Department of Biomedical Engineering - DiVA portal22847/FULLTEXT01.pdfmain: 2006-12-21 8:52 — -1(1) Institutionen för Medicinsk teknik Department of Biomedical Engineering Examensarbete

main: 2006-12-21 8:52 — -1(1)

Institutionen för Medicinsk teknikDepartment of Biomedical Engineering

Examensarbete

Visual Evaluation of 3D Image Enhancement

Examensarbete utfört i Medicinsk teknikvid Tekniska högskolan i Linköping

av

Karin Adolfsson

LITH-IMT/MI20-EX--06/437--SE

Linköping 2006

Department of Biomedical Engineering Linköpings tekniska högskolaLinköpings universitet Linköpings universitetSE-581 85 Linköping, Sweden 581 83 Linköping

main: 2006-12-21 8:52 — 0(2)

main: 2006-12-21 8:52 — i(3)


Examensarbete utfört i Medicinsk teknik

vid Tekniska högskolan i Linköpingav

Karin Adolfsson


Handledare: Björn Svenssonimt, Linköpings universitet

Mats Anderssonimt, Linköpings universitet

Henrik Einarssoncontextvision

Martin Hedlundcontextvision

Examinator: Hans Knutssonimt, Linköpings universitet

Linköping, 8 December, 2006

main: 2006-12-21 8:52 — ii(4)

main: 2006-12-21 8:52 — iii(5)

Avdelning, Institution

Division, Department

Division of Medical InformaticsDepartment of Biomedical EngineeringLinköpings universitetSE-581 85 Linköping, Sweden

Datum

Date

2006-12-08

Språk

Language

� Svenska/Swedish

� Engelska/English

�

⊠

Rapporttyp

Report category

� Licentiatavhandling

� Examensarbete

� C-uppsats

� D-uppsats

� Övrig rapport

�

⊠

URL för elektronisk version

http://urn.kb.se/resolve?urn=

urn:nbn:se:liu:diva-7944

ISBN

—

ISRN


Serietitel och serienummer

Title of series, numberingISSN

—

Titel

TitleVisuell utvärdering av tredimensionell bildförbättring


Författare

AuthorKarin Adolfsson

Sammanfattning

Abstract

Technologies in image acquisition have developed and often provide imagevolumes in more than two dimensions. Computer tomography and magnetresonance imaging provide image volumes in three spatial dimensions. The imageenhancement methods have developed as well and in this thesis work 3D imageenhancement with filter networks is evaluated.

The aims of this work are; to find a method which makes the initial parametersettings in the 3D image enhancement processing easier, to compare 2D and 3Dprocessed image volumes visualized with different visualization techniques andto give an illustration of the benefits with 3D image enhancement processingvisualized using these techniques.

The results of this work are;

• a parameter setting tool that makes the initial parameter setting mucheasier and

• an evaluation of 3D image enhancement with filter networks that shows asignificant enhanced image quality in 3D processed image volumes with ahigh noise level compared to the 2D processed volumes. These results areshown in slices, MIP and volume rendering. The differences are even morepronounced if the volume is presented in a different projection than thevolume is 2D processed in.

Nyckelord

Keywords Visualization, Medical Image Enhancement, MIP, Volume Rendering, 3D ImageEnhancement.

main: 2006-12-21 8:52 — iv(6)

main: 2006-12-21 8:52 — v(7)

Abstract

Technologies in image acquisition have developed and often provide image volumesin more than two dimensions. Computer tomography and magnet resonance imag-ing provide image volumes in three spatial dimensions. The image enhancementmethods have developed as well and in this thesis work 3D image enhancementwith filter networks is evaluated.

The aims of this work are; to find a method which makes the initial parametersettings in the 3D image enhancement processing easier, to compare 2D and 3Dprocessed image volumes visualized with different visualization techniques and togive an illustration of the benefits with 3D image enhancement processing visual-ized using these techniques.

The results of this work are;

• a parameter setting tool that makes the initial parameter setting much easierand

• an evaluation of 3D image enhancement with filter networks that shows asignificant enhanced image quality in 3D processed image volumes with ahigh noise level compared to the 2D processed volumes. These results areshown in slices, MIP and volume rendering. The differences are even morepronounced if the volume is presented in a different projection than thevolume is 2D processed in.

v

main: 2006-12-21 8:52 — vi(8)

main: 2006-12-21 8:52 — vii(9)

Acknowledgments

First of all I would like to thank all the employees at Contextvision AB, for help-ing me with various things and for the friendly and inspiring atmosphere. Specialthanks to Henrik Einarsson and Martin Hedlund for their supervision.

I also would like to thank my examiner Professor Hans Knutsson and supervi-sors Björn Svensson and Mats Andersson at IMT, for always listening, answeringquestions and for guidance of the work.

I also give my gratitude to Professor Örjan Smedby for his willingness to share hisclinical knowledge with me.

Thanks also to my opponent Henrik Brodin for reading my report and givingvaluable suggestions and remarks.

The support from my mentor, Professor Jan Hillman is gratefully acknowledged.

To my sons, Dennis and Emil Adolfsson who have put up with a sometimes over-strained and impatient mother.

