digital imaging systems. medical imaging systems projection radiography computed tomography nuclear...
TRANSCRIPT
Digital Imaging Systems
Medical Imaging Systems
Projection Radiography
Computed Tomography
Nuclear Medicine
Ultrasound Imaging
Magnetic Resonance Imaging
Projection Radiography
Computed Tomography
Emission Tomography
Ultrasound Imaging
Magnetic Resonance Imaging
Medical Imaging Signals
X-ray transmission through the body
Gamma ray emission from within the body
Ultrasound echoes
Nuclear magnetic resonance induction
Computed Radiography
Digital Radiography
Analogue v Digital Signals
The “real world” information (signal) is often in analogue form.Computer deals with digital numbers.In order to transfer, manipulation, display, storage of the real world information in computers, the analogue signals need to be converted into a form that is used by computer, that is in digital form.
Analogue
Analogue information come from “real world” objects
light reflected from object
x and radiation passing through the body
ultrasound / radio waves
Electrical signals formed in recording the above radiations
Analogue (cont.)
Analogue is a “continuous” signal in that if you were to measure it between 2 points, you would have an infinite number of values
Analogue (cont.)
We, as humans, can only perceive analogue informationWe convert analogue data to digital for use in computers but we also need to reconvert it back to analogue for humans to perceive, eg
lightsound
Digital
Digital data is discrete, compared to continuous
Typified by steps – finite number of values between 2 points
Digital (cont.)
More easily manipulated and stored – hence well suited for use in computers
Can be copied exactly (with error checks) where as analogue information looses quality every time it is copied eg photocopies, film copies use analogue techniques
Generally can not be viewed by humans
Forms of Digital Data
Bistable (Bit)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
Forms of Digital Data
One bistable value is called a “bit” – a binary digit
A bit is of little value by itself, but can be one of several bit to form a “byte”. A byte is generally referred to 8 bits.
Byte – with 4 bits example:1 2 3 4 values
0 0 0 1 1
0 0 1 0 2
0 0 1 1 3
1 1 1 1 15
Forms of Digital Data (cont.)
Number of values in a byte depends on its “bit depth”
• 1 value – 21 = 2• 2 values – 22 = 4• 8 values – 28 = 256• 10 values – 210 = 1024
Commonly, especially in imaging, values will range from 0 to 2n – 1, where n is the bit depth eg. 8 bit depth – values range from 0 to 255
Forms of Digital Data (cont.)
In terms of computing, common values of the bit depth are
8 – 256 values16 – 65,536 values32 – 4,294,967,296 values
In digital images8 – 256 values (simple grey scale images)10 – 1,024 values (medical images)12 – 4,096 values (medical images)24 – 16,777,216 values (colour images)
Digital Computer Hardware
●Input devices●ADC (analogue to digital converters) – from CR, MRI, CT,
SPECT, PET, U/S, film scanners
● Keyboards
● Storage• Volatile – RAM
• Non-volatile – ROM, hard drives, CD, MOD, tape
• Stored as bits
• Measurement – Kbytes, MB, GB
Computer Hardware Structure
Digital Computer Hardware (cont.)
CPUCalculations
Control of data flow
Measurement – speed in calculations / second • Hertz – MHz, GHz
Output devicesMust pass through DAC – digital to analogue conversion
• monitors, printers, sound speakers
Central Processing Unit
Computer Softwares
System Control Software – Operating Systems
Programming Software – Programming Languages
Application Software – Digital Imaging Applications
Graphical User Interface – IDL, Matlab
Basics of Images
Images can be analogue or digital
AnaloguePhotographs
X-ray / nuclear medicine films
Can not be manipulated
DigitalStored in memory (can be displayed on a monitor)
Can be manipulated, copied exactly
Can be grey scale (of any bit depth) or colour (24 bit depth)
Medical Image Conversion Process
Patient
Image
Acquisition
Analogue
Image
ADC
Digital
Image
Image
Processing
Digital
Image DAC
Digital to
Analogue Conv.
Diagnostic
Image
Viewing
Analogue
Digital
Digital
Analogue
ADC Process
ADC Process consist of 4 stages:Sampling
Sensing
Quantising
Coding
This process converts analogue information to digital data, i.e. discrete values / integers.
ADC Process
ADC Process - Sampling
In the sampling section of the ADC process, a sampling rate needs to be established.
This is the rate at which the analogue information is “read” or sampled
The higher the sampling rate, the more accurately the digital data will represent the analogue information.
In a digital image, the rate determines the no. of pixels in a row, i.e. the spatial resolution of the image.
