Automatic measurement of D-score in human endometrium images Javier Rojas

ABSTRACT This document presents a method to identify an reconstruct endometrium glands in images of samples of endometrium tissue, using non-rigid registration.

1.

INTRODUCTION

The endometrium hyperplasia is a pathology which is correlated to the presence of adenocarcinoma, and its presence is used to estimate the likelihood of developing this kind of cancer. To diagnose endometrium hyperplasia the pathologist used different methods, such as verbal descriptions [7], making thus to this process something difficult of reproduce and validate. In 1985 an advance was presented with the introduction of the WHO classification scheme [7], that allowed some standardization of the diagnosis process. This scheme is based on the evaluation of qualitative characteristics of the analyzed samples, such as the nuclear atipicity and the nuclear complexity of the glands. Despite the advances made with this methodology over the traditional diagnosis process, the WHO scheme has sensibility problems [7]; there are several diagnosis that according to the WHO schema

are severe and that finally don’t develop cancer. The medical community agrees about considering the WHO scheme insufficient to do a proper diagnosis of endometrium hyperplasia [4, 14]: several studies have found that this kind of diagnosis is hard to reproduce, thing that makes this scheme less reliable and less sensitive. The indicator known as D-score [1] has shown a larger sensitivity that the evaluation of qualitative characteristics made by the WHO classification [14]. This indicator considers qualitative and quantitative characteristics of the endometrium samples used for the diagnosis, and is earning space as an standard method in this task. The D-score is defined as: D-score = 0.6229 + 0.0439 × (percentage of stroma’s volume) −3.9934 × ln(std. dev. of shortest nuclear axis) −0.1592(density of the superior surface of the glands) (1)

2.

RELATED WORK

Une of the most compelling reasons to perform the analysis of endometrium samples images maually is that the images have a large amount of noise, color and shape variations, along with discontinuities in the searched shapes —see figure 1(a). This two characteristics —the shape variability and the gland segments discontinuity— make the measurement of the D-score an interesting problem in image processing; the identification and reconstruction of the glands can be stated more formally in this area as detection of closed shapes and edge linking. Several automatic approaches in the area to analyse histology images [6,8,10,12] aren’t adequate for

a force inversely proportional to the distance separating them. A problem of this thecnique is that the distance between segments in the image is not sufficient to discriminate the glands, given that these tend to be grouped very near to each other, see figure 1(a). (a)

(b)

Figure 1: Typical images of endometrium samples

Shih [11] proposes the usage of mathematical morphology operations to modify the edges of the segments iteratively until connecting them. Due to the nature of these operations, there is dependence from the initial orientation of the edges of the segments for this method to work properly.

this problem due to very strong assumptions over the kind of searched shapes, such as that they are complete, that can be modelled mathematically, etc.

3.

Techniques based in the topology of the image, like the one used in [2], allows to find directly the closed regions —the glands— in the same. However, this approach isn’t completely applicable due to the assumption made by for the method that the searched objects don’t have any discontinuity in its borders; in other words, the contours are easily identifyables and they stay closed. Nattkemper resumes in [9] several techniques to detect cells in histology images. A very popular approach to that problem is the Hough transform [5], which uses a mathematical definition given previously that describes the searched object (as a line, or a ellipse) to locate the objects of interest in the image, estimating the parameters that give the best fit to every shape found. Although the Hough transform solves the issue of the segments discontinuity that define a gland, it has several drawbacks: t only allows to recognize shapes defined previously, it must be possible to have a mathematical representation of them, and it is very slow. Hai-Shan [12] presents another scheme to detect shapes in an image through parameter estimation, similar to the Hough transform, and shows its application in the detection of cell contours, that unfortunately has the same issues of the Hough transform. The problem of connecting discontinuous segments in binary images has been examinated from other perspectives; Zhu [13] presents an strategy based on potential functions, in which the extreme points of the segments attract each other mutually, with

METHODOLOGY

The approach to identify the glands in the endometrium samples images can be described as follows • The image is segmented, obtaining a binary image to work with. • A topological tree is created from the binary image, which allows to discard several regions and fix some segmentation errors. • Several subsets of segments of the binary image are created. • Within each subset we try to find which segments definitively are part of a gland.

3.1

Image preprocessing and segmentation

Thanks to the staining procedure applied to the samples it is possible to identify visually three different kinds of tissue within the image, see Fig. 1 1. The border of the endometrium glands, with light brown color. 2. The nuclei of the glands, in white color. 3. The background of the sample, with violet color. The identification of every tissue type is made through a classification procedure based on the RGB colors in the image, using a machine learning classifier.

3.1.1

Image preprocessing

To correct the lighting and staining differences in the processed images —caused by environmental conditions, the stain medium application, and other factors [3]— is necessary a preprocessing stage that equalizes the analyzed image. This process allows to train the classifier with some typical images, and then equalize the histogram of the analyzed image to match more closely the histogram of the images used for training, and hence achieving better performance when processing the image with the classifier.