Karin AdolfssonLinköping, 8 december, 2006

vii

main: 2006-12-21 8:52 — viii(10)

main: 2006-12-21 8:52 — ix(11)

Contents

1 Introduction 3

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.1 Visualization techniques in clinical use . . . . . . . . . . . . 4

1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

I Local adaptive filtering 7

2 Local adaptive filtering 9

2.1 Image orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1.1 Mapping requirements . . . . . . . . . . . . . . . . . . . . . 112.1.2 Interpretation of the orientation tensor . . . . . . . . . . . . 12

2.2 Calculation of the control tensor . . . . . . . . . . . . . . . . . . . 132.2.1 The m-function . . . . . . . . . . . . . . . . . . . . . . . . . 132.2.2 The µ-function . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3 Generation of the adaptive filter . . . . . . . . . . . . . . . . . . . 16

3 Enhancement parameter setting tool, T-morph 17

3.1 Initial parameter setting of the m-function . . . . . . . . . . . . . . 173.2 Initial parameter setting of the µ- function . . . . . . . . . . . . . . 203.3 Result of the parameter setting tool . . . . . . . . . . . . . . . . . 223.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

II Visualization techniques 25

4 Visualization techniques 27

4.1 Multi-planar reformatting . . . . . . . . . . . . . . . . . . . . . . . 274.2 Image-order volume rendering . . . . . . . . . . . . . . . . . . . . . 28

4.2.1 Maximum intensity projection . . . . . . . . . . . . . . . . 304.3 Object-order volume rendering . . . . . . . . . . . . . . . . . . . . 30

ix

main: 2006-12-21 8:52 — x(12)

5 Results visualization techniques 315.1 Visualization with slices . . . . . . . . . . . . . . . . . . . . . . . . 31

5.1.1 3D enhancement in test volume . . . . . . . . . . . . . . . . 315.2 Visualization with MIP . . . . . . . . . . . . . . . . . . . . . . . . 34

5.2.1 Evaluation of test volume . . . . . . . . . . . . . . . . . . . 345.2.2 Evaluation of MRA renal arteries . . . . . . . . . . . . . . . 365.2.3 Evaluation of MRA cerebral arteries . . . . . . . . . . . . . 38

5.3 Visualization with volume rendering . . . . . . . . . . . . . . . . . 415.3.1 Evaluation of MRA renal arteries . . . . . . . . . . . . . . . 415.3.2 Evaluation of MRA cerebral arteries . . . . . . . . . . . . . 42

5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

6 Discussion 476.1 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Bibliography 49

main: 2006-12-21 8:52 — 1(13)

Contents 1

List of Figures

1.1 Processing chain from 3D volume to enhanced image . . . . . . . . 4

2.1 Flow chart of local adaptive filtering, for 3D signals . . . . . . . . . 102.2 Orientations in testvolume . . . . . . . . . . . . . . . . . . . . . . . 112.3 Orientations in MIP cerebra MRA . . . . . . . . . . . . . . . . . . 112.4 Plot of m(x, σ; α, β, j) as a function of x in the interval (0,1) . . . 142.5 Plot of µ(x; α, β, j) as a function of x in the interval (0,1) . . . . . 152.6 Plot of three different orientation tensors . . . . . . . . . . . . . . 15

3.1 Flow chart of the m- function parameter setting . . . . . . . . . . . 183.2 Display of the parameter setting tool m-function . . . . . . . . . . 183.3 Illustration of the initial m-function with displayed ‖T‖ values, red

is regions with noise, green is regions with low contrast and blue isregions with high contrast . . . . . . . . . . . . . . . . . . . . . . . 19

3.4 Illustration of the new m-function . . . . . . . . . . . . . . . . . . 193.5 Flow chart of the µ- function parameter setting . . . . . . . . . . . 203.6 Illustration of the parameter setting tool µ- function . . . . . . . . 203.7 Illustration of λn / λn−1, µ- functions. There are two µ-functions,

one for the plane case and one for the line case. . . . . . . . . . . . 213.8 Illustration of the new µ- function in the plane case . . . . . . . . 213.9 Result test volume with added noise, SNR 10 dB . . . . . . . . . . 223.10 Result test volume with added noise, SNR 5 dB . . . . . . . . . . . 223.11 Result MR-volume processed with 3D image enhancement . . . . . 23

4.1 Image-order volume rendering . . . . . . . . . . . . . . . . . . . . . 284.2 Different ray paths in image-order volume rendering . . . . . . . . 294.3 Object-order volume rendering . . . . . . . . . . . . . . . . . . . . 30

