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- Abstract
- I. Introduction
- II. Review of Previous Work
- III. Approach
- IV. Experimental Results and Discussion
- V. Analysis of TCGA GBM Cohort
- VI. Conclusion
- References

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IEEE Trans Med Imaging. Author manuscript; available in PMC 2013 July 30.

Published in final edited form as:

Published online 2012 December 4. doi: 10.1109/TMI.2012.2231420

PMCID: PMC3728287

NIHMSID: NIHMS480985

Hang Chang, Member, IEEE,^{} Ju Han, Member, IEEE, Alexander Borowsky, Leandro Loss, Member, IEEE, Joe W. Gray, Paul T. Spellman, and Bahram Parvin, Senior Member, IEEE^{}

Hang Chang, Life Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720 U.S.A;

Hang Chang: vog.lbl@gnahch; Ju Han: vog.lbl@nahj; Alexander Borowsky: ude.sivadcu@yksworobda; Leandro Loss: vog.lbl@ssolal; Joe W. Gray: ude.usho@ojyarg; Paul T. Spellman: ude.usho@pamlleps; Bahram Parvin: vog.lbl@nivrap_b

The publisher's final edited version of this article is available at IEEE Trans Med Imaging

See other articles in PMC that cite the published article.

Automated analysis of whole mount tissue sections can provide insights into tumor subtypes and the underlying molecular basis of neoplasm. However, since tumor sections are collected from different laboratories, inherent technical and biological variations impede analysis for very large datasets such as The Cancer Genome Atlas (TCGA). Our objective is to characterize tumor histopathology, through the delineation of the nuclear regions, from hematoxylin and eosin (H&E) stained tissue sections. Such a representation can then be mined for intrinsic subtypes across a large dataset for prediction and molecular association. Furthermore, nuclear segmentation is formulated within a multi-reference graph framework with geodesic constraints, which enables computation of multidimensional representations, on a cell-by-cell basis, for functional enrichment and bioinformatics analysis. Here, we present a novel method, Multi-Reference Graph Cut (MRGC), for nuclear segmentation that overcomes technical variations associated with sample preparation by incorporating prior knowledge from manually annotated reference images and local image features. The proposed approach has been validated on manually annotated samples and then applied to a dataset of 377 Glioblastoma Multiforme (GBM) whole slide images from 146 patients. For the GBM cohort, multidimensional representation of the nuclear features and their organization have identified (i) statistically significant subtypes based on several morphometric indices, (ii) whether each subtype can be predictive or not, and (iii) that the molecular correlates of predictive subtypes are consistent with the literature.

Data and intermediaries for a number of tumor types (GBM, low grade glial, and kidney renal clear carcinoma) are available at: http://tcga.lbl.gov for correlation with TCGA molecular data. The website also provides an interface for panning and zooming of whole mount tissue sections with/without overlaid segmentation results for quality control.

Our main *motivation* for quantifying morphometric composition from histology sections is to gain insight into cellular morphology, organization, and sample tumor heterogeneity in a large cohort. In tumor sections, robust representation and classification can identify mitotic cells, cellular aneuploidy, and autoimmune responses. More importantly, if tissue morphology and architecture can be quantified on a very large scale dataset, then it will pave the way for constructing databases that are prognostic, the same way that genome-wide array technologies have identified molecular subtypes and predictive markers. Genome-wide molecular characterization (e.g., transcriptome analysis) has the advantage of standardized techniques for data analysis and pathway enrichment, which can enable hypothesis generation for the underlying mechanisms. However, array-based analysis (i) can only provide an average measurement of the tissue biopsy, (ii) can be expensive, (iii) can hide occurrences of rare events, and (iv) lacks the clarity for translating molecular signature into a phenotypic signature. Though nuclear morphology and context are difficult to compute as a result of intrinsic cellular characteristic and technical variations, histology sections can offer insights into tumor architecture and heterogeneity (e.g., mixed populations), in addition to, rare events. Moreover, in the presence of a very large dataset, phenotypic signatures can be used to identify intrinsic subtypes within a specific tumor bank through unsupervised clustering. This facet is orthogonal to histological grading, where tumor sections are classified against known grades. The tissue sections are often visualized with hematoxylin and eosin stains, which label DNA content (e.g., nuclei) and protein contents, respectively, in various shades of color. Even though there are inter- and intra- observer variations [1], a trained pathologist can characterize the rich content, such as the various cell types, cellular organization, cell state and health, and cellular secretion. If hematoxylin and eosin (H&E) stained tissue sections can be quantified in terms of cell type (e.g., epithelial, stromal), tumor subtype, and histopathological descriptors (e.g., necrotic rate, nuclear size and shape), then a richer description can be linked with genomic information for improved diagnosis and therapy. This is the main benefit of histological imaging since it can capture tumor architecture.

Ultimately, our goal is to mine a large cohort of tumor data in order to identify morphometric indices (e.g., nuclear size) that have prognostic and/or predictive subtypes. The Cancer Genome Atlas (TCGA) offers such a collection; however, the main *issue* with processing a large cohort, is the inherent variations as a result of (i) the sample preparation protocols (e.g., fixation, staining), practiced by different laboratories, and (ii) the intrinsic tumor architecture (e.g., cell type, cell state). For example, with respect to heterogeneity in the tumor architecture, the nuclear color in the *RGB* space found in one tissue section may be similar to the cytoplasmic color in another tissue section. Simultaneously, the nuclear color intensity (e.g., chromatin content) can vary within a whole slide image. Therefore, image analysis should be tolerant and robust, with respect to variations in sample preparation and tumor architecture, within the entire slide image and across the tumor cohort.