ADC Process - Sampling
Sampling rate and aperture size are similar
Aperture size is the time interval between sampling points and given by:
sampling rate = 1
aperture
Increase the sampling rate, aperture size decreases.
ADC Process - Sensing
Sensing is the act of reading the analogue information, at the preset sampling rate.
As an example, the analogue information could be a voltage between 0 and +5 volts.
At that particular sampling point, the voltage will be “sensed”.
ADC Process - Quantising
Quantising is setting the number of digital values that are available, i.e. the bit depth.
As an example, if the bit depth is 8, there are 256 possible values that voltage (from previously) of between 0 and +5 V can be converted to.
Quantising part of the ADC is responsible for the contrast resolution of the image.
ADC Process - Coding
Coding converts the analogue value to the equivalent digital value.
From the example previously, 0 to +5V at 8 bit depth
Each digital step = 5V 256 = 0.01953125V
eg. voltage sampled = 1.4895V is coded at 76.2624. Values must be discrete so the value is rounded down to 76.
The pixel value at that point is 76.
Errors in the ADC Process
Sampling rate (and hence aperture size)Higher the rate, the smaller the pixel size
• truer representation of the object
• larger file size
Low sampling rate leads to errors resulting from under-sampling.
Nyquist's theorem sets minimum sampling rate.
Nyquist's Theorem
Nyquist's theorem is quite simple: it says that we must sample at least twice as as fast as the highest frequency in the signal.
In imaging, the sampling points must be at half of the distance of the size of the smallest object
Under-sampling
Sampling in Images Object Sample
Sample size:-
- & object similar in size
- smaller than object
Sampling Process Image Representation
edge representation of the edge
Errors – Sampling Rate
Under-sampling errors result in aliasing
Aliasing, in a static digital image, appears as a “blocky” image or “steps” along edges within the image.
Aliasing
resulting from
under-sampling
Errors in the ADC Process
Quantisation Error
These result from not having set an adequate bit depth to the ADC process
The greater the number of quantisation values (bit depth) the greater is the accuracy of representation of the analogue information
Quantisation Error
Closely related is the quantisation rounding error.
eg. 8 bit depth vs 4 bit depthpreviously – 8 bit depth 1.4895V is coded at 76.2624
ie. pixel value of 76
4 bit depth - digital step = 5V 16 = 0. 3125V
voltage sampled = 1.4895V 0. 3125V = 4.7764 which is rounded up ie. pixel value of 5
There are error in this rounding process. These are greater the smaller the number of quantisation values.
Quantisation Error
The rounding is greater with a smaller bit depthMax quantisation errors = rounding value x 100
no. of quantisation values
Bit Depth No of Values Max Quantisation Error %
1 2 25.0
4 16 3.125
6 64 0.781
8 256 0.195
10 1024 0.049
4 Bit Depth
2 Bit Depth
8 Bit Depth
Quantisation Error
If the image display contrast has been optimised for the viewing condition, quantisation errors will not appear to the view until the bit depth is below 5 (32 values).
A typical human observer can only perceive approx 30 shades of grey, hence an optimised image at 6 bit depth will appear the same as 10 bit depth image.
Quantisation Error
Given the above, why in medical images do we use bit depths of 10 or 12?
A 10 or 12 bit depth, eg. in CT, will give a more accurate representation of the intensity of the anatomy’s ability to attenuate the beam
Also, how do we know what anatomy we need to have the displayed contrast optimised for view. Do we optimise viewing contrast for, eg. in a CT, the entire slice or for the liver
Basics of Images
Images are representations of “real world” objects
Photo of a friend is a representation of them
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
Basics of Images
All images are 2 dimensional – with the possible exception of holograms.
Can use “tricks” to be perceived as 3D analogue –
• cross – eyed until perceive depth or hidden objects
• coloured lens
digital –• depth perception – shading, perspective
• colour lens
Basics of Digital Images
Digital images are a 2D array of values – often thought of having X and Y axes or row and columns
0 1 2 3 4 4 60 152 120 22 215 34 1 0 1171 3 114 199 134 88 20 60 1992 234 72 65 17 145 185 235 1813 141 214 169 134 85 234 237 684 241 154 141 231 145 236 35 275 45 95 65 127 123 94 47 1666 127 98 137 149 67 45 52 297 162 81 83 189 69 195 94 1718 64 123 130 100 58 226 214 34
102 189 174 35 169 203 243 135213 235 219 137 22 195 168 208227 103 192 243 102 220 187 21
Basics of Digital Images (cont.)