5.1 Test volume for studying noise reduction. . . . . . . . . . . . . . . 325.2 Slice of test volume with and without noise added . . . . . . . . . 325.3 Slice of test volume 2D and 3D processed . . . . . . . . . . . . . . 335.4 Slice of test volume with and without noise added . . . . . . . . . 335.5 Slice of test volume 2D and 3D processed . . . . . . . . . . . . . . 345.6 Test volume for studying image enhancement visualized with MIP 345.7 Test volume with noise added visualized with MIP . . . . . . . . . 355.8 Test volume with noise added 2D and 3D processed . . . . . . . . 355.9 Axial slice and unprocessed volume visualized with MIP, renal MRA 365.10 2D and 3D processed volume of renal MRA . . . . . . . . . . . . . 375.11 Axial slices of renal MRA . . . . . . . . . . . . . . . . . . . . . . . 375.12 2D and 3D processed volumes of renal MRA . . . . . . . . . . . . . 385.13 Unprocessed and 3D processed volume of cerebral MRA . . . . . . 385.14 Un-, 2D and 3D processed volumes of cerebral MRA, MIP . . . . . 395.15 Un-, 2D and 3D processed sub-volumes of cerebral MRA, MIP . . 405.16 Un-, 2D and 3D processed volumes of renal MRA, volume rendering 415.17 Un-, 2D and 3D processed volumes of cerebral MRA, volume rendering 43

main: 2006-12-21 8:52 — 2(14)

2 Contents

5.18 Un-, 2D and 3D processed volumes of cerebral MRA, volume rendering 44

List of Tables

5.1 Measured degree of stenosis in MRA 1 renal arteries. . . . . . . . . 365.2 Measured degree of stenosis degree in MRA 2 renal arteries. . . . . 385.3 Measured degree of stenosis in MRA renal arteries visualized with

volume rendering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.4 Measured degree of stenosis degree in MRA 2 renal arteries visual-

ized with volume rendering. . . . . . . . . . . . . . . . . . . . . . . 42

main: 2006-12-21 8:52 — 3(15)

Chapter 1

Introduction

Image enhancement in two dimension is a well known and used technique. Butthe technologies in image acquisition have developed and these techniques oftenprovide image volumes in three or more dimensions, as in computer tomography,CT and magnetic resonance imaging, MRI. Three dimensions may contain twospatial coordinates and one temporal coordinate or three spatial coordinates as in3D image volumes, which will be used in this thesis work. New methods for imageenhancement is needed with larger and more numerous filters as the dimensionalityof the signal increases. A new method for 3D filtering is used in this work for imagevolume enhancement. This filtering method is less time consuming than earlierfiltering techniques. This thesis work is part of a research project involving theDepartment of Biomedical Engineering at Linköping University and ContextvisionAB. All clinical image volumes used in this study are from the Center for MedicalImage Science and Visualization (CMIV) in Linköping.

1.1 Background

The developed method of 3D filters can perform fast processing of 3D signals. Howthe effect of this enhancement should be visualized to give a high clinical valueneeds however to be evaluated. This might seem straightforward but the visualresult may highly depend on the choice of visualization technique and software.The entire processing chain is shown in figure 1.1 and gives an overview of thealgorithm.

To be able to capture the enhancement effect this requires use of visualizationsoftware, in this thesis work Analyze 7.0 is used. The experienced subjective imagequality will be evaluated and how it is affected by different visualization methods.

3

main: 2006-12-21 8:52 — 4(16)

4 Introduction

Figure 1.1. Processing chain from 3D volume to enhanced image visible for the observer.

1.1.1 Visualization techniques in clinical use

The most commonly used visualization method of 3D images in clinics are slices,multi-planar reformatting (MPR) and maximum intensity projection (MIP). Slicesare used to get a quick overview of status, revealing hemorrhages or tumors. MPRis used to examine 3D CT and MRI images and gives an apprehension about theanatomy in different projections, since coronal, sagittal and axial projections areshown simultaneously. Prevalence of tumors or hemorrhages is exposed with thistechnique. To examine angiographies MIP is used, both with CT and MRI images,with or without contrast media (MRI). Volume rendering methods except MIPare not frequently used in the daily work, but have a growing potential with newfaster techniques. It is however used when examining angiography images whereMIP images don’t show underlying structures. In most clinics the visualizationsystem are integrated in the manufacturer’s apparatuses, but there are a numberof commercial visualization systems on the market. The goal with visualization inmedicine is to give accurate anatomy and function mapping, enhanced diagnosisand accurate treatment planning.

1.2 Objectives

The aims of this thesis work are:

• to find a method which makes the initial parameter settings in the 3D en-hancement processing easier and

• to compare 2D and 3D processed image volumes visualized with differenttechniques and

• to give an illustration of the benefits with 3D enhancement processing visu-alized using different visualization techniques.

Setting the parameters in the 3D enhancement processing can be difficult with-out some clue of what values the parameters should have to achieve desired result.

main: 2006-12-21 8:52 — 5(17)

1.3 Thesis outline 5

The degree of difficulty increases as the dimensionality of the signal increases.A tool that gives a first suggestion of how the parameters should be set will becreated to make the initial parameter setting easier.

The effects that the 3D enhancement processing has on different visualizationtechniques has not yet been studied. This thesis work will give a first indicationof how the visualization methods affects the 3D processing. The results will begiven visualized with different visualization methods.

1.3 Thesis outline

This thesis work is divided into two parts. The first part, covers the theory oflocal adaptive filtering and the result of the parameter setting tool. In chapter2, image orientation, calculation of the control tensor i.e. the mapping functionsand generation of the adaptive filter is explained. Chapter 3 gives a descriptionof the parameter setting tool and shows results in test volumes and clinical imagevolumes.