Stained whole mount tissue sections are scanned at either at 20X or 40X, which results in larger images in the order of 40kby-40k pixels or higher. Each image is partitioned into blocks of 1k-by-1k pixels for processing, and cells at the borders of each block are excluded during the processing. The details of the computational pipeline can be found in our earlier paper [2]. Our approach evolved from our observation that simple color decomposition and thresholding misses or over-estimates some of the nuclei in the image, i.e., nuclei with low chromatin contents are excluded. Further complications ensue as a result of diversity in nuclear size and shape (e.g., the classic scale problem).

The general approach is shown in Figure 1, where the primary *novelty* is in the image-based modeling of inherent ambiguities that are associated with technical variations and biological heterogeneity. Image-based modeling captures prior knowledge from a diverse set of annotated images (e.g., a dictionary) needed in order to model the foreground and background representations. Each annotated image is independent of other images and signifies one facet (e.g., color space, nuclear shape and size) of the diversity within the cohort. Moreover, each image is represented in the feature-space as the Gaussian Mixture Model (*GMM*) of the Laplacian of Gaussian (*LoG*) and *RGB* responses. Collectively, the reference dictionary of annotated images provides the means for color normalization and for capturing global statistics for segmenting test images. The computed global statistics can then be coupled, through a graph cut formulation, with the intrinsic local image statistics and spatial continuity for binarization. Having segmented an input test image, each segmented foreground region is subsequently validated for nuclear shape. If needed, it is decomposed through geometric reasoning. A secondary novelty is in the details of the computational pipeline. For example, we introduce the concept of (i) “color map normalization” for registering a test image against each of the images in the reference library, and (ii) “blue ratio image” for mapping *RGB* images into the gray space; thus, *LoG* responses can be computed efficiently in one channel. All important free parameters are selected through cross-validation. Thus far, close to 1000 whole slide images have been processed, and the data has been made publicly available through our website at http://tcga.lbl.gov. In addition, segmentation results, from the whole mount tissue sections, are available for quality control through a web-based zoomable interface.

Essentially, nuclear segmentation provides the basis for morphometric representation on a cell-by-cell basis. As a result, tumor histology can be represented as a meaningful data matrix, where well-known bioinformatics and statistical tools can be readily applied for hypotheses generation. For example, a large cohort facilitates tumor subtyping based on computed morphometric features. Each subtype can then be (i) tested for its prognostic value, and (ii) utilized for identifying molecular basis of each subtype for hypothesis generation. In the case of GBM, prognostic and/or predictive subtypes have also been posted on our Web site.

Organization of this paper is as follows: Section II reviews previous research with a focus on quantitative representation of the H&E sections for translational medicine. Sections III and IV describes the details of the image-based modeling for nuclear segmentation and experimental validation, respectively. Section V examines one application of nuclear segmentation of morphometric subtyping and molecular association for hypothesis generation. Lastly, section VI concludes the paper.

Several excellent reviews for the analysis of histology sections can be found in [3], [4]. From our perspective, four distinct works have defined the trends in tissue histology analysis: (i) one group of researchers proposed nuclear segmentation and organization for tumor grading and/or prediction of tumor recurrence [5], [6], [7], [8]. (ii) A second group of researchers focused on patch level analysis (e.g., small regions) [9], [10], [11], using color and texture features, for tumor representation. (iii) A third group focused on block-level analysis to distinguish different states of tissue development using cell-graph representation [12], [13]. (iv) Finally, a fourth group has suggested detection and representation of the auto-immune response as a prognostic tool in cancer [14]. In contrast to previous research, our strategy is based on processing a large cohort of tumors, to compute morphometric subtypes, and to examine whether computed subtypes are predictive of outcome. Since tumor histology is characterized in terms of nuclear and cellular features, a more detailed review of nuclear segmentation strategies follows.

The main barriers in nuclear segmentation are technical variations (e.g., fixation) and biological heterogeneity (e.g., cell type). These factors are visible in TCGA dataset. Present techniques have focused on adaptive thresholding followed by morphological operators [15], [16]; fuzzy clustering [17], [18]; level set method using gradient information [14], [19]; color separation followed by optimum thresholding and learning [20], [21]; hybrid color and texture analysis followed by learning and unsupervised clustering [6]; and representation of nuclei organization in tissues [22], [23] that is computed from either interactive segmentation or a combination of feature detector. Some applications combine the above techniques; Several examples are given below. In [24], iterative radial voting [25] was used to estimate seeds for partitioning perceptual boundaries between neighboring nuclei. Subsequently, seeds were used to segment each nucleus through the application of multiphase level sets [26], [27]. In [28], the input image was initially binarized into foreground and background regions with a graph cut framework, the seeds were then selected from a binarized image using a constrained multi-scale *LoG* filter, with the combined results being refined using a second iteration of the graph cut. Similarly, in [29], the input image was first normalized through histogram equalization, and then binarized based on color-texture extracted from the most discriminant color space. This was followed by an iterative operation to split touching nuclei based on concave-points and radial-symmetry. In their experiment, they had 21 images where 5 of them were annotated. Nuclei, in all images, had similar size with high chromaticity. Recently, a spatially constrained expectation maximization algorithm [30] was demonstrated to be robust to “color nonstandardness” in histological sections with color being represented in the HSV space. However, our analysis of the GBM cohort indicates that strict incorporation of color and spatial information will not be sufficient as demonstrated in Section IV B (MRGC vs MRGC-CF). A more related work, described in [31], was based on a voting system that uses multiple classifiers built from different reference images; we will refer to this method as MCV, for short, in the rest of the paper. Compared to the previous approaches, MCV provides a better way to handle the variation among different batches. However, due to the lack of smoothness constraints and local statistical information, the classification results can be noisy and erroneous, as demonstrated in Figure 8. Some of these concepts have also been utilized in our earlier paper [2], but the results posted on our website are for the current implementation outlined in this paper.

