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Cursul II
• Notiuni Curs I
• Semnale si sisteme
• Reprezentarea imaginii
• Caracteristicile si factorii calitativi ai imaginilor medicale
University Politehnica of Bucharest 1
Cursul II
• Notiuni Curs I
• Semnale si sisteme
• Reprezentarea imaginii
• Caracteristicile si factorii calitativi ai imaginilor medicale
University Politehnica of Bucharest 2
What is Medical Imaging?
• Using an instrument to see the inside of a human body
• Non-invasive
• Some with exposure to small amount of radiation (X-ray, CT and nuclear medicine)
• Some w/o ( ultrasound)
• The properties imaged vary depend on the imaging modality
• – X-ray ( projection or CT): attenuation coefficient to X-ray
• – Nuclear medicine (PET, SPECT): distribution of introduced radio source
• – Ultrasound: sound reflectivity
• – MRI: hydrogen proton density, spin relaxation
Projection vs. Tomography
• Projection:
• A single image is created
for a 3D body, which is a
“shadow” of the body in a
particular direction
(integration through the
body)
Projection vs. Tomography• Tomography
• A series of images are generated, one from each slice of a 3D object in a particular direction (axial coronal sagital)
• To form image of each slice, projections along different directions are
• first obtained, images are then reconstructed from projections (back-projection, Radon transform)
Anatomical vs. Functional Imaging• Some modalities are very good at depicting anatomical structure (bone, different tissue types,
boundary between different organs)
• – X-ray, X-ray CT
• – MRI
• Some modalities do not depict anatomical structures well, but reflect the functional
• status (blood flow, oxygenation, etc.)
• – Ultrasound
• – PET, functional MRI
• Boundaries between the two classes are blurring as the imaging resolution continues to improve
Common Imaging Modalities
• Projection radiography (X-ray)
• Computed Tomography (CT scan or CAT Scan)
• Nuclear Medicine (SPECT, PET)
• Ultrasound imaging
• MRI
• Optical imaging
Spectrul electromagnetic
The electromagnetic spectrum comparing the size of objects that can be studied with various
techniques.
Waves Used by Different Modalities
Lesson II
• Notiuni Curs I
• Semnale si sisteme
• Reprezentarea imaginii
• Caracteristicile si factorii calitativi ai imaginilor medicale
University Politehnica of Bucharest 10
Semnale si sisteme
The object being imaged is an input signal
– Typically a 3D signal
• The imaging system is a transformation of the input signal to an
output signal
• The data measured is an output signal
– A 2D signal (an image, e.g. an X-ray) or a series of 2D signals
(e.g. measured projections from a CT scan), or 4D data (a series of 3D
volume in time)
• Image reconstruction
– An inverse process: from the measured output signal -> desired
images of the object (a series of 2D slices)
INPUT SIGNAL -> SYSTEM or PROCESS -> OUTPUT SIGNAL
Input signal: µ(x; y) is the linear attenuation coefficient
for x-rays of a body component along a line
• Imaging Process: integration over x variable:
Output signal: g(y)
Example: Projection X-Ray
Exemple de semnale
Transformarile semnalelor
Sisteme liniare -Proprietati
Sisteme liniare invariante la translatie -
SLIT
Sisteme liniare invariante la translatie - SLI
Transformata Fourier: cazul 1D
Transformata Fourier: cazul 2D
Frecventa spatiala
• Astfel, transformata Fourier a unei imagini este o reprezentare in domeniul frecventei.
• Multe prelucrari de imagine presupun eliminarea din imagine a componentelor de o anumita frecventa, de exemplu cele de nivel coborat sau cele de nivel inalt.
• Aceste operatii sunt usor de realizat pe transformata Fourier a imaginii.
• O prelucrare de imagine bazata pe transformata Fourier are loc in trei pasi:
•• Se calculeaza transformata Fourier a imaginii
• Se proceseaza reprezentarea in domeniul Fourier
• Se calculeaza transformata Fourier inversa, obtinandu-se imaginea prelucrata
Transformata Fourier: cazul 2D
Fourier: Exemple
Fourier: Exemple
Proprietatea de convolutie si raspunsul in
domeniul frecventa
• A more complicated 2-D Fourier spectrum is obtained when a chest radiograph is transformed to the spatial frequency domain as illustrated in the next figure. The transformed data show a broad range of spatial frequencies, with significant vertical and horizontal features, as might be expected from the horizontal ribs and vertical vertebral column displayed in the radiograph.
