Cursul_2_5

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





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

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


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


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





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)


Reprezentari diferite ale unui semnal

bidimensional


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:


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


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)


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:

•


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


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



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



Sampling and Reconstruction



Example: Adjusting Brightness(Thomas Funkhouser course slides)


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


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


medical images

IMAGE QUALITY

Medical Imaging is the Process of Converting Tissue Characteristics into a

Visual Image


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


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


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.


Contrast Sensitivity

Effect of Contrast Sensitivity on Object Visibility


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


Cursul V



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.


Blur and Visibility of Detail

Effect of Blur on Visibility of Image Detail


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.


Noise

Effect of Noise on Object Visibility


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.


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.


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.


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.


• 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

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