Clinical motivation
3.2 X-ray imaging
risk of lung cancer (Hohbergeret al., 2014). In CT, emphysema stands out as homogeneous, dark spots (low attenuation) inside the lung. Even more relevant for this project, the characteristics/morphology of lung nodules may change depending on emphysema severity. This is challenging to include in any CAD-system.
3.2 X-ray imaging
The technology behind the CT-images we observe are based on radiation. The image is created in a process of several steps. First one needs an X-ray tube, which is a vacuum tube with a cathode and an anode. By charging the cathode, high-speed electrons begin to fire towards the anode, then quickly de-accelerate as they hit the nucleus of the anode. This results in energy being released in form of X-ray radiation (Gonzalez and Woods, 2010a).
To penetrate the body, one would need a sufficient voltage for the energy of the X-rays, but at the same time minimizing the dose and maximizing the image quality. As the X-rays penetrate the body, they will interfere with different objects in the body, and it is these scattered rays we want to capture to create an image. One way to capture the rays, is using a phosphor screen that converts X-rays into light. Then the light signal is digitized, and based on the amplitudes, one can predict which elements it has passed through, to create an image.
Note that lung nodules below 5 mm size are rarely detected in conventional X-rays, and the number of false negatives is high.
3.2.1 Computed Tomography
One of the most important imaging modalities in the detection and evaluation of lung nodules down to 1-2 mm size is computed tomography (ct). It uses the concept of X-ray imaging with back projections to create a 2D-image.
The idea is to apply ordinary X-ray imaging from different angles around the ob-ject of interest, then capturing the rays in a small detector, and back proob-jecting the resulting photons. By doing so over several angles, one can add/integrate over the resulting back projections, which results in asinogram. This transfor-mation is called theradon transform. Then to get the resulting 2D-image, as we observe as a CT image, we apply the inverse radon transform.
All the steps can be summarized as follows:
38 C H A P T E R3 C L I N I C A L M OT I VAT I O N
1. Compute 1-D Fourier transformGθ(ω,θ) = F(дθ(x,y)) of each back projection (or angleθ)
2. Apply a window functionw onGθ(ω,θ), to reduce ringing artifacts. The most common window function is theHanning window
3. Apply the inverse 1-D Fourier transform of the filtered back projection
⇒ fθ(x,y)=F−1{Gθ ·w}
4. Integrate over fθ(x,y)for all back projections. This results in the recon-structed image f(x,y)
In the continuous case, we could formulate the reconstruction by a single equation:
f(x,y)=∫ π
θ=0fθ(x,y)dθ =∫ π
θ=0д(xcosθ +ysinθ,θ)dθ (3.1) whereд(ρ,θ)is the sinogram andρ =xcosθ+ysinθ.
This concept can be used to create images of a volume instead. There are several ways of doing this. A simple approach is to apply the 2D scanner at different increments of a specified range. Then stacking these images, or using some kind of reconstruction method, results in a CT image stack of the 3D volume. The problem with this approach is that there is a trade-off between resolution and dose which is difficult to control. Therefore, what is commonly done is to do a helical scan. Using a spiral scan motion, the 2D scanner is applied continuously in a specified range. Then one can reconstruct the volume as a 2D image stack since one control the spiral motion. This results in reduced dosage, while achieving similar resolution.
3.2.2 Hounsfield Units
X-rays penetrating the body interfere with a medium, causing X-ray attenuation that is used for image creation. There is a significant difference in output ampli-tude whether the ray has penetrated human tissue, air or bone. By experiments one have been able to find attenuations coefficients µ for a lot of different relevant mediums.
Because the most common medium in the human body is water, this attenuation in water is used as reference. If the measured signal is lower than expected (amplitude for water), it would indicate that the ray has passed through some other tissue. Since the attenuation coefficients of all relevant mediums are known, we could try to map the light signal amplitudes to some values that
3.2 X-R AY I M AG I N G 39
have some solid physical interpretation.
This is what we callCT-numbers, and these are:
CTnumber = µT issue −µH20
µH20
×1000 (3.2)
By using water as reference, theCTnumber of water is defined as zero. More dense mediums, such as soft tissue or bone, have positive CT, and vice versa.
These are what we callHounsfield Units(hu).
Inside the body, the HU’s approximate range is (-1000, 3000), where -1000 is for air, and 3000 for dense bone. Inside the lung we typically only have HU-values in the range (-1000, 1000), but at times one may observe intensities larger or smaller, due to different artefacts in the imaging modality - one of which is salt and pepper noise. However, there are disagreements of the limits in literature. Some say that the limits are in the range [-1024, 1024].
The various intensities in CT images actually have a physical meaning, and any image preprocessing should not alter with these values. Another consequence is that segmentation of larger objects can be easily generalized since each object displays a range of intensities. This is an argument to why most lung segmentation methods are based directly on these intensities. Using other modalities, one can rarely use these simple approaches.
One could also try similar approaches to detect nodules, but for instance blood vessels have similar HU-values, which results in segments where it is challenging to separate these from nodules. Therefore, more advanced and efficient methods were proposed (Li, 2007). Some of these are based on deep learning, which is the approach most state-of-the-art algorithms are based on (Wu and Qian, 2019).