In chapter 4, theory about the different visualization methods is provided,which includes multi-planar reformatting, image-order volume rendering and object-order volume rendering. Chapter 5 reveals the results of the visual evaluation of3D enhancement including both test volumes and clinical images.

main: 2006-12-21 8:52 — 6(18)

6 Introduction

main: 2006-12-21 8:52 — 7(19)

Part I

Local adaptive filtering

7

main: 2006-12-21 8:52 — 8(20)

main: 2006-12-21 8:52 — 9(21)

Chapter 2

Local adaptive filtering

The idea of local adaptive filtering is to enhance detectability of features in animage and at the same time reduce the noise level. Another advantage with thelocal adaptive filtering is that the signal high frequency content is steerable. Theoptimal filter is the Wiener filter, see equation (2.1),

W (u) =H2(u)

H2(u) + η2(u)(2.1)

where H2(u) is the spectrum of the signal and η2(u) is the spectrum of thenoise. The problem with Wiener filters is that they work well on stationary signalsand an image or an image volume is highly non-stationary. To solve this problemthe spectrum in equation (2.1) is made local instead of global. The result is anadaptive, local Winer filtering, Wlocal(u, ξ) that is optimized for each neighbor-hood. The problem with the local Wiener filter is that the computational effort istoo high. Instead we will use a steerable filter that has many desirable features ofthe local Wiener filter. The basis for control of the adaptive filter is the informa-tion contained in an orientation tensor, T, which will be explained in chapter 2.1.

In local adaptive filtering there are a number of calculation steps to pass be-fore the enhanced image is available, see figure 2.1. A presentation of these stepswill be given in this chapter. The theory of local adaptive filtering is valid formultidimensional signals, [10].

9

main: 2006-12-21 8:52 — 10(22)

10 Local adaptive filtering

3D Volume

?

?Local structure estimation

Enhancement filters LP and HP?

Mapping functions

?

Generation of adaptive filter

?

Enhanced 3D Volume

Figure 2.1. Flow chart of local adaptive filtering, for 3D signals

2.1 Image orientation

An image or volume consists of different structures, in three dimensions thesestructures can be a combination of lines, edges, planes or isotropic regions. Theselocal structures have different orientations which can be used for image enhance-ment using adaptive filtering. To estimate the local structures or local orientationsin the image, filters with different directions are used to detect these orientations.Often a quadrature filter set is used which produces a local phase-invariant mag-nitude and phase. The magnitude of the different filters gives a tensor descriptionof the local structures. The local structure is valid for simple signals, which meansthat they locally only vary in one direction see equation (2.2), [1, 10],

S(ξ) = G(ξ · x) (2.2)

where S and G are non-constant functions, ξ is the spatial coordinates and x

is a constant orientation vector in the direction of the signals maximal variation.A tensor, T, of order two can be defined from these simple neighborhoods and thesignals dimensionality will determine the size of the tensor. In three dimensionsthe tensor has nine components, see equation (2.3), [11, 10]. Figure 2.2 and 2.3illustrate different orientations in two images. The colors correspond to differentorientations, this representation of orientations is only valid for 2D images.

T(ξ) =

t1 t4 t5t4 t2 t6t5 t6 t3

=

x21 x1x2 x1x3

x1x2 x22 x2x3

x1x3 x2x3 x23

= xxT (2.3)

main: 2006-12-21 8:52 — 11(23)

2.1 Image orientation 11

Figure 2.2. Orientations in 2D testvolume. To the left the original image and to theright image of the different orientations, the colors correspond to different orientations

Figure 2.3. Orientations in MIP cerebral MRA. To the left the original image and to theright image of the different orientations, the colors correspond to different orientations

2.1.1 Mapping requirements

To represent the local orientation with tensors three requirements must be met,the uniqueness requirement, the uniformity requirement and the polar separabilityrequirement. The uniqueness requirement implies that all pairs of 3D vectors x

and −x are mapped to the same tensor see equation (2.4). This means that arotation of 180 degrees gives the same orientation [6].

T(x) = T(−x) (2.4)

The second requirement, the uniformity requirement, means that the mappingshall locally preserve the angle metric between 3D planes and lines that is rotation

main: 2006-12-21 8:52 — 12(24)


invariant and monotone with each other see equation (2.5), this means that a smallchange in angle will give a small change of the tensor.

‖δT‖ = c ‖δx‖r=const. (2.5)

where r = ‖x‖ and c is a ”stretch” constant, [6].The polar separability requirement implies that the norm of the tensor is not

dependent on the direction of x, because the information carried by the magnitudeof the original vector x does not depend on the vector angle, see equation (2.6),[6].

‖T‖ = f(‖x‖) (2.6)

One mapping that meets all three of the requirements and maps the vector x

to the tensor, T is given by the equation (2.7), [6].

