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    For further supplement, we have calculated the CPU time (in seconds) used by our approach and other methods when dealing with the 126 TMA testing images. The average CPU time of our ap-proach was 1.84 s, which is close to the average of the HH-based method (1.82 s), P-based method (1.95 s), and CMF-based method (1.83 s) and better than the LBP-based method (9.8 s) and the LH-based method (3.15 s).
    5. Discussion and conclusion
    The segmentation of tumour epithelium in histopathology is a critical initial step for tumour quantification, biomarker assess-ment, and prognosis determination in colorectal cancer. In this pa-per we propose a novel cascade-learning approach to first distin-guish epithelium from Pifithrin-α (PFTα) and then discriminate between nor-mal and tumour epithelium. Our method has been designed as a morphometry-based approach in a way to enable for a more infor-mative high-level features that can encode biologically meaningful information.
    The major contribution of our approach consists in four points. First, a novel unsupervised level set segmentation method is pro-posed for epithelium segmentation to deal with intensity inhomo-geneity. This is by integrating local information about the appear-ance of the epithelium into the level set formulation as a prior knowledge. We demonstrated the superiority of the proposed level set method FSPF, compared to SPF as a reference method. Second, we developed and combined a new set of appearance (e.g. WAI-based) and shape (e.g. ALI-based) features. They can encode mean-ingful information to measure the regularity structure of epithe-lium in a way to be invariant to staining differences, and hence 
    they can deal with different biomarkers. We found that the seg-mentation performance obtained by our approach outperformed that of other methods (e.g. HH-based, LBP-based, LH-based, P-based, and CMF-based approaches) to confirm the ability of our solution in providing a generic solution to deal better with un-seen patterns. Moreover, results indicated that combining both ap-pearance and shape models led to significant performance im-provement. Third, a robust classification framework based on self-organizing maps has been used, which is able to map the high dimensional feature space into a few numbers of prototypes (or weights) to improve the robustness of the classification to noise. Our classifier has demonstrated its robustness to different noise models when compared to RBF − SV M, as one of the most widely used classifier in histology tissue classification. Finally, our ap-proach can provide an e cient solution in producing results within an acceptable diagnostic time on which clinical decisions can be e ciently made.
    A potential limitation of our approach is that since it is a color-independent approach (in order to be able to deal with both pos-itively and negatively stained tumour areas) it might be confused when other compartments such as lymphocytes are presented in the images.
    In conclusion, this paper presents a novel approach to the seg-mentation of epithelium in colorectal cancer. Our method has been designed as a morphometry-based approach to enable for a more informative high-level features that can encode biologically mean-ingful information. This is by segmenting epithelium from a com-plicated background and then extracting a set of new shape and appearance descriptors from the segmented epithelial regions. In this work, two self-organizing maps have been used to reduce the dimensionality of the feature space of the training set and build a classifier to discriminate between normal and tumour epithe-lium in an e cient and robust way.We focused on evaluating our approach on images stained for different biomarkers when a lim-ited number of training images are provided. Results show that our method performs very well in segmenting epithelial regions and distinguishing between normal and tumour regions on both TMA and WSI. Moreover, our proposed framework has demonstrated its robustness to laboratory-dependent staining differences, noise, and scanner-dependent intensity inhomogeneities. Our approach could be adopted to deal with more complex cases of prostate and breast cancer histology (including different staining such as H&E) at dif-ferent level of magnifications. As a future development, our sys-tem could be extended to deal with multi-class tissue segmenta-tion by using additional SOMs to learn the appearance and shape model of the new tissues. This could help in overcoming the main limitation of our approach. Moreover, one could further improve the performance of our system by reducing the effect of noise and artifacts in the input images using stain normalization techniques (Ciompi et al., 2017). Also outlier removal methods and feature se-lection techniques (Zhu & Wu, 2004) could be integrated in the segmentation framework to improve the robustness of the pro-posed system.