A comparison between MCV and MRGC (as shown in (c) and (d), respectively) based on the same reference image, as shown in (a). Even though the test image and the reference image are slightly different in color space, compared with MCV, MRGC still produces **...**

In summary, the main limitations of the above techniques are that they are often applied to a small dataset that originate from a single laboratory, ignore technical variations that are manifested in both nuclear and background signals, and are insensitive to cellular heterogeneity (e.g., variation in chromatin contents). Our goal is to address these issues by processing whole mount tissue sections, from multiple laboratories, to construct a large database of morphometric features, and to enable subtyping and genomic association.

Details of the proposed approach are shown in Figure 2, which leverages several key observations for segmenting nuclear regions: (i) global variations across a large cohort of tissue sections can be captured by a representative set of reference images, (ii) local variations within an image can be captured by local foreground(nuclei)/background samples detected by *LoG* filter, and (iii) color normalization, against a reference image, reduces variations in image statistics and batch effects between a test and a reference image. These concepts are integrated within a graph cut framework to delineate nuclei or clumps of nuclei from the background. Having performed foreground and background segmentation, we then partitioned potential clumps of nuclei through geometric reasoning. In the rest of this section, we summarize (a) the representation of prior models from a diverse set of reference images, (b) the methodology for color normalization, (c) an effective approach for color transformation for dimensionality reduction, (d) the details of feature extraction from each test image, (e) the multi-reference graph cut formalism for nuclei/background separation, and (f) the partitioning of a clump of nuclei into individual nucleus.

The purpose of this step is to capture the global variations for an entire cohort from a reference library. For bioinformatics analysis, the target dataset consists of 377 individual tissue sections, and a representative of *N* (*N* = 20) reference images of 1k-by-1k pixels at 20X have been selected. Each reference image is selected to be an exemplar of tumor phenotypes based on staining and morphometric properties. Therefore, it is reasonable to suggest that each reference image has its own unique feature space, in terms of *RGB* and *LoG* responses, which leads to 2*N* feature spaces for all reference images:

$$\{{\mathbb{F}}_{{\mathit{\text{RGB}}}_{1}}^{1},{\mathbb{F}}_{{\mathit{\text{RGB}}}_{2}}^{2},\cdots ,{\mathbb{F}}_{{\mathit{\text{RGB}}}_{N}}^{N},{\mathbb{F}}_{{\mathit{\text{LoG}}}_{1}}^{N+1},{\mathbb{F}}_{{\mathit{\text{LoG}}}_{2}}^{N+2},\cdots ,{\mathbb{F}}_{{\mathit{\text{LoG}}}_{N}}^{2N}\}$$

(1)

where ${\mathbb{F}}_{{\mathit{\text{RGB}}}_{i}}^{i}\text{and}{\mathbb{F}}_{{\mathit{\text{LoG}}}_{i}}^{N+i}$ are *RGB* feature space and *LoG* feature space for the *i ^{th}* reference image, 1 ≤

$${\mathit{\text{GMM}}}_{l}^{k}(p)=\sum _{j=1}^{D}\tilde{p}({f}^{k}(p)|j)P(j)$$

(2)

where a mixing parameter *P*(*j*) corresponds to the weight of component *j* and ${\sum}_{j=1}^{D}P(j)=1$. Each mixture component is a Gaussian with mean μ and covariance matrix Σ in the corresponding feature space (e.g., 3-by-3 and 1-by-1 matrices in *RGB* and single scale *LoG* spaces, respectively):

$$\tilde{p}({f}^{k}(p)|j)=\frac{1}{{(2\pi )}^{\frac{3}{2}}|\mathrm{\Sigma}{|}_{j}^{\frac{1}{2}}}\xb7\text{exp}(-\frac{1}{2}{({f}^{k}(p)-{\mu}_{j})}^{T}{\sum}_{j}^{-1}({f}^{k}(p)-{\mu}_{j}))$$

(3)

*P*(*j*) and (μ_{j}, Σ_{j}) for (*C _{p}*|

The purpose of color normalization is to close the gap, in color space, between an input test image and a reference image. As a result, the prior models, constructed from each reference image, can be better utilized. We evaluated a number of color normalization methods and chose the color map normalization described in [31] for its effectiveness in handling histological data. Let

