Image Resolution Radiology (Modulation Transfer Function)

Image resolution can be directly visualized with images of a bar pattern where the limiting resolution can be determined by the smallest set of line pairs that can be seen.

00:00 Introduction to MTF
00:39 Image Resolution Definition
03:08 Visual Resolution X-ray Radiography
04:05 Visual Resolution Computed Tomography (CT)
04:39 Point Spread Function (PSF)
06:50 Modulation Transfer Function (MTF)
08:44 PSF to MTF (Point spread function to Modulation transfer function)
10:42 MTF in Computed Tomography (CT)
11:05 MTF in X-ray Imaging
Linear Systems for X-ray Technologists
When images are taken on a real x-ray system there will always be some blurring that takes place in the system due to the size of the focal spot and the size of the detector. The idea of linear systems modeling is that we can model the blurring in our x-ray system.

The blurring of the image that occurs when an image is made on an x-ray system can be thought of as starting with a perfect, ‘ideal image’ and then blurring it out more. As the size of the detector elements gets larger the blurring will be increased.

We can think about each point in an ideal image and what happens in reality is that in the measured image each point in the ideal image is blurred by adding contributions from its neighbors. That blurring is called a point spread function (PSF). Each point in the image gets spread to the neighboring points in the image.

As the PSF gets larger there is more blurring into neighboring regions and as the PSF gets smaller there is less blurring.

The blurring is usually modeled in 2D on the images (both up and down and left to right). The blurred shape we see is function of the system and it is called Point Spread Function.

In the figure for the perfect system, we can easily see all of the bar patterns. But in a real system the bar patterns will be blurred and the neighboring objects become hard to tell apart (visually differentiate).

In the next section we will describe how this linear system can be used to make measurements of spatial resolution.
Modulation Transfer Function (MTF) (Frequency Space)

In the real system the contrast is reduced for the higher resolution bars (seen on the bottom of the figure). Next, we will introduce a method to describe the resolution directly in frequency space.

Each of the bar patterns has a given width and this is measured in units of line pairs per mm (lp/mm).

The wider bar patterns have a lower frequency (fewer line pairs per mm) and the narrow bar patterns have a higher frequency (more line pairs per mm).

On the bottom of the figure we have a curve that goes down for higher frequencies. This curve is called the Modulation Transfer Function (MTF). The MTF is used to describe how quickly the ability to see the finer bar patterns goes down (i.e. how does the system effect the higher spatial frequencies).

The modulation transfer function (MTF) describes the frequency behavior of the system and is a curve that has lower values for high frequencies which represent the small image structures.
Small image structures correspond to high frequencies, and large image structures correspond to low frequencies.

We described the point spread function (PSF) and the modulation transfer function (MTF). In this section we will describe the link between the PSF and the MTF.

The point spread function (PSF) is a blurring function that is measured in the image space. The PSF is often assumed to be symmetric. If we take the Fourier Transform of that point spread function, we get the MTF or the Modulation Transfer Function.

This is the same Fourier transform that is used in MRI imaging where the data is collected in Frequency space and the Fourier transform is used to convert to image space (image reconstruction).

The advantage of using the MTF compared with direct visual observation is that MTF provides a very quantifiable number, that is not dependent on a subjective reader.

The different points on the MTF curve describe the system resolution can be compared from system to system. It is standard process to report the frequency (x-axis value) when the MTF curve is at 50% of the maximum value (MTF50), and when the MTF curve is at 10% of the maximum value (MTF10).

We can do this over and over on different systems and get a quantifiable number and all we have to do is scan a wire. If the wire is much smaller than the size of the detector, then all we can ignore the size of the wire.

So all we need to do is to scan a wire and take the Fourier Transform to get the MTF.

That relates to how well you can see the small structures in your image and we can do this in a quantifiable and repeatable way. This gives the same type of information as the direct observation of bar patterns but is less dependent on the reader of the images.

Rad Take-home Point: The modulation transfer function (MTF) is the Fourier transform (frequency space representation) of the point spread function (PSF).

Видео Image Resolution Radiology (Modulation Transfer Function) канала How Radiology Works