Download Digital Computers

Why would cause
the image to look
this way?
Small matrix
Zoomed to excess
Spatial Resolution
By definition: The ability of imaging equipment to demonstrate
two objects as two objects
Which demonstrates better spatial resolution?
1 mm
1 cm
=1
lp/mm
of spatial
resolution
=8
lp/cm
of spatial
resolution
MR spatial resolution tops out at 1 lp/mm,
or 2 lp/mm for surface coils
Which image has the best spatial resolution? 10 cm: Prove it
If the monitor is 500 pixels across, how many lp/mm are resolved
by each image?
500 pixels/250 mm = 2 2 what? 2 pixels/mm or 1 lp/mm
pixel size
250 mm/500 mm = .5 .5 is what?
25 cm FOV
10 cm FOV
500 pixels/100 mm = 5 pixels/mm or 2.5 lp/mm
100 mm/500 mm = .2 mm pixels
If there were 1000
pixels, how would
resolution change?
Dynamic range is to digital, what gray scale is
______________
is analog x-ray images
What are CT numbers based on, and
what number is it given? Water, 0
What is the range of CT numbers +1000 to -1000
What is another name
for CT numbers?
(after the inventor)
Hounsfield units
Windows
What is the name of the function
that controls the range of displayed
pixel values?
For example: A window
width of 5
______
Window width describes
the range of pixel values
Windows
What is (are) the name(s) of the
function that sets the middle of
the range of any given window width
+7
0
-7
1
2
3
4
5
For example: This window
center level
width of 5 has a ______or_____
of 2
Three common window settings. What are they called?
Soft tissue window
Bone window
Lung window
How Digital Computers Work
History of computational devices
Bits
Bytes
Pixels
Matrix
Dynamic range
Machine language
Processors (8,10,12 bits etc.)
Base 10 numbering
Binary numbering system
Hounsfield units (CT numbers)
Pascal’s calculator - 1642
A mechanical
device, not
programmable
A series of gears, turned by hand, rotated a wheel with numbers
that showed in a window. When the number in the ones column
reached nine, it turned the wheel in the tens column to 1, and
the ones column returned to zero.
Pascal invented his device to relieve the fatigue of spirit
associated with the work of doing arithmetic.
Jacquard’s Loom - 1804
Instructions for weaving
patterns into cloth were fed
into Jacquard’s machine
by this early version of
punched cards that were
made of wood.
The red arrows show the
cards entering and leaving
the machine.
A mechanical device,
that was programmable
Babbage’s Difference Engine - 1822
A crank was turned to perform a mechanical progression
of numbered gears in columns that, like Pascal’s calculator,
represented increasing powers of ten.
Hollerith’s tabulator
In 1880 it took 9 years to tally
the results of the US census.
Herman Hollerith built an
electromechanical calculator
that used punched cards to
input data on the population
(age, gender, numbers in
family, etc), and reduced the
time to do it in half, on a
greater population, with a
more detailed analysis.
Like Pacal’s calculator, and Babbage’s difference engine numbers
were carried over from one column to the next. The great advantage
of this device was the use of electric motors to drive mechanical
parts, and punched cards to input data.
Mark I - 1944
An electromechanical
device, that was
programmable.
Banks of mechanical switches where driven by electric motors.
Switches opened and closed to perform computations.
Punched cards were used to input data.
ENIAC - 1946
“Computers of the
future may weigh no
more than 1.5 tons.”
Popular Science, 1949
The first fully electronic calculator used 18,000 vacuum tubes
that replaced the switches of Mark I. Data was
accomplished by turning knobs, reconfiguring telephone
patch cords, and punched cards.
Vacuum Tubes and Transistors
Vacuum tube: When the grid is positively
charged electrons are drawn from the cathode
to the anode, creating a closed circuit (1).
When the grid is negatively charged electrons
are repelled, and circuit is open (0).
Grid
Cathode
Transistors: Similar in principle to the
Anode
operation of a vacuum tube. The solid
state semi-conducting material allowed
this switching device to use less energy
and produce less heat in a smaller
component.
Generations of Electronic Computers
1st
Vacuum tube
2nd Transistors
3rd Integrated Circuit (IC)
Three Things a Computer Does
1. Arithmetic functions
2. Comparison functions
3. Memory
Accomplished with accuracy and speed
What is Digital Imaging?
Digital Imaging is the transforming of energy:
(from light photon, sonic, magnetic, x-ray, or
gamma radiation sources) to electrical signals
that are measured and assigned discrete binary
values.
Binary data is processed into image information
which may be displayed on a monitor, enhanced,
printed, and stored as a computer file.
What is the name of the first electronic computer and when was
it completed?
At what point in the acquisition of image data does digital
imaging and analog imaging differ
What switching devices were used in the first three generations of
electronic computers?
Define digital. How is it different from analog?
What is the name of the memory (registers of switching elements)
that is being used when a program is being run?
How is RAM different than secondary memory?
Step 1. Send the energy on its way
Step 2. Capture the remnant energy in an IR or digital detector
Step 3. Sample the captured energy and transform it to
electrical signals
Step 4. Assign the signals discrete values in an Analog to Digital
Converter (ADC)
Step 5. Use those values to set the registers in RAM (On/OFF)
Step 6. Display the image on a monitor
Step 7. Save the image on a secondary storage device
Random access memory (RAM) (345): Semiconductor switches in microchips have
addresses: locations which may be accessed directly (randomly): a quick, electronic
process. When a program (such as word processing) is loaded from a secondary storage
device (such as a hard drive) it is copied into a RAM chip. As changes are made they are
made in RAM. The program must be saved back to the hard drive to be retained. RAM
is also called volatile memory, which means that when power is turned off data in RAM
is lost.