- input image
*I*and reference image*Q*have*K*and_{I}*K*unique color triplets in terms of (_{Q}*R, G, B*), respectively; - ${\mathbb{R}}_{C}^{I/Q}$ be a monotonic function, which maps the color channel intensity,
*C*{*R, G, B*} from Image*I*/*Q*to a rank that is in the range [0,*K*)/[0,_{I}*K*);_{Q} - (
*r*) be the color of pixel_{p}, g_{p}, b_{p}*p*, in image*I*, and $({\mathbb{R}}_{R}^{I}({r}_{p}),{\mathbb{R}}_{G}^{I}({g}_{p}),{\mathbb{R}}_{B}^{I}({b}_{p}))$ be the ranks for each color channel intensity; and - the color channel intensity values
*r*and_{ref}, g_{ref}*b*, from image_{ref}*Q*, have ranks:$${\mathbb{R}}_{R}^{Q}({r}_{\mathit{\text{ref}}})=\lfloor \frac{{\mathbb{R}}_{R}^{I}({r}_{p})}{{K}_{I}}\times {K}_{Q}+\frac{1}{2}\rfloor \phantom{\rule{0ex}{0ex}}{\mathbb{R}}_{G}^{Q}({g}_{\mathit{\text{ref}}})=\lfloor \frac{{\mathbb{R}}_{G}^{I}({g}_{p})}{{K}_{I}}\times {K}_{Q}+\frac{1}{2}\rfloor \phantom{\rule{0ex}{0ex}}{\mathbb{R}}_{B}^{Q}({b}_{\mathit{\text{ref}}})=\lfloor \frac{{\mathbb{R}}_{B}^{I}({b}_{p})}{{K}_{I}}\times {K}_{Q}+\frac{1}{2}\rfloor $$

As a result of color map normalization, the color for pixel *p*: (*r _{p}, g_{p}, b_{p}*), will be normalized as (

In order to reduce the computational complexities for integrating the *LoG* responses, the *RGB* space is transformed into a gray level image to accentuate the nuclear dye. While several techniques for color decomposition have been proposed [34], [33], they are either too time-consuming or do not yield favorable outcomes. The color transformation policy needs to enhance the nuclear stain while attenuating the background stain. One way to realize such a transformation is by: $BR(x,y)=\frac{100*B(x,y)}{1+R(x,y)+G(x,y)}\times \frac{256}{1+B(x,y)+R(x,y)+G(x,y)}$, where *B*(*x, y*), *R*(*x, y*) and *G*(*x, y*) are the blue, red and green intensities at position (*x, y*). We refer to this transformation as the blue ratio image in the rest of this manuscript. In this formulation, the first and second terms accentuate and attenuate nuclear and background signals, respectively. Subsequently, the *LoG* responses are always computed at a single scale from the blue ratio image. Figure 3 demonstrates that the blue ratio image method has an improved performance compared to an alternative method [33].

Our approach integrates both color and scale information, where the scale is encoded by the *LoG* response.

- Normalization of the input test image against every reference image, as described in Section III-B;
- Conversion of each normalized image into the blue ratio image, as described in Section III-C;
- Application of a
*LoG*filter on each of the blue ratio images, at a single scale; and - Representation of each pixel, from the test image, by its
*RGB*color in each of the normalized images and*LoG*response from each of the blue ratio images.

As a result, each pixel in the test input image is represented by 2*N* features, where the first *N* features are *RGB* colors from the normalized images, and the last *N* features are *LoG* responses computed from the blue ratio of the normalized images. All 2*N* features are assumed to be independent per selection of images in Section III-A. The rational for integrating both color and scale information is that: (i) in some cases, color information is insufficient to differentiate nuclear regions from background; (ii) the scales (e.g., *LoG* responses) of the background structure and nuclear region are typically different; and (iii) the nuclear region responds well to blob detectors, such as a *LoG* filter [28].

In this section, we first present the background material on graph cut formalism, and then proceed to the details of the image-based modeling for incorporating intrinsic and extrinsic variations.

Within the graph cut formulation, an image is represented as a graph *G* = *, Ē*, where is the set of all nodes, and *Ē* is the set of all arcs connecting adjacent nodes. Usually, the nodes and edges correspond to pixels () and their adjacency relationship, respectively. Additionally, there are special nodes known as terminals, which correspond to the set of labels that can be assigned to pixels. In the case of a graph with two terminals, the terminals are referred to as the source (S) and the sink (T), which correspond to specific labels. The labeling problem is to assign a unique label *x _{p}* (0 for background, and 1 for foreground) for each node

$$E=\sum _{p\in \overline{V}}{E}_{\mathit{\text{fitness}}}({x}_{p})+\beta \sum _{(p,q)\in \overline{E}}{E}_{\mathit{\text{smoothness}}}({x}_{p},{x}_{q})$$

(4)

Where *E _{fitness}*(

The optimization algorithms could be classified into two groups: Goldberg-Tarjan “push-relabel” methods [36], and Ford-Fulkerson “augmenting paths” [37]. The details of the two methods can be found in [38].

We recognize that the training data set cannot fully capture the intrinsic variations of the nuclear signature. Therefore, the data fitness term is expressed as a combination of the intrinsic local probability map and learned global property map. The local probability map has the advantage of capturing local intrinsic image property in the absence of colormap normalization, thus, diversifying the data fitness term. Equation 4 is rewritten as

$$E=\sum _{p\in \overline{V}}({E}_{gf}({x}_{p})+{E}_{lf}({x}_{p}))+\beta \sum _{(p,q)\in \overline{E}}{E}_{\mathit{\text{smoothness}}}({x}_{p},{x}_{q})$$

(5)

where *E _{gf}* is the global data fitness term encoding the fitness cost for assigning

