L11: Digital Image Processing (DIP)

Question 1

Images

Answer 1

Are representations of “real world” objects

• Radiograph / nuclear medicine scan is a representation of the anatomy and / or physiology of that patient

Must be able to be perceived as that object

Can be analogue or digital

Question 2

Form of information used in computers

Answer 2

Digital

• Enables transfer, manipulation, display, and storage of ‘real world’ info in computers

Question 3

Analogue information

Answer 3

Come from “real world” objects

• light reflected from object
• x and γ radiation passing through the body
• ultrasound / radio waves
• electrical signal form a transducer recording the above radiations

It is “continuous” in that if you were to measure it between 2 points, you would have an infinite number of values

Question 4

Form of information that humans perceive

Answer 4

Can only perceive analogue information

If converting data to digital for use in computers, need to reconvert it back to analogue for humans to perceive, e.g

• light
• sound

Question 5

Digital data

Answer 5

Discrete, compared to continuous

• Typified by steps – finite number of values between 2 points

More easily manipulated and stored – hence well suited for use in computers

• Can be copied exactly (with error checks) whereas analogue information loses quality every time it is copied e.g. photocopies, film copies use analogue techniques
• Generally, cannot be viewed by humans

Question 6

Digital hardware

Answer 6

Computers

• Input devices
• ADC (analogue to digital converters) – separate topic – from CR, MRI, CT, Nuc Med cameras, U/S, film scanners
• Keyboards
• Storage
  ○ Volatile – RAM
  ○ Non-volatile – ROM, hard drives, CD, thumb drives, tape
  ○ stored as bits
  ○ Measurement – kB, MB, GB, etc.

CPU

• Calculations
• Control of data flow
• Measurement – speed in calculations / second
• Hertz – MHz, GHz

Output devices

• Must pass through DAC – digital to analogue conversion
• monitors, printers, sound speakers

Question 7

Forms of digital data

Answer 7

Binary - Consists of 2 values

• 0 or 1
• off or on
• magnetised or not magnetised
• laser hole or no laser hole

In terms of images, black or white – no shades of grey

One binary value is called a “bit” – a binary digit

• Bit – a zero or a 1

A bit is of little value by itself, but can be one of several bit to form a “byte”

• Byte – consist of 8 bits

computing now uses multiple bytes eg. a 16 bit system will be 2 bytes (2 x bytes of 8 bits)

Question 8

Bit depth

Answer 8

Number of values in a byte depends on its “bit depth”

• 1 value – 2^1 = 2
• 2 values – 2^2 = 4
• 8 values – 2^8 = 256
• 10 values – 2^10 = 1024

Commonly, especially in imaging, values will range from 0 to 2^n – 1, where n is the bit depth
e.g. 8-bit depth – values range from 0 to 255

Question 9

Digital image processing system

Answer 9

Question 10

Digital image processing classes

Answer 10

• Image enhancement
• Image restoration
• Image analysis
• Image compression
• Image synthesis

Question 11

Image enhancement

Answer 11

Brightness adjustment, contrast enhancement, image averaging, convolution, frequency domain filtering, edge enhancement

Question 12

Image restoration

Answer 12

Photometric correction, inverse filtering

Question 13

Image analysis

Answer 13

Segmentation, feature extraction, object classification

Question 14

Image compression

Answer 14

Lossless and lossy compression

Question 15

Image synthesis

Answer 15

Tomographic imaging, 3D reconstruction

Question 16

Spatial resolution

Answer 16

Ability of an imaging system to resolve and render on the image a small high-contrast object.

• Most people can see objects as small as 200 μm
• Spatial resolution of the eye is 200 μm

Question 17

Resolution in space

Answer 17

A measure of how small an object one can see on an image

Question 18

Line pair

Answer 18

High-contrast line that is separated by an interspace of equal length

Question 19

Spatial frequency

Answer 19

Frequency of line pairs

Question 20

What affects the spatial resolution of an image

Answer 20

• depends on the resolution of the imaging system that produced it,
• characterized by its point spread function, PSF,
• or equivalently by its modulation transfer function, MTF,
• and the size of the pixels used to represent the digitized image.

Question 21

Point spread function (PSF)

Answer 21

Describes the response of a focused optical imaging system to a point source or point object

Question 22

Line spread function (LSF)

Answer 22

describes how an imaging system blurs a theoretically infinitely narrow line, representing the system’s response to a linear input

Question 23

Modulation transfer function (MTF)

Answer 23

Ratio of info available and info transferred

Question 24

Rule of pixel size

Answer 24

Sampling distance (d) or pixel size should be about one-third of the FWHM (full width half maximum) to avoid significant loss of spatial resolution

Question 25

The FWHM of the PSF of a certain CT imaging system is 2mm. How small should the pixels be? If the field of view (FOV) is 25cm, how many pixels are there along each side of the image?

