and the ground truth.

<p>Stain matrix is estimated using the proposed method by changing the number of selected sub-bands.</p

Results of nuclei detection algorithm in [2, 28] trained and tested for different stain deconvolution algorithms.

<p>Values show the mean and standard deviation for each of the precision, recall, and F1 score measures. Note that the evaluated algorithms are dynamically estimating stain colour based on current information. Thus, consistency of the algorithm could improve the detection accuracy. However, we did not include stain normalization in this experiments to avoid affecting the deconvolution results.</p

Sample images from the datasets used in our experiments.

<p>Images a, b, and c are samples from colon, breast, and lung cancer images, respectively. All of the datasets are H&E stain images. One can notice the huge variation in the colour appearance as they are applied to different tissue types and processed in different labs using two different scanners. These variations in colour appearance are really challenging for most of the stain deconvolution algorithms.</p

Blind source separation using sub-band decomposition with ICA.

<p>A filtering operator is applied to the observed signal <i>x</i>_<i>i</i> to extract independent and dependent sub-bands. The unmixing matrix is then estimated using a selected set of sub-bands which maximises independency among sources.</p

Correlation between the density maps and the ground truth.

<p>Indices a, b, c, d, and e of the x-axis show the correlation results for the Proposed method, Macenko <i>et al.</i> [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169875#pone.0169875.ref011" target="_blank">11</a>], Ruifrok and Johnston [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169875#pone.0169875.ref010" target="_blank">10</a>], BCD [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169875#pone.0169875.ref013" target="_blank">13</a>],and ICA [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169875#pone.0169875.ref012" target="_blank">12</a>], respectively. Due to the high difference in the correlation margin between ICA and the other algorithms in the H density estimation for the second dataset, ICA has been removed in order to make the correlations of the other algorithms noticeable.</p