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Medical Image Segmentation with 3D Slicer: A Beginner's Guide

3D Slicer is an open source software that is widely used for image processing, visualization, filtering, and so forth. In this article, I would like to discuss its effectiveness and application in medical image segmentation. This software is completely FREE, and there is a continuous development of many add-ins/extensions for this platform. You may download the software from 3D Slicer Webpage. After downloading, the installation procedure is straightforward, you may also follow the instructions mentioned in their webpage.

Medical image segmentation to extract the size or volume of an organ or complex airways/channels from computed tomography (CT) or micro-computed tomography (𝛍CT) is very interesting and has been playing a crucial part in biomedical engineering. For example, human nasal cavities or airways have such a complex formation that from the CT scans, we are unable to extract the volume. However, with the power of modern image processing tools, we can manually trace the nasal airways path slice by slice and finally obtain the volume of the cavities.

In this tutorial, I am going to highlight the 3D Slicer's interface, and how we can do the manual/automatic segmentation for the purpose of extracting the volume or shape information. When you launch the software, you will see the following welcome window. The window has four sectional views. The three black windows show the transverse (or, axial), sagittal (or, longitudinal), and coronal (or, frontal) views of the CT images. The other blue colored section highlights the three dimensional reconstruction of the segmented images.

3D Slicer Interface after Launching

Medical images are often processed as .DICOM file, which can be easily opened in 3D Slicer. In the welcome window, there are options to load different format of data, but Digital Imaging and Communications in Medicine (DICOM) images are smoothly handled by the 3D Slicer. In the following, I have opened a CT scan of a human brain with a tumor, which is available in 3D Slicer's sample data for demonstration. Our task here is to find the volume of the tumor quantitatively from the CT scan images so that physicians can have more in-depth information regarding the size and growth of the tumor. They can make their next decisions confidently based on these data.

Loading the CT images in 3D Slicer

To do so, at first, we need to open the segment editor, which is located at the top of the window where you will see an icon says 'All Module'. Click on it and then, select the segment editor as highlighted below.

Segment Editor of the 3D Slicer

Once you select the segment editor, a new small window will pop-up just like the screenshot shown beneath. You will find some features in that new little window, such as, 'ADD', 'Show 3D' etc.

Adding a New Segment to Start the Segmentation

You need to choose the option 'Add (+)' and then, a new segment will be created named as 'Segment_1' (see below). From the screenshot, you see that a new segment is ready to carry on for further operation.

A New Segment Created in the Property Editor

Now, if you double click on the 'Segment_1', you will see the following options will appear to select the segmentation nature. For example, if we segment a bone, then choose 'bone' in that window; or if the segmentation is related to the brain or tooth, select the respective 'brain' and 'tooth' segmentation features. In our example, it is a tumor that we are going to segment. A tumor is a mass of abnormally growth of tissues, so we can choose the segmentation media as 'tissue'.

Selection of the Type or Nature of Segmentation

So, we have decided how we are going to segment the tumor, now it's time to move forward using the tools to do the segmentation. There are two types of segmentations: automatic and manual. To understand the difference between the automatic and manual segmentation, let me first explain how the CT scans are formatted or processed for image analysis. There are many single images that form the CT scan of an organ, which alternatively implies that a CT scan itself an image that has subsets of many images. So, when we consider automatic segmentation, it is a process of tracing or narrowing a particular section from the CT scan that is done by the software, and manual segmentation is that you need to paint or trace that particular region by hand for all the individual images that eventually form the CT scan. As you see below, the red circled area is the tumor that we need to separate out and get the volume of it. We also see that there are some options, like 'Paint', 'Draw', 'Level Tracing' to trace the tumor. Here, I used the 'Level Tracing' option for that, traced few images or slices and then used the 'Fill between slices' option as an automatic segmentation approach.

Use of the Segmentation Tools

Once the segmentation is done, then we can estimate the volume of the tumor. For that, select again 'All Modules', and from the dropdown menu, click on the 'Quantification', and then hit 'Segment statistics'.

How to Extract Volume Information from 3D Slicer

After that, at the bottom of your window, you will find the volume of the segmented tumor. From the screenshot below, we see the volume of the tumor is approximately 346.99 mm³. Now, remember, this is not an accurate or quantitatively perfect representation of the tumor. However, it gives a reasonable view and idea about the shape and size of the tumor. Below, we can see the looks of the tumor in a three dimensional space.