*Global fitness term:*The global fitness is established based on manually annotated reference images. Let’s assume*N*reference images:*Q*[1,_{i}, i*N*], and for each reference image,*GMM*s are used to represent the nuclei and background in both*RGB*space and*LoG*response space, respectively: ${\mathit{\text{GMM}}}_{\mathit{\text{Nuclei}}}^{k},{\mathit{\text{GMM}}}_{\mathit{\text{Background}}}^{k}$, in which*k*[1, 2*N*], and the first*N GMM*s are for*RGB*space, and the last*N GMM*s are for*LoG*response space. Details can be found in III-A.An input test image*I*is first normalized as*U*with respect to every reference image,_{i}*Q*. Subsequently,_{i}*RGB*color and*LoG*responses of*U*are collected to construct 2_{i}*N*features per pixels, where the first*N*features are from the normalized color(*RGB*) space, and the second*N*features are from*LoG*response. Let*p*be a node corresponding to a pixel;*f*(^{k}*p*) be*k*feature of^{th}*p*;- α be the weight of
*LoG*response; - ${\mathbf{p}}_{i}^{k}$ be the probability function of
*f*being Nuclei(^{k}*l*= 1)/Background(*l*= 0):$${\mathbf{p}}_{l}^{k}(p)=\frac{{\mathit{\text{GMM}}}_{l}^{k}(p)}{{\sum}_{j=0}^{1}{\mathit{\text{GMM}}}_{j}^{k}(p)}$$ - λ
_{i}be the weight for*Q*:_{i}where · is$${\lambda}_{i}=\frac{1}{3}\sum _{C}^{C\in \{R,G,B\}}{\lambda}_{i}^{C}\phantom{\rule{0ex}{0ex}}{\lambda}_{i}^{C}={H}^{C}({Q}_{i})\xb7{H}^{C}({U}_{i})/(\parallel {H}^{C}({Q}_{i})\parallel \xb7\parallel {H}^{C}({U}_{i})\parallel )$$*L*_{2}norm,*H*(·) is the histogram function on a single color channel^{C}*C*{*R, G, B*} of an image. Intuitively, λ measures similarity between two histograms derived from*Q*and_{i}*U*, which are represented with 20 bins. Based on our experiments, the λs become stable when the number of bins reaches 20; conversely, histograms with less than 20 bins are considered to have insufficient resolution. The similarity parameter weighs the fitness of the prior model, constructed from_{i}*Q*, to the features extracted from the normalized image_{i}*U*._{i}

The global fitness term is now defined aswhere the first and second terms integrate normalized color features and$${E}_{gf}({x}_{p}=i)=-\sum _{k=1}^{N}{\lambda}_{k}\mathit{\text{log}}({\mathbf{p}}_{i}^{k}({f}^{k}(p)))-\alpha \xb7\sum _{k=N+1}^{2N}{\lambda}_{k-N}\mathit{\text{log}}({\mathbf{p}}_{i}^{k}({f}^{k}(p)))$$(6)*LoG*responses, respectively.*Local Fitness Term:*While the global fitness term utilizes both color and*LoG*information in the normalized space, it does not utilize information in the original color space of the input image. As a result, local variation may be lost for a number of reasons, i.e., non-uniformity in the tissue sections, local lesions, etc. The local data fitness of a pixel,*p*, is computed from foreground and background seeds in a local neighborhood around*p*that corresponds to peaks detected by a*LoG*filter on the blue ratio image, where positive and negative peaks often, but not always, correspond to the background and foreground (nuclei), respectively. The accuracy can be improved by a cascade of filters as follows:- Seeds detection: This step aims to collect local foreground and background seeds by incorporating local and global image statistics. Typical positive and negative peak responses, associated with the
*LoG*filter, are shown in Figure 4(a). Most of the time, the*LoG*filter detects foreground and background locations correctly, but there is a potential for errors. The protocol consists of three steps:- Create a blue ratio image (Section III-C): In this transformed space, the peak of the intensity histogram always corresponds to the preferred frequency of the background intensity as shown in Figure 4(b).
- Construct distributions of the foreground and background: Apply the
*LoG*filter on the blue ratio image, detect peaks, and construct a distribution of the blue ratio intensity at the peaks corresponding to the negative and positive*LoG*responses. A small subset of seeds can be mislabeled, but most can be corrected in the following step. - Constrain the seed selection: Seeds (e.g., peaks of the
*LoG*response) are constrained by three criteria: (i) the*LoG*responses must be above a minimum conservative threshold for removing strictly noisy artifacts; (ii) the intensity associated with the peak of the negative*LoG*responses (e.g., foreground peaks) must concur with the background peak, specified in step (a); and (iii) within a small neighborhood of*w*_{1}×*w*_{1}, the minimum blue ratio intensity, at the location of negative seeds, is set as the threshold for background peaks, as shown in Figure 5.

- Local foreground/background color modeling: For each pixel,
*p*, foreground and background statistics within a local neighborhood,*w*_{2}×*w*_{2}, is represented by two GMMs in the original color space. These GMMs correspond to the nuclei and background models (e.g., ${\mathit{\text{GMM}}}_{\mathit{\text{Nuclei}}}^{\mathit{\text{Local}}}\text{and}{\mathit{\text{GMM}}}_{\mathit{\text{Background}}}^{\mathit{\text{Local}}}$), respectively.

