Background
Standard cancer diagnosis and prognosis procedures such as the Nottingham Grading System for breast cancer incorporate a criterion based on cell morphology known as cytonuclear atypia. Therefore, algorithms able to precisely extract the cell nuclei are a requirement in computeraided diagnosis applications.
However, unlike other modalities such as needle aspiration biopsy images, H&E stained surgical breast cancer slides are a particularly challenging image modality due to the heterogeneity of both the objects and background, low objectbackground contrast and frequent overlaps as illustrated in Figure 1. As a consequence, existing extraction methods which are largely reliant on color intensities do not perform well on such images.
Figure 1. Ground truth (Left) magnified 250 × 250 region of a frame and (right) the same region with the nuclei delineated by a pathologist. Nuclei delineated with a thinner outline are hard to distinguish from the background. Dark and bright areas can indiscriminately occur inside and outside nuclei.
Materials and methods
We propose a method based on the creation of a new image modality consisting in a grayscale map where the value of each pixel indicates its probability of belonging to a cell nuclei. This probability map is calculated from texture and scale information in addition to simple pixel color intensities. The resulting modality has a strong objectbackground contrast and evens out the irregularities within the nuclei or the background. The actual extraction is performed using an AC model with a nuclei shape prior included to deal with overlapping nuclei.
Feature model
First, a color deconvolution [1] is applied in order to separate the immunohistochemical stains from which 3 grayscale images are produced: a haematoxilin image, an eosin image and a third residual component orthogonal in RGB space. Next, local features based on Laws’ texture measures [2] are computed for each pixel of the 3 obtained images. 5 different 1dimensional convolution kernels (L5 = (1, 4, 6, 4, 1), E_{5} = (–1, –2, 0, 2, 1), W_{5} = (–1, 2, 0, –2, 1), S_{5} = (–1, 0, 2, 0, –1) and R_{5} = (1, –4, 6, –4, 1)) are used to compute 25 different 5 × 5 kernels by convolving avertical 1dimensional kernel with a horizontal one. The 5 × 5 kernels are applied at every pixel to extract 25 features which are then combined into 15 rotationally invariant features after normalizing by the output of the L_{5}^{T} × L_{5} kernel and smoothing with a Gaussian kernel of standard deviation σ = 1.5 pixels.
The same process is repeated at 4 different scales after locally resampling the image using Lanczos3 sinc kernels. Resampled images are locally computed around each pixel to allow the computation of the 15 texture features for the same pixel at different scales. Local texture features are computed at 1:1, 1:2, 1:4 and 1:8 scales for every pixel.
Probability map
The resulting 180dimensional feature vector x is used to compute the probability p_{n}(x) of each pixel to belong to a cell nuclei. Let μ_{n} (resp. μ_{b}) be the mean of the feature vectors for the pixels belonging to the nuclei (resp. to the background). A class dependent LDA is performed in order to find two directions in the feature space, w_{n} and w_{b}, such that the projection of the classes on these directions has a maximum interclass scatter over withinclass scatter ratio. The estimated class probability associated with the feature vector x is then calculated from the linear scores l_{n} = (x – μ_{n}) · w_{n} and l_{b} = (x – μ_{b}) · w_{b} using the softmax function:
The resulting probability map exhibits strong contrast between the objects and the background. Moreover, nuclei and background appear more homogeneous than in the original image. A post processing step is also applied to fill small holes still remaining in nuclei (larger holes are not removed to prevent the unintended deletion of interstices between different nuclei).
AC model including shape prior
The actual extraction of cell nuclei is performed from the probability map with an AC model with shape prior information. The total energy E(γ) associated to a contour γ is a weighted sum of an image term E_{i}(γ) and a shape term E_{s}(γ). The latter is itself the weighted sum of a smoothing term E_{sm}(γ) and a shape prior term E_{sp}(γ).
The shape prior term allows to control the perturbations δr(t) of a contour around a circle at different frequencies k of the Fourier components by adjusting the coefficients f_{k}. Detailed formulas and explanations for this and the other energy terms can be found in the work of Kulikova et al. [3]. The shape prior information allows to properly extract overlapping nuclei according to their expected shape without arbitrarily discarding the overlapping parts.
The detection of nuclei is performed by a marked point process model the details about which the interested reader can find in [4]. An empirical study in [5] shows that this particular combination of MPP and AC overperforms other stateoftheart methods for nuclei detection and extraction.
Results and discussion
The training set used for the LDA consists of 6 1024×1024 images where the nuclei have been manually delineated by a pathologist. Object and background parameters used in the AC model are also calculated from the training set. Weight parameters for the energy terms in the AC model are adjusted with a grid search. Images used for training are distinct from the images used for validation.
Figure 2 shows results obtained with the AC model applied to the probability map sidebyside with results obtained with the same AC model applied to the original image (in fact, the slightly better performing haematoxilin image from the color deconvolution was used instead of the red channel from the RGB image commonly used in other methods [6]). On the original image, the contours have a tendency to match irregularities within the cell nuclei rather than their actual boundaries. This problem is largely improved by using the probability map where the nuclei boundaries are much more salient and other irrelevant features are smoothed out.
Figure 2. Extraction results The top row is obtained using the probability map and the bottom row is obtained using the haematoxilin channel after the image color deconvolution.
References

Ruifrok AC, Johnston DA: Quantification of histochemical staining by color deconvolution.
Analytical and Quantitative Cytology and Histology 2001, 23:291299. PubMed Abstract

Laws K: Textured image segmentation. PhD thesis. University of Southern California; 1980.

Kulikova M, Jermyn I, Descombes X, Zhizhina E, Zerubia J: A marked point process model with strong prior shape information for extraction of multiple, arbitrarilyshaped objects.
Proc. SignalImage Technology and InternetBased Systems 2009.

Descombes X, Minlos R, Zhizhina E: Object extractionusing a stochastic birthanddeath dynamics in continuum.
J. Math. Imaging Vis 2009, 33(3):347359. Publisher Full Text

Kulikova MS, Veillard A, Roux L, Racoceanu D: Nuclei extraction from histopathological images using a marked point process approach.
Proc. SPIE Medical Imaging, San Diego, California, USA, 2012

Dalle J, Li H, Huang CH, Leow W, Racoceanu D, Putti TC: Nuclear pleomorphism scoring by selective cell nuclei detection.