The 3D Shape Extracted from Segmentation with Volume Statistics

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A Taylor Series Expansion to Approximate a Function near a Point

The Taylor series expansion up to seventh terms for approximation of near point x =1 is,
Taylor series expansion up to seventh terms

Letting starting point xₒ is at 0 and the step size (xi - xₒ) is 1. Now, the value of eˣ at x = 1 is to be calculated by Taylor series expansion on the basis of the starting point and its derivatives at x = 0 with step size 1. A MATLAB program is written to evaluate this value from zero order approximation to sixth order approximation and show the improvement of accuracy and minimization of truncation error as well.
The true value of is 2.718281828459046. The truncation error is the difference between true and approximate values. The following MATLAB program describes each steps of the calculation. 

Taylor Series Implementation by a MATLAB Program

% Taylor Series expansion to approximate exp(x) near point x=1
function e = taylorseries(x0,x1,h)
e0=exp(x0);              % calculates exp(x) value when x=0
derivative1=1;           % all the six derivatives calculated at x=0
% zero order approximation
        disp (e);        % display of exp(x) and error at command prompt          
% first order approximation        
        disp (e);       
% second order approximation
        disp (e);        
% third order approximation
        disp (e);        
% fourth order approximation        
        disp (e);        
% fifth order approximation                      
        disp (e);        
% sixth order approximation
        disp (e);        

Table 1: Outputs from the Above Program to Approximate at x=1

Approximation of an exponential function by Taylor series

The above table tells us as the order of the Taylor series increases the truncation error also decreases. However, after sixth and higher order approximations, improvement of the accuracy is not much significant. So, we can stop the approximation to first seven terms of the Taylor series and the approximate value of ex near point x = 1 is 2.718.

Finding Roots of a Equation by Newton-Raphson Method

In this tutorial, we are interested to the roots of the following function.

f(x) = sin x + 2 - 0.1 x

To find the value of x or roots of the equation, Newton-Raphson method is applied. For the proper initial guess for x, graphical method is applied to visualize the characteristics of this nonlinear function. This graphical technique also helps to find multiple roots for the unknown function. The following MATLAB commands generate the plot of the function, f(x). This function is plotted with respect to the values of x from -50 to +50.

>> X=-100:100;
>> plot(X,(sin(X)+2-(0.1*X)))

From the following figure 1, it is clear that the equation has seven roots and plotting the function helps to get the roots. The function changes its sign from, x = 10 - 11, 11 -12, 16 -17, 18 - 19, 21 - 22, 25 - 26, and 27 - 28. And, the roots of the equation must lie between these intervals. Now, to get good approximations of the roots, a Newton-Raphson algorithm is written in MATLAB.

Plot of the function f(x) to identify the intervals where roots of the function lie

Figure 1: Plot of the function f(x) to identify the intervals where roots of the function lie.

The program is developed by MATLAB user defined function called “sinusoidal”. The initial assumptions for approximating seven roots of x are 10.5, 11.5, 16.5, 18.5, 21.5, 25.5 and 27.5 respectively. The codes are given below. It is straightforward to run the program seven times as we have seven initial guesses for the corresponding roots.

Newton-Raphson Algorithm by MATLAB

% Definition of a function "sinusoidal" to solve equation by Newton-Raphson
function [x,ea] = sinusoidal(X, etol)
format long;
% Input: X=21.5, etol=Tolerance definition for error
% Output: x=Solution of equation, ea=Calculated error in loop
% Program Initialization
solution = 21.5;
% Iterative Calculations
while (1)
    solutionprevious = solution;

% Implementation of Newton-Raphson Method 
    solution = X - (sin(X)+2-(0.1*X))/(cos(X)-0.1);               
if solution~=0                         % Approximate percent relative error
    ea=abs((solution - solutionprevious)/solution)*100;      
if ea<=etol,                  % Condition to meet specified error tolerance
x = solution;

% Display of output parameters

Program Outputs: 

>> sinusoidal (10.5,1e-10)
ans =
>> sinusoidal(11.5, 1e-10)
ans =
>> sinusoidal (16.5,1e-10)
ans =
>> sinusoidal (18.5,1e-10)
ans =
>> sinusoidal (21.5,1e-10)
ans =
>> sinusoidal (25.5,1e-10)
ans =
>> sinusoidal (27.5,1e-10)
ans =

So, the seven roots from the program are 10.637, 11.562, 16.108, 18.721, 21.809, 25.745 and 27.436. In all the cases, the error tolerance limit is kept extremely small (0.0000000001) to get more accurate and precise results.

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