T ≡ r−1xxT (2.7)

Where r is any constant greater than zero and x is a constant vector pointingin the direction of the orientation [6].The norm of T is given by:

‖T‖2 ≡∑

ij

t2ij =∑

n

λ2n (2.8)

2.1.2 Interpretation of the orientation tensor

Simple neighborhoods are represented by tensors of rank 1. Acquired data fromthe physical world are seldom simple and in higher dimensional data there existsstructured neighborhoods that are not simple. The rank of the tensor will reflectthe complexity of the neighborhood. The distribution of eigenvalues and the corre-sponding tensor representations will be given for three different cases of T in threedimensions. The eigenvalues of T are λ1 ≥ λ2 ≥ λ3 ≥ 0 and ei is the eigenvectorcorresponding to λi, [11].

In the plane case, a simple neighborhood, λ1 ≫ λ2 ≈ λ3 is

T ≈ λ1e1eT1 (2.9)

and this case corresponds to a neighborhood that is approximately constanton planes in a given orientation. The orientation of the planes is given by e1.

In the line case, a neighborhood of rank 2, λ1 ≈ λ2 ≫ λ3 is

T ≈ λ1(e1eT1 + e2e

T2 ) (2.10)

main: 2006-12-21 8:52 — 13(25)

2.2 Calculation of the control tensor 13

and this case corresponds to a neighborhood that approximately constant onlines. The orientation of the lines is given by the eigenvector corresponding to thesmallest eigenvalue, e3.

In the last instance the isotropic case, a neighborhood of rank 3, λ1 ≈ λ2 ≈ λ3

is

T ≈ λ1(e1eT1 + e2e

T2 + e3e

T3 ) (2.11)

and this case corresponds to an approximately isotropic neighborhood, whichmeans that there exists energy in the neighborhood but no typical orientation, asin regions with noise, [11].

2.2 Calculation of the control tensor

The information about the local structure that are stored in the orientation tensor,T0 is the basis for the calculation of the control tensor, C. To guarantee that theadaptive filter is slowly varying between the neighborhoods, the orientation tensoris low-pass filtered. This is important since the filters are shift-variant (the kernelcoefficients are dependent of the filter’s spatial position). The output from thelow-pass filter T describes the variation of events in the neighborhood (2.12) [3].

T = hlp ∗ T0 (2.12)

After low-pass filtering the local structure tensor the eigenvalues of T areremapped with two mapping functions, the m-function and the µ-function whichgives the control tensor, C. The control tensor’s largest eigenvalue γ1 controlsthe high-pass characteristics of the adaptive filter and is calculated with the m-function. The second and third eigenvalues, (γ2 and γ3), of the control tensor arecalculated with the µ-function and controls the shape of C, [3].

2.2.1 The m-function

The mapping between the orientation tensor and the control tensor is done withtwo mapping functions, it is the eigenvalues of the local structure tensor that aremapped see equation (2.13).

T =∑

i

λieieTi

C =∑

i

γieieTi

(2.13)

The mapping function that controls the high pass content of the signal is calledthe m-function, shown in equation (2.14) [3].

main: 2006-12-21 8:52 — 14(26)


m(x, σ ; α, β, j) =

[

xβ

xβ+α + σβ

]1/j

(2.14)

The variable x is position dependent and equals ‖T‖ =√

λ21 + λ2

2 + λ23 and

corresponds to the local energy in the image with the maximum value one. Theestimated local noise level answers to σ and can be seen as a threshold betweennoise and signal. The σ value is supposed to be so close to the local noise level aspossible, to get the best filtering result. The parameter α is used to compress thesignal this will equalize the local signal amplitude in all regions where the signalis above the noise. The parameter α should be used with care in signals with highlocal noise levels. Variable j equals the number of iterations. To adjust the slopebetween noise and signal the parameter β is used [3].

The largest eigenvalue of the control tensor is γ1 and is calculated by the m-function, see equation (2.15). The γ1 value scales the high pass content in theadaptive filter, i.e changes the size of T. In figure 2.4, two plots display the m-function for different values of α and σ [3].

γ1 = m(x, σ; α, β, j) (2.15)

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

Figure 2.4. Plot of m(x, σ; α, β, j) as a function of x in the interval [0,1], β = 2 and j

= 1. To the left σ = 0.05 and different values of α; 0.2, 0.3, 0.4 and 0.5 (top curve). Tothe right α = 0.3 and different values of σ; 0.1, 0.2, 0.3, 0.4 and 0.5 (bottom curve).

main: 2006-12-21 8:52 — 15(27)

2.2 Calculation of the control tensor 15

2.2.2 The µ-function

The µ-function is the second mapping function and is used to control the contentin the band pass filters regarding how anisotropic the adaptive filtering should be.An other way to think about it is to see it as the shape of the control tensor i.e. theshape of the adaptive filter, see equation (2.16) for calculation of the µ-function[3].

µ(x ; α, β, j) =

[

(x (1 − α))β

(x (1 − α))β + (α (1 − x))β

]1/j

(2.16)

The variable x is position dependent and equals λn

λn−1

, where λn are the eigen-

values of T. The parameter α determines the value of λn

λn−1

for which the µ-functionis 0.5 and the parameter β determines the slope in the transition area. In figure2.5 two plots display the µ-function for different values of α and β [3].