Fourier - Aplicatii
A chest radiograph is illustrated in (a) with its 2-D Fourier spectrum in (b). The spatial
frequency data show a broad range of values with significant vertical and horizontal
features associated with the vertebral column and ribs, respectively.
• A potential use of the FT and its inverse is the removal of unwanted or corrupt data from a digital image and this process is illustrated in the final figure below.
• An extreme example of a corrupt image may be generated by adding together the two images.
• The Fourier spectrum in panel (b) portrays the frequency characteristics of the summed image.
• The undesirable features attributable to the sinusoidal pattern may be removed by editing of the data in the frequency domain as in panel (c), before the inverse FT is performed to recover an image largely free of artifact, as in panel (d).
Fourier - Aplicatii
• The use of the FT and its inverse to remove unwarranted information from an image.
• (a) An image obtained by adding the sine wave and chest radiography images together with its equivalent Fourier spectrum in (b). The unwanted interference caused by the sinusoidal brightness pattern can be removed by editing the spatial frequency information as shown by the blackened areas in (c).
• The inverse FT then recovers the original chest image largely undistorted as shown in (d). Further refinement of the editing process would ideally allow complete restoration of the image quality.
Fourier – Aplicatii: eliminare zgomot
Fourier – Aplicatii: filtrare in domeniul
frecventa
Lesson III
• Notiuni Curs I
• Semnale si sisteme
• Reprezentarea imaginii
• Caracteristicile si factorii calitativi ai imaginilor medicale
University Politehnica of Bucharest 30
Reprezentarea imaginii
• semnal bidimensional in spatiul continuu= definit ca o functie de 2 variabile in spatiu continuu: f(x,y)
• f(x,y) = interpretata ca o functie de luminanta variabila in spatiul bidimensional (x,y)-> r(x,y)
• => d.p.d.v. al notatiei f(x,y) = functie definita in domeniu spatial
• Teoretic -> modelul imaginii intr-un spatiu continuu nelimitat-> un plan bidimensional, dar abordarea folosita inpractica -> dimensiunea imaginii este intotdeauna limitata la un spatiu finit (dreptunghi)
University Politehnica of Bucharest 31
Reprezentari diferite ale unui semnal
bidimensional
University Politehnica of Bucharest 32
Grayscale image Surface representation
profiles along indicated horizontal, vertical, and diagonal lines
• Imagistica Medicala -> rezultatul majoritatii tehnicilor de
obtinere ale imaginilor medicale -> imagini cu nivele de gri
• Culoarea = subliniaza contrastul in imagini cu nivele de gri
(afisarea in Matlab a unei radiografii cu functia imagesc) -
explicatia
• O imagine color = reprezentata printr-o functie vector:
University Politehnica of Bucharest 33
Informatia de culoare in reprezentarea
unei imagini
TBGR yxfyxfyxfyxf )],(),,(),,([),( =
• Images must be digitized
• Analog continuous –space continuous-value -> 2D
image => discretization of 2 kinds:
– Spatial sampling
– Amplitude quantizing analog function = matrix of
numbers
University Politehnica of Bucharest 34
Image Representation: Digitization &
Sampling
• ideal spatial sampling =
the analogue image a 2-D sampling signal s(x,y) (formed
of an infinite number of periodically repeated Dirac impulses)
University Politehnica of Bucharest 35
Spatial sampling
∑ ∑∞
−∞=
∞
−∞=
∆−∆−=i k
yiyxkxyxs ),(),( δ
The sampled image =
analogue image (“to be sampled” image) the sampling
function:
∑ ∑∞
−∞=
∞
−∞=
∆−∆−∆∆=
∗=
i k
s
yiyxkxyixkf
yxsyxfyxf
),(),(
),(),(),(
δ
• only those discrete values of the analogue image are
needed that correspond to the nodes of the sampling grid:
•
University Politehnica of Bucharest 36
Spatial sampling
• The information carried
by the intermediate image
values is lost
• so that the image matrix
= the complete image
content
),( yixkff ∆∆=
Sampling
• Sampling = choosing which points you want to have represent a given image;
• analog image -> sampling = a mapping from a continuum of points in space to a discrete set
• digital image -> sampling = a mapping from one discrete set of points to another (smaller) set
University Politehnica of Bucharest 37
Spatial sampling = Example
• a pixel is a point…
• It is NOT a box, disc or teeny wee light
• It has no dimension
• It occupies no area
• It can have a coordinate
• More than a point, it is a SAMPLE
University Politehnica of Bucharest 38
University Politehnica of Bucharest 39
Spatial sampling = Example
(Thomas Funkhouser course slides)
http://www.cs.brown.edu/exploratories/freeS
oftware/repository/edu/brown/cs/exploratori
es/applets/sampling/introduction_to_samplin
g_guide.html
University Politehnica of Bucharest 40
(Thomas Funkhouser course slides)
Sampling and Reconstruction
(Thomas Funkhouser course slides)
University Politehnica of Bucharest 41
Example: Adjusting Brightness(Thomas Funkhouser course slides)
University Politehnica of Bucharest 42
Digitization
• the representation of an object, image, sound, document or
a signal (usually an analog signal) by a discrete set of its points or samples
• The result:
– digital representation or digital image, for the object,
– digital form for the signal
• To obtain numbers tractable by computers, the sample values obtained by
sampling are consequently digitized by an analogue to- digital (A/D)
converter.