X and Y axes (row & columns) do not have to be of the same length
Each Cartesian point or pixel (picture element) in an image has a value that is an integer and can be described as:
I (x, y)eg I (3,6) = 149 from previous array
In the previous array, X & Y axes started at 0, but in some image formats, start at 1.
Basics of Digital Images (cont.)
Maximum value of I (x, y) will depend upon the bit depth and equal 2n – 1, where n is the bit depth eg. in 8 bit depth image, integer values range
from 0 to 255
This is often referred to as the depth of the image.
Intensity map of pixel values. Note: max value <= 255
can use this mapping to visualise contour boundaries
Note: the flat area of zeros represent black in the image
Basics of Digital Images (cont.)
The previous array or image was a grey scale image.
It had intensities ranging from 0 to 255, which when converted to analogue for humans to perceive, will give a variation of intensities, normally viewed from white (255) to black (0). Could be from a colour to no colour (black)
Basics of Digital Images (cont.)
Concept of digital images to display
digital image inside monitor
(not visible) 3 x colour guns (R,G, B)
R – intensity of 128
G – intensity of 128
B – intensity of 128
display on monitor
R OUTPUT
Gshade of grey
B (value of 128)
128Pixel Value
I (x,y)
O (x,y)
Basics of Colour Digital Images
Colour images are the equivalent of 3 grey scale images
Each array represents the values for red, green and blue
Red Green Blue0 1 2 3
0 186 186 72 1351 119 16 97 602 202 108 2 823 153 157 113 1644 203 174 242 995 252 244 135 1566 222 135 64 2427 101 35 91 91
0 1 2 30 247 123 27 2471 100 120 113 2102 202 124 105 823 104 157 169 2034 67 70 142 555 17 31 173 1686 53 44 160 1847 46 232 10 59
0 1 2 30 22 181 164 1231 203 240 31 1442 140 2 42 2453 89 139 204 274 2 154 185 1255 33 46 165 306 129 106 43 1357 60 91 74 99
Basics of Colour Digital Images
The notation isIc (x, y) where Ic is the colour
Each colour array is often referred to as a bandThe visible displayed colour is a mix (additive) of the 3 colour values
eg blue (0, 0, 255)
Possible no. of colours – 16,777,216
Basics of Colour Digital Images (cont.)
Concept of colour digital images to display
digital image inside monitor 3 x colour arrays (not visible) 3 x colour guns
(R,G, B)R – intensity =
109G – intensity =
249B – intensity = 65
display on monitorR OUTPUTG hue of additiveB colour
R = 109G = 249B = 65
Pixel Value
I (x,y)
red, green & blue colour bands
image – mix of the 3 bands
Digital Image Files
Image are stored as a specific file format, eg as jpeg (jpg), gif, tiff, targa (tga - which is used in Imaging Concepts), etc.
Medical images are now using a format called DICOM
The image file itself contains 2 separate areas
image data
header
Digital Image Files (cont.)
Header stores information about the type of format (see later)
the number of rows and columns
colour or grey scale
the location in the first pixel value
in the DICOM format for medical imaging – includes:- imaging modality, patient details inc. space for report and reasons for the test.
Digital Image Files (cont.)
Image file size is determined by both the image data and the header size.Image data size is determined by the number of rows x columns x bit depth (in bytes)eg. 1000 rows and columns 1000 x 1000 x 8 bit depth (1 byte) = 1 MB 1000 x 1000 x 10 (or 12) bit (2 bytes) = 2 MBColour image (3 bands) 1000 x 1000 x 8 bit (1 byte) = 3 MB
The file size must then add in the size of the header (in bytes)
Image files can become very large so means of making them smaller in size is commonly used. This is called compression. (This will discussed in detail later)
Other colour image formats
To save storage space, some other colour file formats have been developed.
Colour palettes are used to replace the 3 separate bands in a “normal” colour image
The palette is a separate list of colour values, RGB values (intensities), that are used in that image.
The I (x,y) value “looks up” the value of a colour in the palette.
Only the colours used in the image have values in the palette eg. if the image has 3 colours, the palette will only have 3 rows.
Even if a large number of colours are used, storage space is less than the format that uses 3 band of colours
0 1 2 3 4 Red Green Blue0 1 6 19 31 13 1 12 56 2001 20 30 22 14 7 2 44 67 1642 13 27 1 17 3 3 100 15 1633 28 25 35 27 34 4 35 156 2074 27 19 17 34 11 5 65 51 355 25 1 29 29 4 6 0 0 255 - Blue6 10 11 28 10 18
Image Palette
Grey / Colour Manipulation
The pixel values, I (x,y), in the image are stored on the hard drive of the computer and do not change. This is the store image, Is (x,y)
The viewed grey scale and colour can be changed – as seen on the monitor
This is achieved through the use of “look-up tables” (LUT)
Is (x,y) is compared to a displayed value,
Id (x,y), which is used to the display intensity.