The local fitness term is defined as:where$${E}_{lf}({x}_{p}=i)=-\gamma \mathit{\text{log}}({\mathbf{p}}_{l}(f(p)))$$(7)*f*(*p*) refers to the*RGB*feature of node*p*in the original color space, γ is the weight for local fitness,**p**_{l}is the probability function of*f*being Nuclei(*l*= 1)/Background(*l*= 0):$${\mathbf{p}}_{l}(p)=\frac{{\mathit{\text{GMM}}}_{l}^{\mathit{\text{Local}}}(p)}{{\sum}_{j=0}^{1}{\mathit{\text{GMM}}}_{j}^{\mathit{\text{Local}}}(p)}$$*Smoothness Term:*While both local and global data fitness terms are encoded by t-links (links between node and terminals) in the graph, the smoothness term, which ensures the smoothness of labeling between adjacent nodes, is represented by n-links (links between adjacent nodes). Here, we adopt the setup from [39] for n-links, which approximates a continuous Riemannian metric by a discrete weighted graph so that the max-flow/min-cut solution for the graph corresponds to a local geodesic or minimal surface in the continuous case. Consider a weighted graph constructed in III-E:*G*=*, Ē*, where is the set of image pixels, and*Ē*is the set of all edges connecting adjacent pixels. Let,- {
*e*|1 ≤_{k}*k*≤*n*} be a set of vectors for the neighborhood system, where_{G}*n*is the neighborhood order, and the vectors are ordered by their corresponding angle ϕ_{G}_{k}w.r.t. the +*x*axis, such that 0 ≤ ϕ_{1}< ϕ_{2}< ϕ_{nG}< π. For example, when*n*= 8, we have_{G}*e*_{1}= (1, 0),*e*_{2}= (1, 1),*e*_{3}= (0, 1),*e*_{4}= (−1, 1), as shown in Figure 6(a); *w*be the weight for the edge between pixels:_{k}*p*and*q*, where*p*and*q*belong to the same neighborhood system, and $\overrightarrow{pq}=\pm {e}_{k}$;*L*be a line formed by the edges in the graph, as shown in Figure 6(c);- |
*C*|_{G}be the cut metric of*C*:where$$|C{|}_{G}=\sum _{e\in {\overline{E}}_{C}}{w}_{e}$$*Ē*is the set of edges intersecting contour_{C}*C*; - |
*C*|_{R}be the Riemannian length of contour*C*; and, *D*(*p*) be the metric(tensor), which continuously varies over points*p*in the 2D Riemannian space;

*C*|_{R}of contour*C*can be written as,where$$\int \frac{\mathit{\text{det}}D(p)}{2{({u}_{L}^{T}\xb7D(p)\xb7{u}_{L})}^{\frac{3}{2}}}{n}_{C}dL=2|C{|}_{R}$$*u*is the unit vector in the direction of the line_{L}*L*, and*n*is a function that specifies how many times line_{C}*L*intersects contour*C*. Following the approach in [39], the local geodesic can be approximated by the max-flow/min-cut solution (|*C*|_{G}→ |*C*|_{R}) with the following edge weight setting:where, δ is the cell-size of the grid, ϕ$${w}_{k}(p)=\frac{{\delta}^{2}\xb7|{e}_{k}{|}^{2}\xb7\u25b3{\varphi}_{k}\xb7\mathit{\text{det}}D(p)}{2\xb7{({e}_{k}^{T}\xb7D(p)\xb7{e}_{k})}^{\frac{3}{2}}}$$(8)_{k}is the angular difference between the*k*and (^{th}*k*+ 1)^{th}edge lines, ϕ_{k}= ϕ_{k+1}− ϕ_{k}, andwhere $\mathbf{u}=\frac{\nabla I}{|\nabla I|}$ is a unit vector in the direction of image gradient at point$$D(p)=g(|\nabla I|)\xb7\mathbf{I}+(1-g(|\nabla I|))\xb7\mathbf{u}\xb7{\mathbf{u}}^{T}$$(9)*p*,**I**is the identity matrix, and $g(x)=\mathit{\text{exp}}(-\frac{{x}^{2}}{2{\sigma}^{2}})$*Optimization:*The construction of the graph, with two terminals, source S and sink T, is defined in Table I. This graph is partitioned via the max-flow/min-cut algorithm proposed in [41] to label the input image into foreground and background. The optimization method belongs to a class of algorithms based on augmenting paths, and the details can be found in [41].

A key observation we made is that the nuclear shape is typically convex. Therefore, ambiguities associated with the delineation of overlapping nuclei could be resolved by detecting concavities and partitioning them through geometric reasoning. The process, shown in Figure 7, consists of the following steps:

- Detection of Points of Maximum Curvature: The contours of the nuclear mask were extracted, and the curvature along the contour was computed by using $k=\frac{x\prime y\u2033-y\prime x\u2033}{{(x{\prime}^{2}+y{\prime}^{2})}^{3/2}}$, where
*x*and*y*are coordinates of the boundary points. The derivatives were then computed by convoluting the boundary with derivatives of Gaussian. An example of detected points of maximum curvature is shown in Figure 7. - Delaunay Triangulation (DT) of Points of Maximum Curvature for Hypothesis Generation and Edge Removal: DT was applied to all points of maximum curvature to hypothesize all possible groupings. The main advantage of DT is that the edges are non-intersecting, and the Euclidean minimum spanning tree is a sub-graph of DT. This hypothesis space was further refined by removing edges based on certain rules, e.g., no background intersection.
- Geometric reasoning: Properties of both the hypothesis graph (e.g, degree of vertex), and the shape of the object (e.g., convexity) were integrated for edge inference.