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1mu−func a=0.9 b=2.0 j=1.0

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1mu−func a=0.3 b=5.0 j=1.0

Figure 2.5. Plot of µ(x; α, β, j) as a function of x in the interval [0,1], j = 1. To theleft β = 2 and different values of α; 0.1, 0.3, 0.5, 0.7 and 0.9 (curve to the right). To theright α = 0.3 and different values of β; 1, 2, 3, 4 and 5 (top curve).

The µ-function controls the shape of the control tensors and can make themmore or less isotropic. In 2D the tensors can be seen as ellipses and the eigenvaluesof the tensors controls the isotropy of them, see figure 2.6.

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 2.6. Plot of three different orientation tensors, to the left a tensor representing asimple neighborhood, in the middle a tensor representing an approximately simple neigh-borhood and the the right a tensor representing an isotropic neighborhood (illustrationof 2D tensors)

main: 2006-12-21 8:52 — 16(28)


In three dimensions the µ-function is used twice to calculate γ2 and γ3 seeequation (2.17).

γn = γ1

n∏

j=2

µj (2.17)

The control tensor C is then calculated from the γ values as shown in equation(2.18)

C = γ1e1eT1 + γ2e2e

T2 + γ3e3e

T3

C = γ1

[

e1eT1 + µ2

[

e2eT2 + µ3

[

e3eT3

] ] ] (2.18)

2.3 Generation of the adaptive filter

Now it’s time to put it all together, the adaptive filter consists of the low passfilter, Flp(ρ) and the tensor controlled high pass filters, Fhp(u,C), se equation(2.19). The low pass filter i supposed to filter the signal in regions where γ1 isclose to zero, since in this regions the high pass content is low and it is supposedto preserve the local mean of the signal [3].

F (u,C) = Flp(ρ) + ahpFhp(u,C) (2.19)

The constant ahp is the high-pass amplification factor and C is the controltensor. The ahp can amplify the high-pass part of the filter. It is initially set tounity, but can be increased during the processing. The ahp value can be thoughtof as a magnification factor to the m-function.

For signals of three dimensions there are at least six spherically separable highpass filters Fk(u) which can be expressed as equation (2.20) [3].

Fhp(u,C) =∑

k

ckFk(u) (2.20)

where ck is the weighting coefficients which are signal-dependent and calculatedby the scalar product between the control tensor and the filter associated dualtensors Mk i.e. ck = C • Mk. For calculation of Mk see equation (2.21).

Mk = α nk nTk − β I (2.21)

In three dimensions α is 54 , β is 1

4 , nk is the direction of filter k and I is theidentity tensor.

main: 2006-12-21 8:52 — 17(29)

Chapter 3

Enhancement parameter

setting tool, T-morph

In the enhancement part of the adaptive filtering the m -function is used to de-termine the high-pass content of the filter response. Three parameters, σ, α andβ regulate the enhancement of different local energy levels in the volume. Theoptimal choice of the parameters may differ between volumes depending on noiselevel, amount of small structures and so forth. Step two in the parameter set-ting is to determine how anisotropic the adaptive filtering shall be. This is doneby optimizing the parameters of the µ-functions. To facilitate the initial settingsof the parameters in the m- and µ-functions a tool that depends on the localcharacteristics of the volume is created, which will be described in this chapter.

3.1 Initial parameter setting of the m-function

T-morph is created to make the initial parameter setting easier and it goes througha number of steps to calculate the parameters, see figure 3.1 for illustration. Itstarts with the manual selection of small regions with specific characteristics, i.e.regions with noise, low contrast and high contrast. The tensor data in these regionsare then collected and an average of these values are used for calculation of ninerepresentative tensors, three for regions containing noise, three for regions withlow contrast and three for regions with high contrast. These nine tensors are thendisplayed in the initial m-function to get an idea of the volume properties. It ispossible to set the desired γ1 values for the different types of regions. In this stepyou are able to enhance some characteristics and reduce others. The tool thencalculates the new parameter values using a least square solution and finally thenew m-function is displayed.

17

main: 2006-12-21 8:52 — 18(30)

18 Enhancement parameter setting tool, T-morph

Select characteristic regions

?

Calculate T in the neighborhood

?

mean ( T) in the neighborhood

?

Display ‖T‖ values

?

Set desired γ1 values

?

min∑

(m( ‖T‖; σ, α, β ) - mdesired )2

?

Display new m -function

Figure 3.1. Flow chart of the m- function parameter setting

The purpose of this tool is to facilitate the initial parameter setting, dependingon the characteristics of the volume. The manual part of the tool is to select regionswith noise, low contrast and high contrast. The user can decide what γ1 valuesthat are desired for these regions, but a default value is initially set. See figure 3.2for illustration.

Figure 3.2. Display of the parameter setting tool m-function

The tensor information in the selected regions makes the basis for the newparameters. In a neighborhood of the selected point all the tensors are calculated

main: 2006-12-21 8:52 — 19(31)

3.1 Initial parameter setting of the m-function 19

and an average of these are used to display the γ1 values for the different charac-teristics of the volume, see figure 3.3. It has been seen that collecting one singlevoxel with the desired characteristics is hard, therefore an average of the nearestneighborhood is used. The neighborhood consists of a region that is 5 × 5 × 5voxels in size.