• The finite code: only limited-precision numbers => the measured values
rounded to the nearest of the available levels ( 256, 4096, or 65,536 levels
corresponding to 8-, 12-, or 16-bit fixed point)University Politehnica of Bucharest 43
As any natural image has limited dimensions, the result of
digitization is a finite set of numbers representing the sample
values — picture elements, pixels*, that may be arranged into a
matrix.
Contemporary systems use matrices of sizes approximately
in the range between ∼0.3 and (rather rarely) ∼16 Mpixels (Mpx),
corresponding to square matrices of 512 × 512 to 4096 × 4096;
however, many systems use the rectangular (nonsquare) format.
This image size, together with the bit depth, determines the memory
requirements (unless data compression is used): e.g., a 5-Mpx 16-bit
gray-scale image requires 10 Mbytes of memory space, and a color
image three times as much.University Politehnica of Bucharest 44
Digitization
Cursul IV
Cuprins
• Caracteristicile si factorii calitativi in imaginile
medicale:
– calitatea imaginii,
– contrastul imaginii,
– Sensibilitate la contrast,
– Functia de transfer a modulatiei
– Contrastul local
– Factorul incetosare - blur si vizibilitatea detaliului,
– zgomot, artefact, distorsiune,
– compromisuri,
– Caracteristicile tesutului
Characteristics and quality factors in
medical images• the internal structures and functions of the human body are not generally
visible
• images = created through which the medical professional -> into the body
to diagnose abnormal conditions & guide therapeutic procedures
• The medical image is a window to the body
• No image window reveals everything
• Different medical imaging methods reveal different characteristics of the
human body
• the range of image quality and structure visibility -> depending on
characteristics of the imaging equipment, skill of the operator, and
compromises with factors such as patient radiation exposure and imaging
time.University Politehnica of Bucharest 47
Characteristics and quality factors in
medical images
Components Associated with the Medical Imaging Process
48University Politehnica of Bucharest
The figure is an overview
of the medical imaging
process.
The five major
components are:
• the patient,
• the imaging system,
• the system operator,
• the image itself, and
• the observer.
• The objective = make an object within the patient's body visible to the observer.
• The visibility: depends on the characteristics of the imaging system and the
manner in which it is operated.
• Most medical imaging systems have a number of variables that must be
selected by the operator
• They can be changeable system components, such as intensifying screens in
radiography, transducers in sonography, or coils in magnetic resonance imaging
(MRI).
• most variables are adjustable physical quantities associated with the imaging
process: kilovoltage (radiography), gain (sonography), and echo time (TE) (MRI)
• The values selected -> determine the quality of the image and the visibility of
specific body features. University Politehnica of Bucharest 49
Characteristics and quality factors in
medical images
IMAGE QUALITY
Medical Imaging is the Process of Converting Tissue Characteristics into a
Visual Image
50University Politehnica of Bucharest
The task of every imaging system is to translate a specific tissue characteristic into image
shades of gray or color.
If contrast is adequate, the object will be visible.
The degree of contrast in the image depends on characteristics of both the object and the
imaging system.