Steps in the delineation of overlapping nuclei: (Top row) identifying points of maximum curvature where potential folds are formed, (middle row) formation of partitioning hypotheses through triangulation, (bottom row) stepwise application of geometric **...**

This method is similar to the one proposed in our previous work [42]; however, a significant performance improvement has been made through triangulation and subsequent geometric reasoning. Please refer to [43] for details.

In this section, we (i) discuss parameter setting, and (ii) evaluate performance of the system against previous methods.

In order to capture the technical variation, we manually selected and annotated 20 reference images of the size of 1k-by-1k pixels at 20X, and a subset is shown in Figure 9. Nuclear segmentation was also performed at 20X, and only the top *M* = 10 reference images with the highest weight of λ were used. Essentially, this was a trade-off between performance and computational time cost (see in Figure 13). The number of components for *GMM* was selected to be *D* = 20, while the parameters for *GMM* were estimated via *EM* algorithm. Other parameter settings were: α = 0.1, β = 10.0, γ = 0.1, *w*_{1} = 100, *w*_{2} = 100, and σ = 4.0 (the scale for both seeds detection and *LoG* feature extraction), in which σ was determined based on the preferred nuclear size at 20X, *w*_{1} was selected to minimize the seeds detection error on the annotated reference images, and all other parameters were selected to minimize the cross validation error from the following discretization: *D* {5, 10, 15, 20, 25, 30}, α {0.05, 0.10, …, 0.95, 1.00}, β {5, 10, …, 95, 100}, γ {0.05, 0.10, …, 0.95, 1.00}, *w*_{2} {50, 60, …, 190, 200}. The optimal γ value is relatively small, which can be attributed to the fact that the global statistics from the well-constructed reference images, cover most of the heterogeneity in our dataset, and the role of local statistics is simply to assist the global statistics with improved discriminating powers.

A subset of reference image ROI, with manual annotation overlaid as green contours, indicating significant amounts of technical variation. Nuclei with white hollow regions inside are pointed out by arrows.

Two-fold cross validation, with optimized parameter settings, was applied to the reference images, and a comparison of average classification performance was made between our approach, random forest [44], and the most related work (Here, we refer it to MCV: multi-classifier voting, for short) in [31], as shown in Table II. Our experiment indicates that

- By incorporating both global and local statistics (MRGC vs MRGC-GF), our system better characterizes the variation in the data.
- By incorporating the
*LoG*response as a feature (MRGC vs MRGC-CF), we can encode the prior scale information into the system. As a result, ambiguous background structures are excluded, which leads to an increase of precision. However, there is also a decrease in the recall when compared to MRGC-CF, which is due to the fact that the tiny fragments inside the nuclei, as indicated by Figure 9, can also be eliminated. - MRGC with multi-scale
*LoG*features (MRGC-MS) has the best performance. We evaluated*LoG*responses at three scales, σ {2, 4, 6}, to compensate for a wide variation in the nuclear size. Improvement in segmentation is marginal, and it comes with a significant increase in the computational cost of about 40%. The*LoG*filter is simply used for seed detection to represent the underlying image statistics, and as long as a single scale can provide sufficient statistics, multiscale*LoG*is redundant. Besides, in processing whole slide images, computational throughput is an important factor.

We also provide an intuitive example, shown in Figure 10, demonstrating the effectiveness of the local probability map. It is clear that the local probability map (Figure 10(c)) helps to characterize nuclei with the low chromatin content, as shown in the blue bounding boxes. Another example, shown in Figure 11, further demonstrates the effectiveness of our approach on the segmentation of low chromatin nuclei.

A comparison among our approach, MCV, and random forest. (a) Original image patch; (b) Detected seeds, Green: Nuclei region; Blue: background; (c) Local Nuclei Probability established based on seeds; (d) Classification by our approach; (e) Classification **...**

Finally, a comparison of the segmentation performance between our current approach and our previous approach [2] is indicated in Table III, where the correct nuclear segmentation is defined as follows. Let

*MaxSize*(*a, b*) be the maximum nuclear size of nuclei*a*and*b*, and*Overlap*(*a, b*) be the amount of overlap between nuclei*a*and*b*.

Subsequently, for any nucleus, *n _{G}*, from ground truth, if there is one and only one nucleus,

Comparison of average segmentation performance between our current approach(MRGC), and our previous approach [2], in which $\mathit{\text{precision}}=\frac{\#\mathit{\text{correctly\_segmented\_nuclei}}}{\#\mathit{\text{segmented\_nuclei}}}$, and $\mathit{\text{recall}}=\frac{\#\mathit{\text{correctly\_segmented\_nuclei}}}{\#\mathit{\text{manually\_segmented\_nuclei}}}$.

The reader may question the classification performance since both precision and recall are not very high. The major reason is that the ground truth (annotation) for the reference images is created at the object (nucleus) level, which means the hollow regions (loss of chromatin content for various reasons) inside the nuclei will be marked as the nuclear region rather than the background, as indicated by Figure 9.

Having evaluated the performance of the system, we applied our method to a cohort of 377 GBM whole slide images, from 146 patients, for bioinformatics analysis. Figure 12 shows a few snapshots of our classification and segmentation results; Complete results for all the GBM tissue sections (and a few other tumor types) are available through the NIH web site at http://tcga-data.nci.nih.gov/tcga/. Following segmentation, each nucleus is represented by a multidimensional feature vector, which includes over 52 morphometric indices such as nuclear size, cellularity, cytoplasmic features, etc., [2]. The density distribution of each index is then computed per histology section and aggregated per patient.