3.1.2

Image segmentation

A multilayer perceptron is used to segment the image; the segmentation quality of this classifier has shown experimentally good enough to identify the gland borders in the analyzed images. The training data for the classifier is selected manually from a subset of the test images, and the person using the training application selects which pixels belong to which categories. All the pixels selected are used to train the multilayer perceptron; the testing of the classifier is made interactively with other test images.

3.2

Primitive extraction

After the segmentation process we have a binary image, with the interest objects —the gland borders— in black, and the glands nuclei and background in white. A topological tree of the image’s objects is built and used to improve the results obtained from the segmentation. The whole tree is explored to discard topological nonsenses and to identify the different kind of resulting objects, such as closed glands, or different gland segments (see figure 2) Any region too small (less than 40 pixels) was discarded, and made part of its enclosing region. Besides, any region below the third level of the tree was discarded, and recursively made part of the white region enclosing it. This is a topological impossibility, since it is assumed that the image contains only closed shapes (white-black-white paths in the topological tree), or disjoint segments (whiteblack paths). In this stage is possible to identify glands that are too close from each other; they can be seen in the

Figure 2: Topological tree associated with the binary image

topological tree as a sequence of a white parent, a black son, and two or more white grandchilds. When detected, they are removed from the image and stored for further processing to split them properly using distance maps [2].

3.3

Primitive grouping

The idea behind this stage is to perform registration considering only primitives that are likely to form a particular closed gland. To do this, several subsets of primitives are built, and the gland identification process is performed over each one of them. These sets are built considering the bounding box of every segment: if two bounding boxes overlap each other, then they are part of same subset. To cope with the discontinuities that might exist between the gland segments, every bounding box is enlarged proportionally along the width and height a 10%, and the intersection is calcullated over these new bounding boxes. It is important to note that a segment might be in more than one subset, expressing this way the fact that the particular segment could be part of several glands due to its proximity. It is important to note that this procedure is intended only to reduce the search space for every gland. With these subsets is isn’t necessary to consider all the segments of the image when searching for a gland; only the segments within each subset are examined, since we are assuming that each subset contains at least one gland, but it might contain more segments that are unrelated to it.

3.4

Glands identification

To build these, several criterion are considered, such as their shape, an approximated measure of convexity, and their orientation. For each subset S of segments, every pair of segments within them goes through the following process 1. The centroids of each one of them is calcullated as the average of the x and y positions of the pixels that make part of it. 2. A line between each centroid is traced, and the count of times it passes through a gland segment (a region of black pixels) is stored. This value t should be zero for ideal segments, and it is the main criteria to decide which segments are part of the gland.

Figure 3: Test image

3. If the amount of segments trespassed is less than 3, then the segments are added to a set of segments G that definitively are part of a gland according to the proposed method. 4. The remaining segments in the set S go through the same process against every element in G, choosing as measure t the minimum of the different ti obtained. The choice for the maximum value of t isn’t arbitrary. It is intended to be as general as possible when measuring the proximity of two segments. With a maximum of 2, we consider the event of the centroids being within both segments: in this case, the line joining the centroids will pass through 2 segments —the initial and final segment.

4.

(a) Binary image

(b) after small regions elimination

Figure 4: Binarization and postprocessing

RESULTS

The proposed method is evaluated against a test image (figure 3) The figures 4(a) and 4(b) show the segmentation and postprocessing results. It is important to note that the objects identified as glands in this stage are deleted from the image.

5.

FUTURE WORK

The criteria proposed to define which subset of primitives makes part of a gland isn’t sufficiently general, and so is the criteria for defining sets of related primitives. The usage of bounding boxes

Figure 5: Segments identified. The bounding boxes identify each segment

3069654, Dec. 18, 1962. [6] AC Jalba, MH Wilkinson, and JB. Roerdink. Automatic segmentation of diatom images for classification. Microscopy Research and Technique, 65:72–85, 2004. [7] RJ Kurman and PF Kaminskiand HJ Norris. The behavior of endometrial hyperplasia. A long-term study of untreated hyperplasia in 170 patients. Cancer, 56:403–412, 1985.

Figure 6: Glands found in the image. The bounding box identify each gland found

[8] Joakim Lindblad, Carolina W¨ ahlby, Ewert Bengtsson, and Alla Zaltsman. Image analysis for automatic segmentation of cytoplasms and classification of rac1 activation. Cytometry, 53:22–33, 2003. [9] Tim W. Nattkemper. Automatic segmentation of digital micrographs: A survey. medinfo, 2004.

can’t deal with situations when the glands segments are too close from each other, so in every subset of gland segments we have more data than necessary, thus defeating the purpose of creating these subsets.

[10] Francisco J. Sanchez-Marin. Automatic segmentation of contours of corneal cells. Comput Biol Med., 29:243–258, 1999.

6.

[11] Frank Y. Shih and Vijayalakshmi Gaddipati. General sweep mathematical morphology. Pattern Recognition, 36:1489–1500, 2003.

REFERENCES

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