QCM : Medical Imaging Fundamentals — 11 questions

Questions et réponses du QCM

1. What is aliasing in a sampled image?

A low-frequency component disappearing because of filtering
A reduction in image brightness caused by detector saturation
A high-frequency component appearing as a falsely lower frequency after sampling
A uniform shift of the entire image grid during acquisition

A high-frequency component appearing as a falsely lower frequency after sampling

Explication

Aliasing is the under-sampling artefact in which higher spatial frequencies are misrepresented as lower ones in the sampled image. It is not a brightness issue or a simple shift of the grid.

2. What is aliasing in the context of sampling in imaging systems?

A process of increasing image resolution by adding more samples.
A filtering technique used to remove high-frequency noise from an image.
A phenomenon where high frequencies are accurately represented at all sampling rates.
An artefact caused by under-sampling where higher spatial frequencies appear as lower frequencies.

An artefact caused by under-sampling where higher spatial frequencies appear as lower frequencies.

Explication

Aliasing occurs when sampling is too coarse, causing high spatial frequencies to be misrepresented as lower ones, leading to artefacts in the sampled image.

3. In two-dimensional rectangular sampling, which expression gives the sampled image values?

f_d(m,n)=f(m\Delta x,n\Delta y) for integers m,n
f_d(m,n)=f(\Delta x/m,\Delta y/n) for integers m,n
f_d(m,n)=f(m+\Delta x,n+\Delta y) for integers m,n
f_d(x,y)=f(x/\Delta x,y/\Delta y) for all real x,y

f_d(m,n)=f(m\Delta x,n\Delta y) for integers m,n

Explication

The discrete sampled function is obtained by evaluating the continuous image at grid points spaced by the sampling periods, giving f_d(m,n)=f(m\Delta x,n\Delta y). The other options do not represent rectangular sampling.

4. What is the primary cause of aliasing in digital imaging systems?

Increasing the resolution, which enhances image detail
Sampling too coarsely, causing high frequencies to appear as lower frequencies
Applying anti-aliasing filters, which blur the image
Using too high sampling frequency, leading to oversampling

Sampling too coarsely, causing high frequencies to appear as lower frequencies

Explication

Aliasing occurs when sampling is too coarse, causing high-frequency components to be misrepresented as lower frequencies, leading to artefacts in the image.

5. What sampling condition does the Nyquist-Shannon theorem impose to prevent spectral overlap and aliasing?

The sampling frequencies must be independent of the band limits
The image must be low-pass filtered after sampling
The shifted spectral replicas must not overlap
The sampling periods must be larger than the object width

The shifted spectral replicas must not overlap

Explication

Nyquist-Shannon requires that the shifted replicas of the spectrum do not overlap, which prevents aliasing. This is the basis for the minimum sampling rate condition.

6. What is the primary purpose of anti-aliasing filters in digital imaging systems?

To reduce noise in the image
To limit the bandwidth of the signal before sampling
To increase the resolution of the image
To enhance the contrast of the image

To limit the bandwidth of the signal before sampling

Explication

Anti-aliasing filters are used to limit the bandwidth of the signal before sampling, preventing spectral overlap that causes aliasing. They do not directly increase resolution, contrast, or reduce noise.

7. Why are anti-aliasing filters applied before sampling?

To sharpen all edges before digitization
To convert the image into a higher-resolution continuous signal
To reduce bandwidth so overlapping spectral replicas do not occur
To increase the sampling frequency without changing the detector

To reduce bandwidth so overlapping spectral replicas do not occur

Explication

Anti-aliasing filters are low-pass operations used before sampling to limit bandwidth and stop spectral overlap. The trade-off is increased blurring, not sharpening.

8. When was the concept of the modulation transfer function (MTF) first introduced as a way to characterize system performance in imaging systems?

In the late 19th century, during the initial studies of optics
In the early 20th century, around 1920s
In the 1970s with the advent of digital imaging
During the development of digital computers in the 1950s

In the early 20th century, around 1920s

Explication

The concept of the modulation transfer function (MTF) was developed in the early 20th century, around the 1920s, as a way to quantify how well an optical system can transfer contrast at different spatial frequencies.

9. How does the modulation transfer function (MTF) differ from the line spread function (LSF) in characterizing an imaging system?

MTF describes the spatial resolution, whereas LSF measures the system's contrast at different frequencies.
MTF and LSF are identical, both representing the system's spatial resolution in different forms.
MTF measures the system's frequency response, while LSF describes the spatial spread of a point source.
MTF is used to evaluate noise performance, while LSF assesses image sharpness.

MTF measures the system's frequency response, while LSF describes the spatial spread of a point source.

Explication

The MTF characterizes how contrast at different spatial frequencies is transferred by the system, while the LSF describes the spatial spread of a line impulse, reflecting the system's resolution in the spatial domain.

10. Who is credited with proposing the concept of the modulation transfer function (MTF) as a way to quantify how well an imaging system preserves contrast at different spatial frequencies?

George S. Hounsfield
Harold Nyquist
Lord Rayleigh
Ernst Abbe

Ernst Abbe

Explication

Ernst Abbe is credited with introducing the modulation transfer function (MTF) concept, which characterizes how contrast at various spatial frequencies is transmitted through an imaging system. Lord Rayleigh, Nyquist, and Hounsfield contributed to other aspects of optics, sampling, and imaging but not specifically to the formulation of MTF.

11. What is the primary consequence of insufficient sampling density in an imaging system?

It causes aliasing, where high frequencies are falsely represented as lower frequencies.
It increases the bandwidth of the system, allowing for better contrast.
It reduces noise, leading to clearer images.
It enhances image resolution by capturing more detail.

It causes aliasing, where high frequencies are falsely represented as lower frequencies.

Explication

Insufficient sampling density leads to aliasing, where higher spatial frequencies are misrepresented as lower ones, causing artifacts and distortion in the image.

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Sampling model — formula?

Discrete sampled function: $f_d(m,n)=f(m riangle x,n riangle y)$.

Discrete sampled function

Sampled at regular grid points in space.

Aliasing — cause?

Under-sampling causes high frequencies to appear as low ones.

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