Look-Up Tables
A means of altering the value of the stored pixel, so it can be displayed as a different value ie. a different displayed intensity.
All the potential pixel values, in an 8 bit depth image – 256 values, are put on one side of the table
Any mathematical calculation to alter the output values is then applied to give output values
These values are put on the other side of the table
The display “looks up” the pixel value and then finds the corresponding output value
Input Operation OutputValue Value
0 x 1.5 01 x 1.5 22 x 1.5 33 x 1.5 54 x 1.5 65 x 1.5 86 x 1.5 97 x 1.5 118 x 1.5 129 x 1.5 1410 x 1.5 1511 x 1.5 1712 x 1.5 18
250 x 1.5 255251 x 1.5 255252 x 1.5 255253 x 1.5 255254 x 1.5 255255 x 1.5 255
0
50
100
150
200
250
0 50 100 150 200 250
Stored Image
Dis
pla
yed
Imag
e
Look-Up Table
Operations:- x 1.5 calculation x 1 calculation
Graphical display
Grey scale display
Grey scale images have one band (channel) of pixel values – uses 1 LUT
The output value from the LUT goes to the 3 colour (RGB) guns in the monitor
As the intensities of the RGB colour guns are equal, a grey (white black) colour will be perceived on the monitor
Displayed greys can be manipulated by altering the operation of the LUT
Grey scale display
4Pixel Value
Stored Image Is(x, y)Look-up Table
0 101 112 123 134 14
254 255255 255
colour guns - monitor
R
G
B
14
displayed value
Displayed grey
intensity
14
Displayed Image Id(x, y)
Colour displayColour images have 3 bands (channels) of pixel values and uses 3 LUT’s – 1 for each band3 pixel values form each band, same x,y coordinates, are the input values for each RGB LUT.The output value from the LUT’s goes to the corresponding colour (RGB) guns in the monitorThe values of the intensities of the RGB colour guns will often not be equal, hence a colour (rather than grey) will be perceived on the monitorDisplayed colours can be manipulated by altering the LUT’s of each band.
Colour displayStored Image Is(x, y) Look-up Table
0 101 112 123 134 14
254 255255 255
colour guns - monitor
R
G
B
displayed colour
R = 109G = 249B = 65
Look-up Table0 101 112 123 134 14
254 255255 255
Look-up Table0 101 112 123 134 14
254 255255 255
Red Green Blue
to display
R = 119
G = 255
B = 75
displayed RGB
values
Displayed Image Id(x, y)
Look-up Table0 101 112 123 134 14
254 255255 255
Look-up Table0 101 112 123 134 14
254 255255 255
Look-up Table0 101 112 123 134 14
254 255255 255
0
50
100
150
200
250
0 50 100 150 200 250
Stored Image
Dis
pla
yed
Imag
e
0
50
100
150
200
250
0 50 100 150 200 250
Stored Image
Dis
pla
yed
Imag
e
0
50
100
150
200
250
0 50 100 150 200 250
Stored Image
Dis
pla
yed
Imag
e
Red Green Blue
RedGreen
Blue
Actual Look-Up Table
Graphical display of the
Look-Up Table
Psuedo-colour display
Pseudo-colour images have one band (channel) of pixel values but use 3 LUT’sThe output value from the LUT’s goes to the corresponding colour (RGB) guns in the monitorThe values of the intensities of the RGB colour guns will often not be equal, hence a colour will be perceived on the monitorDisplayed colours can be manipulated by altering the LUT’s of each band.
0 01 12 23 34 4
254 254255 255
Look Up Table0 01 22 43 64 8
254 2255 0
Look Up Table0 2551 2542 2533 2524 251
254 1255 0
Look Up Table
Red Green Blue
4
Stored Image Is(x, y)
Psuedo-colour display
colour guns - monitor
R
G
B
displayed colour
R = 4
G = 8
B = 251
displayed RGB
values
Displayed Image Id(x, y)
0
50
100
150
200
250
0 50 100 150 200 250
Stored Image
Dis
pla
yed
Imag
e
0 01 12 23 34 4
254 254255 255
Look Up Table0 01 22 43 64 8
254 2255 0
Look Up Table0 2551 2542 2533 2524 251
254 1255 0
Look Up Table
Red Green Blue
Actual Look-Up Tables
Graphical display of the
3 Look-Up Tables
Plot of LUT - Red
Plot of LUT - Green
Plot of LUT - Blue