Answer 25

FWHM = 2mm Pixel size less than or equal to 2mm/3 0.6667mm 25cm x 25cm FOV = 250mm x 250mm Total pixel number = 250mm/0.6667mm = 375 pixels required

Question 26

A chest radiograph is 36cm × 43cm. If we want to preserve all the detail in the image, to a spatial resolution of 5 cycles mm^−1, how many pixels would be required?

Answer 26

5 cycles mm^−1 = 5lp/mm = 10 pixels/mm Pixels = (36cm x 10/mm) x (43cm x 10/mm) = 3600 x 4300 = 15 480 000 pixels = 15.48 MP

Question 27

Figure given below shows the MTF curves for four different imaging systems, A–D. Which is the best overall system? Which is the best for imaging small details, less than 0.125 mm in size?

Answer 27

1 object = 0.125mm 1 line pair = 0.25mm lp/mm = 1/0.25 = 4lp/mm At 4, B is the highest, so B is the best The higher the MTF, the better the system.

Question 28

Fundamentals of digital image processing (DIP)

Answer 28

Image characteristics - Grey-level histograms - Brightness, contrast, signal-to-noise ratio Histograms - Basis for a number of real-time image processing techniques Look-up tables

Question 29

Image histogram

Answer 29

Provides an indication of distribution of pixels values - if displayed with a linear LUT, image contrast & brightness Can be used to aid in adjustment of image contrast levels and brightness Does not provide any information about what can be perceived within the image, i.e. does not provided any spatial information

Question 30

Grey-level histogram

Answer 30

Concise initial characterisation of an image, which can be used to assess its overall qualities and determine the appropriate processing steps required to enhance it. The histogram is a plot showing the number of pixels, anywhere in the image, that displays each of the possible discrete pixel values

Question 31

Mean pixel value ā

Answer 31

Can be obtained from the histogram by adding the products of pixel value and corresponding bin heights, and dividing by the total number of pixels. A mean pixel value close to half of the maximum possible value, i.e. 127 or 128 for an 8-bit (256 gray levels) image, indicates optimum brightness. A value significantly below or above this indicates that the image is overall dark or bright, respectively, and by how much pixel values need to be changed in order to correct this.

Question 32

Dynamic range

Answer 32

Question 33

A 12-bit deep CT image, spanning the full range of pixel values available to it (i.e. 4096, from −1000 to +3095). Calculate its dynamic range in dB.

Answer 33

= 20log10(3095 - (-1000)) = 20log10(4095)

Question 34

A typical 10-bit deep fluoroscopy image spanning its full range (i.e. 1024, from 0 to 1023). Calculate its dynamic range in dB.

Answer 34

= 20log10(1023-0)

Question 35

Dynamic range impact on contrast

Answer 35

When the dynamic range of an image covers the available range of the imaging system (2^n for an n-bit system), the image exhibits high contrast. Conversely, when the dynamic range is low, i.e. only a small range of closely spaced gray levels are present in the image, the image has low contrast and looks dull and washed out.

Question 36

Bin heights and average separation of pixel values impact on contrast

Answer 36

Question 37

Noise

Answer 37

Noise is the unwanted, random (stochastic) fluctuations in an image. Characterised by the variance of pixel values, σa^2, but needs to be measured in a region within the image which is expected to have constant gray values and is large enough so that all significant variations are included in the noise measurement

Question 38

Sources of noise

Answer 38

Photon (or quantum) noise, which arises from the discrete nature of electromagnetic radiation and its interactions with matter, and electronic noise in detectors or amplifiers. The process of digitisation is also responsible for adding noise (quantisation noise) to an image.

Question 39

Signal/mean intensity

Answer 39

Characterised by the square of the mean pixel value of the entire image, ā^2.

Question 40

Noise power (PN)

Answer 40

The variance, i.e. the square of the standard deviation, of the pixel values in such a region.

Question 41

Signal-to-noise ratio (SNR)

Answer 41

To understand its significance, the noise should be compared to the average power or intensity of the signal (PS), which is given by the average value of the pixels in the image. The signal-to-noise ratio (SNR or S/N) is the ratio of the intensity of the signal to the noise power; Often expressed in decibels (dB) by taking ten times the logarithm, to the base 10, of the ratio.

Question 42

Contrast-to-noise ratio (CNR)

Answer 42

Equal to the difference in signal-to-noise ratios for the foreground and background, respectively, since the noise is similar whether measured using the foreground or background pixels In images where goal is to distinguish a foreground structure from the background, e.g. tumour from surrounding normal tissue, CNR more useful and SNR