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Leukocyte classification to predict diseases (Part 2)

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Data analysis on number of blood cells, which are white blood cells and red blood cells, per a certain blood volume could help us observe our medical situation. In this blog, we introduce a faster method to recognize disease via the number of leukocytes.

Table of contents

4. Edge detection with Canny method

This method uses both high and low as 2 separated thresholds. The high one would be used firstly to find the starting point of the edge. After that, we determine the path direction of the border based on consecutive pixels having a greater value in comparison of the low. Points with the values less than the low threshold are removed only. Tiny borders will be selected if they are associated with large (easy to see) borders. The Canny procedure is demonstrated as follows:

  • Step 1: Use a Gaussian filter to smoothen the image. This step is meant to reduce the gradient of pixels while moving from one pixel to another and make the image smoother than the original.

  • Step 2: Calculate the gradient of the contour of the smoothed image. Computing the gradient is mainly to construct a function to redefine the slope as well as the increasing and decreasing trend of a certain pixel.

  • Step 3: Remove the non-maxima points. As a side note, we will choose the pixels that are most likely to be considered the highest edge by relying on the gradient calculation in step 2. When a pixel has not reached its peak, we won't evaluate that pixel as an edge.

  • Step 4: The final step is to remove the values that are less than the threshold level. Should you observe an image carefully, there are many values after calculating the gradient that will be selected as the maximum value. However, the maximum value here is only local maximum and only a few points are considered as global maximum. Therefore, we will remove some regions in which the local maximum value is lower than the allowable threshold (the threshold value will depend on the type of model to choose more appropriate).

This method is considered as more superior to other methods because it is less affected by noises and it is also able to detect weak edges. On the other hand, if the threshold is chosen too low, the boundary will be incorrect, or if the threshold is chosen too high, much of the important information about the boundary will be discarded. Based on the predefined threshold level, it will decide which points belong to the true boundary or not to the boundary. The lower the threshold level, the more edges are detected (but also noise and false edges appear). Conversely, if the threshold level is set higher, the fuzzy borders may be lost, or the borders will be broken.

5. Hough transformation to identify blood cells borderlines

Hough transformation is one of the most basic methods for feature extraction in image processing, and especially one of its capabilities is to find and detect circles in images (even imperfect circles).

This method mainly relies on the parameter accumulator after being added up (called “voting”) to get the maximum values. We will identify objects that are supposed to be circular in image with the following formula:

s.t. r is radius of circle, (a, b) is the circle's center.

The x, y values only move in the range |r - a| ≤ x ≤ |r + a| and |r - b| ≤ y ≤ |r + b| so that the above formula is satisfied. The implementation of the algorithm to 'voting' the positions will be like the setting in determining the circle as above. Here we perform 'voting' on a 3D matrix with parameters r, a, b.

Fig 5,6. Simulating the process of determining a circle using the Hough transform

For ease of visualization, we draw two small circles. Our task is to help the computer determine the center of two circles. Pay attention to the circle highlighted in blue and you will see that they have a smaller radius than the radius of the green circle. We have estimated the radius distance of the blue circle to be r = 20 pixels.

So, for each pixel that is said to be the edge (with the image on the edge being colored both blue or green), then proceed to draw a new circle with the center at the position in the cell under consideration - call x = position_row position and y = column_position.

After obtaining the three values of x, y and r, the two values a and b can be deduced easily as follows:

PI = 3.14159265358979323846264338327950
for t in range(361): 
    b = y - r * np.sin(t*PI/180) 
    a = x - y * np.cos(t*PI/180) 
    vote[a, b] += 1

As above, we will select the threshold value and take the positions vote[a, b] > threshold. The higher the threshold value is, the more likely it is to be a perfect circle. However, when the threshold value is too low, we are not sure that it is a circle (maybe even a small curve). In practice, it is virtually impossible to determine the radius in a fixed way, even if it is a human or a program with the best perception. So, when we practice in practice, we choose r in some interval [m, n]. This means that the voting array will increase from 2D to 3D as [a, b, r].

6. References

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