Figure 3.3. Illustration of the initial m-function with displayed ‖T‖ values, red is regionswith noise, green is regions with low contrast and blue is regions with high contrast

The calculation of the new parameters σ, α and β to optimize the m-functionfor the selected volumes uses a least square solution, see equation (3.1).

arg min

3∑

k=1

( m(‖T‖k ; σ, α, σ) − mdesired (k))2 ) (3.1)

The function mdesired defines the desired γ1 value for each type of region andk represents the different regions. When the new σ, α, and β values are calculatedthe suggested m-function is displayed, see figure 3.4.

Figure 3.4. Illustration of the new m-function, the dashed curve represents the newm-function and the solid one the original m-function. Desired value for noise was 0, forlow contrast regions 1,2 and for high contrast regions 1.

main: 2006-12-21 8:52 — 20(32)


3.2 Initial parameter setting of the µ- function

The steps to set the parameters of the µ- functions are very similar to the param-eter setting of the m- function see figure 3.5. But the user can not choose desiredvalues for µ, the desired value for µ is set to 0 or 1 depending on if it is λ2

λ1

orλ3

λ2

and depending on if it is the plane or the line case. The algorithm starts witha selection of volumes containing planes and lines, see the µ- function parametersetting tool in figure 3.6.

Select volumes containing planes and lines

?

Calculate T in the neighborhood

?

mean ( T) in the neighborhood

?

Display λn

λn−1

?

min∑

(µ( λn

λn−1

; α, β ) - µdesired )2

?

Display new µ- function

Figure 3.5. Flow chart of the µ- function parameter setting

Figure 3.6. Illustration of the parameter setting tool µ- function

To use the parameter setting tool for the µ- function, the user select threepoints in the image containing planes and three points containing lines. Thecollected regions are 3 × 3 × 3 in size. The tensor information in these regions isthen collected and λn / λn−1 is calculated. The average value of

∑

λn /∑

λn−1

from each region is calculated and then displayed in the original µ- function, seefigure 3.7.

main: 2006-12-21 8:52 — 21(33)

3.2 Initial parameter setting of the µ- function 21

Figure 3.7. Illustration of λn / λn−1, µ- functions. There are two µ-functions, one forthe plane case and one for the line case.

When the average value of the λ- quotients are calculated a least square solutionyields the parameters to fit the selected regions. In the first µ- function, the planecase, λ1 >> λ2 ≈ λ3, the desired value for λ2

λ1

is zero and the desired value forλ3

λ2

is one, this gives a µ2 value close to zero see equation (2.18). In the second

µ- function, the line case, λ1 ≈ λ2 >> λ3 the desired value for λ2

λ1

is one and the

desired value for λ3

λ2

is zero, this gives a µ2 value close to one. When the leastsquare solution is calculated the new µ- function is displayed with a dashed linein the original µ- function, see figure 3.8.

Figure 3.8. Illustration of the new µ- function in the plane case

main: 2006-12-21 8:52 — 22(34)


3.3 Result of the parameter setting tool

The results of the T-morph are shown in the images below. The parameter settingsshall be seen as a first setting and manual adjustments may be necessary to achievedesired results. In the two first experiments a test volume that consists of aspherically symmetrical signal with sinusoidal variation in the radial direction isused, for more information about the test volume see [3], chapter 10 . In the firsttest, figure 3.9, Gaussian noise were added resulting in a signal-to-noise ratio of10 dB. In test number two, figure 3.10, the signal-to noise ratio, SNR is 5 dB.

SNR = 20[

SDEV (signal)SDEV (noise)

]

.

Figure 3.9. Result test volume with added noise, SNR 10 dB processed with the T-morph

Figure 3.10. Result test volume with added noise, SNR 5 dB processed with the T-morph

main: 2006-12-21 8:52 — 23(35)

3.4 Conclusions 23

The third test is done on a part of a MRI-brain volume. The reason for notchoosing a whole MRI volume is a limitation in computer memory. The size ofthe tested volume is 128 × 128 × 72 voxels. The desired γ- value for noise is setto 0.4, 0 stands for an almost total suppression of noise and 1 stands for neithersuppression nor enhancement of noise, see figure 3.11 for result. The T values ofreal volumes are overall lower then the test volume’s, this makes it important toselect voxels carefully.

