Linear structure elements

In this project we will not use square structure elements, because these elements most likely will be to rough for the low resolution cell nuclei images. We will instead use linear structure elements and rotate them to separate the objects, while still not removing to much of them. Later we will give a full description on how the splitting of objects is done, but as an example a linear structure element of size 3, and how it rotates, is given below.

0 0 0 1 1 1 0 0 0 , 0 0 1 0 1 0 1 0 0 , 0 1 0 0 1 0 0 1 0 , 1 0 0 0 1 0 0 0 1 (4.3)

The morphological algorithm is iterative and includes the following steps

1. Divide the segmented image into two subimages, one with bright objects and one with dark objects as shown in figure 4.6.

2. Label the objects and find the solidity of each object.

3. If an objects solidity is below some constant, c, and the object is larger than a certain size: Split the object into two or more objects.

4. Go back to step 2 until all objects have solidity greater than c or are smaller than the chosen size.

(a) Original image (b) Dark objects (c) Bright objects

A detailed description of the morphological operations

The previous step-wise description of the iterative morphological algorithm didn’t give any details on how the objects where separated. Here we will give a thorough description on how this algorithm actually works, illustrated with images. As- suming we now have a segmented image with only bright or dark objects, which are labeled, the splitting process is as follows:

1. For each object check if the solidity is higher than 0.80 and contains more than a certain number of pixels, if not split the object into two or more. Figure 4.7(a) shows the first object that is checked from figure 4.6(b), but solidity is 0.8519 and nothing is done. The object in (b) in the same figure has solidity less than 0.80 and has to split.

2. The object is eroded with a linear structure element of size two. If the objects in the region are not separated, the linear element is rotated, as shown in (4.3) above. The result after erosion is illustrated in figure 4.7(c). 3. If the structure element is too small to divide the region into several objects, then the length of the element is increased by one and we are back at step 2.

4. After the object is split then the image is dilated with the same rotated structure element the same number of times as it was eroded, and we now have two or more objects. Figure 4.7(d) show the two objects after dilation. 5. Some objects are more problematic than others, and if and object is eroded enough, it will disappear. If that is the case the original object is saved and later put back into the image.

6. When an object is split, the process starts from step one again and is completed when all objects fulfill the solidity and size criterion.

7. Finally we use morphological opening to remove small object and gaps which the iterative algorithm couldn’t handle.

Figure 4.8 shows the original Image 3 in (a) and the image after segmentation and morphology in (b). The next step will be to extract some features which describe the objects and then classify the images based on the information extracted from the objects.

4.5. SEPARATING THE OBJECTS 41

(a) (b)

(c) (d)

Figure 4.7: Morphology on Image 3.

(a) (b)

Chapter 5

Features and Classification

In this chapter we will describe the last steps in our algorithm, namely features, or object descriptors, and classification. There is a lot of theory about these subjects and we will go briefly through some of it, and the choices made in our algorithm.

Features

The goal of an image analysis task is in the end to classify an image, or the objects within it, into one of several classes. We have a number of patients belonging to two classes: good and bad prognosis. For each of the patients we have about 300 cell images. Each of the images contains a single cell nucleus.

After the segmentation and morphology are done, we have two labeled bitmaps per image, giving the pixels belonging to dark and bright objects, which are the basic texture structures of the cell nuclei. As with the morphology we will handle the dark and bright objects separately.

5.1

Object descriptors

In the literature there exist descriptions of a lot of object descriptors that could be extracted, see [5], [8], [23]. We could certainly generate a long list of features describing the structures, and then perform some type of feature dimensionality reduction in order to end up with a low dimensional set of features. However, we do not want to have too many feature candidates to choose from, as this would only increase the risk of selecting seemingly useful but actually useless features, given the limited number of samples available [20]. We therefor limit ourselves to intuitively useful features that may contribute to separation of the two classes.

Object descriptors can be very intuitive and simple, e.g., area and perimeter of an object, but a feature could also be very complex and not that intuitive, e.g., fourier descriptors [5].

But because of the low resolution images, the segmented structures inside the cell nuclei will be small and of a limited number of pixels. It therefor seems rea- sonable to use simple features to describe the objects. From each of the bright and dark objects we have chosen to extract the following area-related and shape- related features:

1. The area of the object

2. The relative area of the object (relative to the area of the nucleus) 3. Compactness

4. Eccentricity

5. Orientation relative to radial direction

Our main attention so far has been on the object structures inside the cell nuclei. But our aim is to correctly classify each cell nucleus image, and in the end classify the patients. So it might also be useful to extract information about each of the cell nuclei as well, such as:

1. Area

2. Compactness 3. Eccentricity 4. Mean gray level 5. Variance of gray level

6. The number of dark and bright objects

We note that the coordinates of the center of mass and perimeter length for both the cell and the objects will be stored. These will not be used directly as features, but will be useful when computing the object features.

5.1. OBJECT DESCRIPTORS 45