IMAGE QUALITY• The quality of a medical image: the imaging method, the
characteristics of the equipment, and the imaging variables selected
by the operator
• Image quality = a composite of at least five factors: contrast, blur,
noise, artifacts, and distortion.
• The human body contains many structures and objects that are
simultaneously imaged by most imaging methods.
• We often consider a single object in relation to its immediate
background
• The visibility of an object is determined by this relationship rather
than by the overall characteristics of the total image.University Politehnica of Bucharest 51
University Politehnica of Bucharest 52
Image ContrastContrast means difference.
In an image, contrast can be in the form of different shades of gray,
light intensities, or colors.
Contrast is the most fundamental characteristic of an image.
An object within the body will be visible in an image only if it has
sufficient physical contrast relative to surrounding tissue.
• The physical contrast of an object must represent a difference in
one or more tissue characteristics.
• For example, in radiography, objects can be imaged relative to their
surrounding tissue if there is an adequate difference in either
density or atomic number and if the object is sufficiently thick.
Image Contrast
When a value is assigned to contrast, it refers to the difference
between two specific points or areas in an image.
In most cases we are interested in the contrast between a specific
structure or object in the image and the area around it or its
background.
The degree of physical object contrast required for an object to be
visible in an image depends on the imaging method and the
characteristics of the imaging system.
Image Contrast
Increasing Contrast Sensitivity Increases Image
Contrast and the Visibility of Objects in the Body
55University Politehnica of Bucharest
The primary characteristic of an
imaging system that establishes the
relationship between image contrast
and object contrast is its contrast
sensitivity.
Consider the situation shown below.
The circular objects are the same size
but are filled with different
concentrations of iodine contrast
medium.
That is, they have different levels of
object contrast. When the imaging
system has a relatively low contrast
sensitivity, only objects with a high
concentration of iodine (ie, high
object contrast) will be visible in the
image.
If the imaging system has a high
contrast sensitivity, the lower-contrast
objects will also be visible.
Contrast Sensitivity• contrast sensitivity = a characteristic of the imaging method and the
variables of the particular imaging system
• It relates to the system's ability to translate physical object contrast into image contrast.
• It is difficult to compare the contrast sensitivity of various imaging methods because many are based on different tissue characteristics.
• certain methods do have higher contrast sensitivity than others.
• Exemplu
• (CT) generally has a higher contrast sensitivity than conventional radiography
• This is demonstrated by the ability of CT to image soft tissue objects (masses) that cannot be imaged with radiography.
University Politehnica of Bucharest 56
Contrast Sensitivity
Effect of Contrast Sensitivity on Object Visibility
57University Politehnica of Bucharest
Consider the image:
Here is a series of objects with
different degrees of physical
contrast. They could be vessels
filled with different concentrations
of contrast medium. The highest
concentration (and contrast) is at
the bottom. Now imagine a
curtain coming down from the top
and covering some of the objects
so that they are no longer visible.
Contrast sensitivity is the
characteristic of the imaging
system that raises and lowers the
curtain. Increasing sensitivity
raises the curtain and allows us to
see more objects in the body. A
system with low contrast
sensitivity allows us to visualize
only objects with relatively high
inherent physical contrast.
Functia de transfer a modulatiei - MTF
Functia de transfer a modulatiei - MTF
Cursul V
Functia de transfer a modulatiei - MTF
Functia de transfer a modulatiei - MTF
Blur and Visibility of Detail• Structures and objects: vary in physical contrast and in size
• Objects: from large organs and bones to small structural features (small calcifications).
• Each imaging method has a limit as to the smallest object that can be imaged and thus on visibility of detail.
• Visibility of detail is limited: all imaging methods introduce blurring into the process
• The primary effect of image blur is to reduce the contrast and visibility of small objects or detail.
University Politehnica of Bucharest 63
Blur and Visibility of Detail
Effect of Blur on Visibility of Image Detail
64University Politehnica of Bucharest
Consider the image below, which
represents the various objects in the
body in terms of both physical
contrast and size.
As we said, the boundary between
visible and invisible objects is
determined by the contrast
sensitivity of the imaging system.
We now extend the idea of our
curtain to include the effect of blur. It
has little effect on the visibility of
large objects but it reduces the
contrast and visibility of small
objects.
