Overview

Simple task

Nuclei segmentation

Overview

Train

Test

Input images sample variability

Overview

Differing Saliency

some nucleus can be easily seen
some are barely distinguishable
some have homogenous structure
some have nucleous in the center

Overview

Varying shape and size

some are elliptical
some are oblong
some are large
some are very small

Overview

Varying level of nuclei attachment

some images are very dense
some are sparse
some have large groups of glued nuclei

Pipeline

Input image

Preprocessing

Morphological pooling

Watershed ensemble generation

Thresholding

Morphological ensemble generation

Technical Details

Watershed pooling

Segmented mask

Preprocessing

Hematoxylin

Eosin

Background

Technical Details

Color deconvolution

Pipeline

Preprocessing

Hematoxylin

Eosin

Background

Hematoxylin Channel Extraction

Technical Details

Color deconvolution

Pipeline

Preprocessing

Reinhard's Color Normalization

References:

Reinhard, E., Adhikhmin, M., Gooch, B., Shirley, P.: Color transfer between images. IEEE Computer Graphics and Applications 21(5) (2001) 34–41
Wang, Y., nd L. Wu, S.C., Tsai, S., Sun, Y.: A color-based approach for automated segmentation in tumor tissue classification. In: Proc. Conf. of the IEEE Engineering in Medicine and Biology Society. (2007) 6577–6580

\begin{matrix} \\ l_{mapped} = \frac{l_{original}-\bar{l}_{original}}{\hat{l}_{original}}\hat{l}_{target}+\bar{l}_{target} \\ \\ \alpha_{mapped} = \frac{\alpha_{original}-\bar{\alpha}_{original}}{\hat{\alpha}_{original}}\hat{\alpha}_{target}+\bar{\alpha}_{target} \\ \\\beta_{mapped} = \frac{\beta_{original}-\bar{\beta}_{original}}{\hat{\beta}_{original}}\hat{\beta}_{target}+\bar{\beta}_{target} \end{matrix}

\begin{matrix} \\ l_{mapped} = \frac{l_{original}-\bar{l}_{original}}{\hat{l}_{original}}\hat{l}_{target}+\bar{l}_{target} \\ \\ \alpha_{mapped} = \frac{\alpha_{original}-\bar{\alpha}_{original}}{\hat{\alpha}_{original}}\hat{\alpha}_{target}+\bar{\alpha}_{target} \\ \\\beta_{mapped} = \frac{\beta_{original}-\bar{\beta}_{original}}{\hat{\beta}_{original}}\hat{\beta}_{target}+\bar{\beta}_{target} \end{matrix}

Target image

Technical Details

Pipeline

Preprocessing

Hematoxylin Channel Extraction

Reinhard's Color Normalization

Target image

Technical Details

Pipeline

Thresholding

Possible algorithms:

K-means clustering
Fuzzy c-means clustering
Gaussian mixture models

2. With spatial information

1. No spatial information

Spatial information Fuzzy c-means clustering
Fast spatial distance weighted Fuzzy c-means clustering
Dictionary model

References:

Zeng, Huang, Kang and Sang. Image segmentation using spectral clustering of Gaussian mixture models. Neurocomputing 144:346–356, 2014.
Guo, Liu, Wu, Hong and Zhang. A New Spatial Fuzzy C-Means for Spatial Clustering. WSEAS Transactions on Computers 14:369-381, 2015.
Dahl and Larsen. Learning Dictionaries of Discriminative Image Patches. In: Proc. British Machine Vision Conference. p.77, 2011.
Hamed Shamsi and Hadi Seyedarabi, Member, IACSITA Modified Fuzzy C-Means Clustering with Spatial Information for Image Segmentation,International Journal of Computer Theory and Engineering, Vol. 4, No. 5, 2012.

Technical Details

Pipeline

Thresholding

K-means clustering

Parameters:

number of color clusters
number of most most intensive clusters to be classified as nuclei

Models

k-means(3,1)
k-means(4,2)
k-means(6,3)

input

color clusters

1

6

5

4

3

2

Technical Details

Pipeline

Thresholding

input

color clusters

top 3

most intensive clusters sum

1

6

5

4

3

2

4+5+6

K-means clustering

Parameters:

number of color clusters
number of most most intensive clusters to be classified as nuclei

Models

k-means(3,1)
k-means(4,2)
k-means(6,3)

Technical Details

Pipeline

Thresholding

Gaussian Mixture Model

Parameters:

number of color clusters
number of most most intensive clusters to be classified as nuclei
which of the distribution parameters (means, covariances,weights) should be updated
which covariance option (diagonal,full,tied,spherical) should be used

Models

GMM(3,1,{means,covariances},diagonal)
GMM(6,3,{covariances},diagonal)
GMM(6,3,{covariances},tied)

References:

Zeng, Huang, Kang and Sang. Image segmentation using spectral clustering of Gaussian mixture models. Neurocomputing 144:346–356, 2014.

Technical Details

Pipeline

Thresholding

Spatial distance weighted fuzzy c-means clustering

Parameters:

number of color clusters
number of most most intensive clusters to be classified as nuclei
fuzziness parameter
spatial information importance
number of neighbours

Models

SDWFCM(3,1,2,0.9,8)
SDWFCM(3,1,2,0.9,24)
SDWFCM(3,2,2,0.9,24)

\begin{matrix} \\v^{(t)}_{i} = \frac{\sum\limits_{k=1}^{n}(u^{(t-1)}_{ik})^{m}x_k }{\sum\limits_{k=1}^{n}(u^{(t-1)}_{ik})^{m} },1\leq i\leq c \\ \\f_{ij}=\frac{\sum\limits_{s_{k}\in NB(s_j)}d_{ik}}{Min\left \{\sum\limits_{s_{k}\in NB(s_j)}d_{lk},1\leq l \leq c \right \}} \\ \\D_{ij}=(1-\lambda )d_{ij}f_{ij}+\lambda d_{ij} \\ \\u^{(t)}_{ik}=\frac{1}{\sum\limits_{j=1}^{c}(D_{ij}/D_{jk})^\frac{1}{(m-1)}} \\ \\J(X;U;V)=\sum\limits_{i=1}^c\sum\limits_{k=1}^n(u_{ik})^m\left \|x_k-v_i \right \|^2 \end{matrix}

\begin{matrix} \\v^{(t)}_{i} = \frac{\sum\limits_{k=1}^{n}(u^{(t-1)}_{ik})^{m}x_k }{\sum\limits_{k=1}^{n}(u^{(t-1)}_{ik})^{m} },1\leq i\leq c \\ \\f_{ij}=\frac{\sum\limits_{s_{k}\in NB(s_j)}d_{ik}}{Min\left \{\sum\limits_{s_{k}\in NB(s_j)}d_{lk},1\leq l \leq c \right \}} \\ \\D_{ij}=(1-\lambda )d_{ij}f_{ij}+\lambda d_{ij} \\ \\u^{(t)}_{ik}=\frac{1}{\sum\limits_{j=1}^{c}(D_{ij}/D_{jk})^\frac{1}{(m-1)}} \\ \\J(X;U;V)=\sum\limits_{i=1}^c\sum\limits_{k=1}^n(u_{ik})^m\left \|x_k-v_i \right \|^2 \end{matrix}

cluster center

spatial distance weighted funcion

weighted distance

membership probabilty

objective function

References:

Hamed Shamsi and Hadi Seyedarabi, Member, IACSITA Modified Fuzzy C-Means Clustering with Spatial Information for Image Segmentation,International Journal of Computer Theory and Engineering, Vol. 4, No. 5, 2012.