Classification and segmentation results indicates tolerance to intrinsic variations: (a) Original images; (b) Nuclear/Background classification results via our approach(MRGC); (c) Nuclear partition results via geometric reasoning.

A particular aspect of bioinformatics analysis relies on subtyping based on a subset of computed morphometric indices (e.g., cellular density), where subtyping is performed through consensus clustering [45], [46]. In our experiment, we evaluated all morphometric indices and discovered that subtyping based on (i) nuclear size and cellularity, and (ii) nuclear intensity and gradient, are statistically stable, where four and two subtypes were inferred, respectively. Figure 14 shows the computed subtypes based on nuclear size and cellularity, where one of the subtypes is predictive of the outcome based on the clinical data. The patients in the GBM cohort received one of the two types of therapies (i) an intensive therapy with either concurrent radiation and chemotherapy, or 4 or more cycles of chemotherapy only, or (ii) a less intensive therapy of either non-concurrent radiation and chemotherapy or less than 4 cycles of chemotherapy only [47]. Although the sample size for the patient receiving the less intensive therapy is small, survival analyses [48] for one of the subtypes in each of the clustering experiments points to a trend in an improved survival for patients receiving the more intensive therapy, as shown in Figure 15. In addition, several computed subtypes, based on other morphometric indices, have also been found to be predictive of the outcome. We also examined molecular correlates of the predictive subtypes. With respect to predictive subtype computed from nuclear size and cellularity indices, we used moderated t-test [49] and identified a set of differentially regulated transcripts for subtype 2 (e.g., predictive subtype) as shown in Figure 16. A total of 10 differentially regulated transcripts were then subject to further bioinformatics analysis for subnetwork enrichment analysis using *Pathway Logic*, which computes and ranks hubs according to their p-values, as shown in Table IV(e.g., IL1, IL6), which impacts tumor proliferation and migration in both normal and malignant cells [50], [51] and the recruitment of the immune response. The relationships between these hubs and the genes associated with them are shown in Figure 17. Among the common regulators, MAPK1 and FN1, which are involved in the proliferation, are highly ranked transcripts in TCGA’s gene tracker for GBM. Furthermore, FN1 is (i) implicated in the invasion and angiogenesis, and (ii) validated as differentially expressed transcripts in GBM versus benign tumors [52]. Finally, TGFB1 is well known to be involved in tumor maintenance and progression through suppression of the immune response and is abundantly produced by GBM [53]. These molecular associations reflect that morphometric subtyping can hypothesize relevant transcripts that are potential targets of therapy, which is consistent with current literature. An example being, FN1, and its role in the induction of angiogenesis. With respect to the predictive subtype computed from nuclear intensity and gradient indices, subnetwork enrichment analysis revealed a large number of hubs from a set of differentially regulated transcripts. In this case, VEGF was discovered to be at the intersection of all pathways curated through enrichment analysis. VEGF is well known to be the hallmark of glioblastoma for the induction of microvasculture formation [54] and has been suggested as a therapuetic target in GBM [55].

Morphometric subtyping reveals four subtypes based on cellularity index and nuclear area: (a) visualization of consensus clustering with four clusters; and (b) distribution of cellularity index per subtype.

Computed subtypes with cellularity and nuclear size is predictive as a result of more aggressive therapy.

Subnetwork enrichment analysis, for the predictive subtype in Figure 15(a), reveals inflammatory hubs that promote tumor differentiation and invasiveness in GBM.

We have shown that morphometric representation of cellular architecture from a large cohort of histology sections can provide new opportunities for hypothesis generation. The main barriers are the batch effect and tumor heterogeneity which hinders nuclear segmentation. However, through image-based modeling, technical and tumor variations can be captured for robust nuclear segmentation from whole slide images. Subsequently, segmented nuclei and corresponding computed morphometric representation enables characterization of tumor histopathology. Our approach for nuclear segmentation addresses technical and biological variations by (i) utilizing global information from a diverse set of annotated reference images, (ii) normalizing the test image against the reference images in the color space, and (iii) incorporating local variations in the test image. Segmentation is formulated within a graph cut framework with geodesic constraint for improved accuracy of the nuclear boundaries. The method has been validated against annotated data and applied to a large dataset of GBM tumor cohort to identify subtypes as a function of cellularity and nuclear size. One of these subtypes is shown to have an increase in survival as a result of a more aggressive therapy with an underlying molecular signature that is consistent with invasiveness and proliferation.

This work was supported by NIH U24 CA1437991 carried out at Lawrence Berkeley National Laboratory under Contract No. DE-AC02-05CH11231.

Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to gro.eeei@snoissimrep-sbup

Hang Chang, Life Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720 U.S.A.

Ju Han, Life Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720 U.S.A.

Alexander Borowsky, Center for Comparative Medicine, University of California, Davis, California, 95616 U.S.A.

Leandro Loss, Life Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720 U.S.A.

Joe W. Gray, Center for Spatial Systems Biomedicine, Oregon Health Sciences University, Portland, Oregon, 97239 U.S.A.

Paul T. Spellman, Center for Spatial Systems Biomedicine, Oregon Health Sciences University, Portland, Oregon, 97239 U.S.A.

Bahram Parvin, Life Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720 U.S.A.

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