When blur is present, and it always
is, our curtain of invisibility covers
small objects and image detail.
Noise• Another characteristic of all medical
images is image noise.
• Image noise, sometimes referred to as
image mottle, gives an image a
textured or grainy appearance.
• The source and amount of image noise
depend on the imaging method.
University Politehnica of Bucharest 65
Noise
Effect of Noise on Object Visibility
67University Politehnica of Bucharest
In the image below we find our
familiar array of body objects
arranged according to physical
contrast and size.
We now add a third factor, noise,
which will affect the boundary
between visible and invisible
objects.
The general effect of increasing
image noise is to lower the curtain
and reduce object visibility.
In most medical imaging situations
the effect of noise is most
significant on the low-contrast
objects that are already close to
the visibility threshold.
Cursul 6
Artifacts, Distortion
• most imaging methods can create image features that do not
represent a body structure or object
• an artifact does not significantly affect object visibility and diagnostic
accuracy.
• But artifacts can obscure a part of an image or may be interpreted as
an anatomical feature.
• Distortion: A medical image should not only make internal body
objects visible, but should give an accurate impression of their size,
shape, and relative positions.
University Politehnica of Bucharest 70
Artifacts
Artifacts: image features that do not correspond to a real object, and are not due
to noise
– artefactul de miscare: blurring or streaks due to patient motion
– artefactul in forma de stea – star artifact: in CT, due to presence of metallic
material in a patient
– artefactul dat de cresterea in intensitate a fascicolului: broad dark bands or
streaks, due to significant beam attenuation caused by certain materials
– artefactul in forma de inel: because detectors are out of calibration
Artifacts, Distortion
Rezolutie sistemului: abilitatea de a separa doua puncte.
Marimea FWHM este egala cu minimul distantei pe care ar trebui sa o aiba cele
doua puncte pentru a percepute separat ca 2 puncte
Meniul Rezolutie – Resolution Tool
Acuratetea
• Acuratetea cantitativa
• Acuratetea diagnosticului
• Sensibilitate
• Specificitate
Tabelul de contingenţă "2x2":
Boala vizată
Total
Prezentă Absentă
Rezultatul
testului
screening
Pozitiv a b a+b
Negativ c d c+d
Total a+c b+d a+b+c+d
Boala vizată
Total
Prezentă Absentă
Rezultatul
testului
screening
Pozitiv a b a+b
Negativ c d c+d
Total a+c b+d a+b+c+d
100×+
=ca
aateaSensibilit
100×+
=db
dateaSpecificit
Compromises
• why we do not adjust each imaging procedure to yield maximum visibility?
• the variables that affect image quality also affect factors such as radiation exposure to the patient and imaging time.
• In general, an imaging procedure should be set up to produce adequate image quality and visibility without excessive patient exposure or imaging time.
• In many situations, if a variable is changed to improve one characteristic of image quality, such as noise, it often adversely affects another characteristic, such as blur and visibility of detail.
University Politehnica of Bucharest 84
TISSUE CHARACTERISTICS AND IMAGE
VIEWS• A combination of two factors makes each imaging method unique.
• These are the tissue characteristics that are visible in the image and
the viewing perspective.
• The specific tissue characteristics vary among the various modalities
and methods.
• A radiologist search for signs of a pathologic condition or injury in
the body.
• Signs can be observed only if the condition produces a physical
change in the associated tissue.
• Many pathologic conditions produce a change in a physical
characteristic that can be imaged by one method but not another.
University Politehnica of Bucharest 85
Examples• In projection imaging (radiography and fluoroscopy), images are
formed by projecting an x-ray beam through the patient's body
and casting shadows onto an appropriate receptor that converts
the invisible x-ray image into a visible light image.
• The primary advantage: is that a large volume of the patient's
body can be viewed with one image.
• A disadvantage is that structures and objects are often
superimposed so that the image of one might interfere with the
visibility of another.
University Politehnica of Bucharest 86
• Tomographic imaging, sonography, single photon emission
tomography (SPECT), positron emission tomography (PET), and
MRI produces images of selected planes or slices of tissue in the
patient's body.
• The general advantage of a tomographic image is the increased
visibility of objects within the imaged plane.
• One factor that contributes to this is the absence of overlying
objects.
• The major disadvantage is that only a small slice of a patient's
body can be visualized with one image.
Examples