There are several different definitions of resolution including spatial resolution, also called 10% MTF resolution, and nominal resolution. Moreover, terms such as voxel size and detectability are also used.
Resolution is the distance between objects (or cavities) at which they can still be identified as independent from each other in an image (Figure 1). Resolution is usually given as a characteristic size (µm) or a spatial frequency (line pairs per mm).
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Figure 1
Lines in patterns with ridges and grooves smaller than the resolution can no longer be distinguished from each other as seen towards the right (center) in the pattern above. |
What is a Point Spread Function (PSF)?
A PSF describes how a single infinitesimally small point in the source object is spread out (blurred, smeared) by the imaging apparatus. Typically PSFs have a gauss-bell like shape.
If the PSF is narrow, this indicates less blurring and thus that small objects can still be discerned (better resolution) As two points are brought closer together, their PSFs begin to overlap and eventually they become difficult to discern (Figure 2 and Figure 3).
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Figure 2
Two Point Spread Functions (PSF) with little overlap. The two source points would still be distinguishable in a final stage. |
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Figure 3
Two Point Spread Functions (PSF) almost entirely overlapping. The two source points would probably no longer be distinguishable in a final image when this close together. |
What is the Modular Transfer Function (MTF)?
This is the Fourier transform of the PSF. It shows how well different spatial frequencies (line pairs per mm) are transferred to the final image (Figure 4). Typically, MTFs drop off with increasing spatial frequency e.g. as objects get smaller and closer together.
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Figure 4. Measurement Transfer Function (MTF) with the 10% MTF level shown as a dotted line. All spatial frequencies with intensities below 10% will be below the resolution of the system. |
How is spatial resolution determined?
Generally, two different methods exist:
- Measure the PSF of the instrument, determine its Fourier transform (MTF) and see at which spatial frequency it drops below a given threshold. Usually 10% of the maximal value is chosen which correlates well with average visual impression by eye (Figure 4).
- Image objects of known geometry such as a series of lattices with decreasing size. By eye, an operator determines the smallest recognizable object. Its characteristic size is then related to resolution. Although visually more intuitive, this method is also more subjective.
What about the Signal to Noise Ratio (SNR)?
There are two general sets of factors determining image resolution.
- The scanner’s build
Examples: detector resolution, X-ray source focal spot size, overall scanner geometry relative to the measurement object, precision of scanner movement during image acquisition - Scan protocol and image reconstruction software
The reconstruction influences the quality of what is visible to the user. For example, different image reconstruction kernels will smear features trading off resolution for noise suppression or using a finer image grid might give more detail but increase computation time and apparent noise. Also, not providing enough acquisition angles will hinder the reconstruction of high quality images.
What does voxel size mean?
Voxel size is the size of a 3D pixel in the rendered image. This can be equated to the nominal resolution of the image.
What is nominal resolution?
Nominal resolution is the smallest possible voxel size of a scanner’s reconstructed image and not to be confused with image resolution or resolution at 10% MTF (see below).
What is the connection between image size and image resolution?
Obviously, the final image resolution can never be better than the voxel size. The voxel size is often chosen in correspondence with the X-ray detector’s pixel size. However, because of other factors, such as the finite spot size of the X-ray source or image reconstruction, resolution is usually further reduced with some information smeared out over neighboring voxels.
How does Scanco determine a scanner's resolution?
A solid aluminum cylinder is scanned and from the reconstructed image, the PSF is assembled from the gradient of the cylinder’s edge. From this PSF the MTF is calculated and the 10% level of maximum MTF criterion is applied. This provides a reproducible measurement of the entire imaging process which is independent of the operator’s level of experience. This method is analogous to ISO recommendations for medical CT.
What is detectability?
Detectability is the smallest size of an object that can still be seen in an image and is not a measure of resolution. When determining detectablility, the imaged object usually has a very high contrast compared to the empty background. The object may appear even if it is smaller than the resolution of the scanner or the voxel size. However, location in the image grid will affect the visibility and estimate of X-ray absorption (Figure 5). The higher the X-ray absorption of the object, the smaller the object can be and still be detected at the same SNR (Figure 6). For instance, a gold particle (high absorption) might be detectable while a glass particle (medium absorption) of the same size might no longer be detectable.
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Figure 5: Blurring of beads slightly smaller than the voxel size: The voxel volumes are only partially filled leading to an underestimation of the attenuation coefficient (partial volume effect) and inaccurate rendering of sizes (positions and real shapes left, rendered image right). |
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Figure 6: Beads of different attenuation and significantly smaller than the voxel size: Even though smaller than the voxel size, the bead with the higher absorption (black) is still detectable in the image. The bead with lower absorption (gray) gives a feeble signal and might be lost in noise (positions and real shapes left, rendered image right). |
How does the SNR influence image quality?
Overall image quality is influenced by both signal-to-noise ratio (SNR) and resolution. Image quality is furthermore influenced by the original object contrast, on which the SNR depends: For example, bone and water will be easier to distinguish than two soft tissues with almost the same X-ray attenuation e.g. if the signal (tissue contrast) is smaller, SNR is smaller. Also, if there is a lot of noise in the image, object details might be obscured by the image noise e.g. if the noise is higher, SNR is smaller.
What influences SNR?
The signal is essentially the X-ray intensity detected by the image sensor. A stronger X-ray source or moving the detector closer to the source will increase signal intensity. Also, the difference in X-ray attenuation between the background and the object to be imaged will define the relevant signal level. Blood in vessels will have a stronger signal if a contrast agent is added. The noise in the image stems mainly from the statistical physical processes involved: X-ray generation, interaction with the imaged object, and detection. With longer observations (integration time) and more measurements (frame averaging) we become more certain of our detected values (mean value) and the noise is reduced (standard error). Instead of averaging over time and acquired frames one can average over image pixels. During the acquisition neighboring pixels can be binned together – 4 into 1, for example. On the down side, we would have a loss of resolution. Another option is to filter the image noise out during reconstruction. This often results in smeared or fuzzier boarders between objects representing a loss of image resolution but reducing the noise locally.
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