Read only memory (ROM) (345): Memory that can only be read (used)
and not written to (changed).
Arithmetic Functions
Integrated circuits (IC) have millions, billions, and trillions of AND,
OR, and NOT gates embedded in the layers of the miniaturized
circuits of the semi-conductor material.
The next seven slides demonstrate:
Step 5. Use those values to set the registers in RAM (On/OFF)
The Basics of Digital Data Storage in
Random Access Memory (RAM)
OFF
In this analogy the light bulb is a
pixel on a monitor
The switch is a bit (binary digit)
in the computer circuitry
The Basics of Digital Imaging
ON
Flip the switch (binary digit or bit) and light up
the bulb (pixel)
Row and columns of pixels
form the matrix
Dynamic range of 2
(21)
How is contrast added to
an image?
Switches.
The more of them in the
ON position, the brighter
the light
ON
OFF
.01V
A difference of .01 V is detectable
in the MR signal
ON
ON
.01V .02V
A difference of .01 V is detectable
in the MR signal
Dynamic range of 256 (28)
4
0
.1V
.2V
.3V
2
1
.4V
OFF
OFF
OFF
OFF
OFF
OFF
ON
ON
OFF
ON
OFF
ON
.5V
.6V
ON
ON
ON
OFF
OFF
ON
OFF
ON
OFF
More bits, in various configurations,
create a greater dynamic range
(analogous to the radiographic scale
of contrast)
ON
ON
ON
OFF
OFF
OFF
OFF
In computer circuitry 8 bits are
grouped together
8 bits = 1 byte
OFF
ON
ON
ON
ON
ON
ON
ON
ON
An 8 bit processor displays a dynamic range of 256 (28)
The maximum required voltage is only 2.55 V
The two positions a switch can be in are numbered: 0 = OFF
1 = On
10011011
11101001
00010111
01011001
OFF
0
Machine language computer code
ON
ON
1
1
OFF
0
OFF
0
ON
1
ON
1
ON
1
The language of computers is binary (two numbers)
Bits are either ON (1) or OFF (0)
Human beans count in decimals (base 10)
because
They have 10 fingers and 10 toes
4
10 10 3 10 2 10 1 10 0
Ten is raised to every power
of itself to create columns
of higher orders
Binary numbering
4
3
2
1
0
2 2 2 2 2
By definition: Any number raised to the power of 0 is 1
Any number raised to the power of 1 is the number itself
* Count from right to left
* Each column is twice the previous
* Pick any column and it will be one more than the sum of all the previous columns
Binary numbering system (344): In the
base 2 numbering system all values are
represented by 0 or 1. Zero = OFF when
representing an open switch. One = ON.
Columns are
derived from:
Columns:
Binary numbering
2
4
3
2
1
0
2 2 2 2
256 128 64 32 16 8 4 2 1
Examples:
0
0
0
0
1
1 1
0
0
1
1 1 1 0 = 14
1 0 1 0 = 42
1 1 1 1 = 127
An 8 bit processor displays a dynamic range of 256
8
2
= one byte = 256 shades of gray
256 128 64 32 16 8 4 2 1
1
1
1
1
1
1
1
1 = 255
0
0
0
0
0
0
0
0=0
When all the bits are ON a pixel is illuminated to max intensity
There are 255 possibilities of bits being ON.
When all the bits are OFF the pixel is black.
8 bits store a dynamic range of 256 from dark to bright.
An 8 bit processor displays a dynamic range of 256
What will a 9 bit processor display?
512 shades of gray
10 bit? 1024
11 bits 2048
12 bit? 4096
13 bits 8192
14
16384
15 bits 22768
16 bit? 44536
What effect does increasing the dynamic range have?
It increases the memory requirements dramatically!
10011011
11101001
00010111
01011001
OFF
0
ON
ON
1
1
OFF
0
OFF
0
32 16
A byte of memory in this midsagittal MRI of the head
defines how brightly one pixel will be illuminated.
ON
ON
ON
1
1
0
4
2
1
= 55
.
George Boole
1815-1864
AND Gate
Off
+
Off = Off
On
+
Off = Off
On
+
On = On
OR Gate
Off
+
Off = Off
On
On
+
+
Off = On
On = On
NOT Gate
Off = On
On = Off
Operation of a Half Adder
1
+
0
0
1
=1
Operation of a Half Adder
0
+
1
0
1
=1
Operation of a Half Adder
1
+
1
1
0
=2
Operation of a Half Adder
0
+
0
0
0
=0
RAM: addressable memory
in an array of ICs
Welcome to RAM
Population: 376,243,101,765
RAM (Random Access Memory)
Altair’s 256 bytes of internal
memory could hardly store
a memo, so in 1979
George Morrow created a
memory board to extend it.
Here he demonstrates how
8K of RAM is concealed
in a trench coat.
In the early years of computing, memory was so precious years
were entered without the century prefix (79 instead of 1979) to
save two bytes. That led to the scare known as Y2K.
Question: What is the unit of measurement
of frequency?
Clue: It is also called cycles per second.
Answer: hertz
Examples:
Kilohertz Thousands of
Megahertz Millions of
Gigahertz Billions of
Terahertz Trillions of
The same prefixes apply
to bytes