Figure 3.11. Result MR-volume processed with 3D image enhancement using the T-morph

3.4 Conclusions

The aim of this part was to find a method to make the initial parameter settingsin the 3D enhancement processing easier. The developed parameter setting toolmakes it much easier to set the initial parameters and the time it takes to reachwanted enhancement effects is much shorter. Often only small manual adjustmentsfrom the suggested values of the parameters is needed. One drawback with themethod is that it is not optimized considering the time it takes find the valuesof the parameters, another is that the selection of voxels in clinical image volumemust be done carefully to get the desired result. Despite of these drawbacks theparameter setting tool gives an easier initial parameter setting.

main: 2006-12-21 8:52 — 24(36)


main: 2006-12-21 8:52 — 25(37)

Part II

Visualization techniques

25

main: 2006-12-21 8:52 — 26(38)

main: 2006-12-21 8:52 — 27(39)

Chapter 4

Visualization techniques

Visualization is any method that operates on multidimensional data to produce animage. The data used in this thesis work is volumetric data in three dimensions.The array of data consists of sampled data and each element is called a voxel.Another way of describing volume visualization is that it is a method of extractingmeaningful information from volumetric data using interactive graphics and imag-ing, [5]. 3D images can be viewed interactively using a number of 3D visualizationtechniques. The optimal choice of the rendering technique is generally determinedby the clinical application. The goal with visualization in medicine is to give accu-rate anatomy and function mapping, enhanced diagnosis and accurate treatmentplanning and the goal with developing visualization techniques is improvement inspeed, an improved access to the data through interactive, intuitive manipulationand measurement of the data. The visualization techniques in clinical applicationsinclude both 2D and 3D display techniques some of them will be described in thischapter. [2, 7].

4.1 Multi-planar reformatting

Two approaches are used to view 3D images with multi-planar reformatting (MPR).In the first, computer user-interface tools make it possible for the operator to selectsingle or multiple planes to be displayed on the screen. Often three perpendicularplanes are displayed simultaneously, with screen cues to their relative orientationand intersection. This method presents familiar 2D images for the operator andallows the operator to orient the planes optimally for examination,[2].

In the second approach, 3D images are presented as a polyhedron representingthe boundaries of the reconstructed volume. The faces of the polyhedron can bemoved in or out parallel to the original face or be moved obliquely to the original.It is also possible to rotate and obtain the desired orientation of the 3D image. Ateach new location of the face, the image is mapped in real time. In this way theoperator always has 3D image-based cues relating the plane being manipulated tothe rest of the anatomy, [2].

27

main: 2006-12-21 8:52 — 28(40)

28 Visualization techniques

4.2 Image-order volume rendering

Volume rendering is a technique that presents the entire 3D volume to the observerafter it has been projected onto a 2D plane. There are two different ways of volumerendering, image-order volume rendering and object-order volume rendering. Themost common approach is image-order, often referred to as ray casting or raytracing, which determine the value of each pixel by sending a ray through the 3Dimage see figure 4.1, [9].

Figure 4.1. Image-order volume rendering

In visualization the scalar values of the intensity are placed at the vertexeson each voxel. Each ray intersects the volume along a series of voxels, which areweighted and summed to achieve the desired rendering result according to the raycasting function. The rays that intersects the volume can be parallel to the viewdirection as in parallel projection or cast from an eye point as in perspective pro-jection. The ray casting function may collect the maximum, minimum or averagegray value along the ray and convert it to a gray scale pixel value on the imageplane, [9].

To generate a discrete ray through the volume there are three different typesof paths; 6-connected, 18-connected and 26-connected. These paths are based onthe relationship between the consecutive voxels along the path, see figure 4.2. Thevoxels are 6-connected if they share a face of the cubic voxels, 18-connected if theyshare a face or an edge and 26-connected if they share a face, an edge or a vertex.The voxels that are connected to the specific path are determining the pixel valueat the image plane. The image quality can be adjusted by choosing smaller orwider sampling intervals. A drawback with this method is that the whole inputvolume must be available at the same time to allow arbitrary view directions, [5].

In some applications alpha values are used, this value determine the objectstransparency. If an object are transparent to some degree it is possible to seewhat is inside that object which can be useful in volume rendering. If an objectare 50 percent opaque the alpha value is 0.5. 1 stands for opaque and 0 for totaltransparency. Often the RGB value is extended with the alpha value so you havea RGBA value. The RGBA values are expressed as equation (4.1), [2, 8].

main: 2006-12-21 8:52 — 29(41)

4.2 Image-order volume rendering 29

Figure 4.2. Different ray paths in image-order volume rendering.To the left 6-connected,in the middle 18-connected and to the right 26-connected.

R =AsRs + (1 − As)Rb

G =AsGs + (1 − As)Gb

B =AsBs + (1 − As)Bb

A =As + (1 − As)Ab

(4.1)

The subscript s refers to the surface of the object and the subscript b refers towhat is behind the object. Transmissivity is the amount of light that is transmittedthrough the object and represents by 1−As. The equation involves that a differentorder of the objects will give a different resulting color, [9].

To get a better interpretation of the image plane a 2D shading technique canbe implied to the image. The simplest 2D shading technique makes the intensityvalue in the output image inversely proportional to the depth of the correspondinginput voxel. This makes features far from the image plane darker and features closeto the image plane brighter. One drawback with this technique is that detailslike surface discontinuities and object boundaries are lost. Better results can beobtained with a 3D shading operation at the intersection point, called gray-levelshading. If (x, y, z) is the intersection point in the data, the gray-level gradient atthat point can be estimated with equation (4.2):

Gx =f(x + 1, y, z)− f(x − 1, y, z)

2Dx

Gy =f(x, y + 1, z)− f(x, y − 1, z)

2Dy

Gz =f(x, y, z + 1) − f(x, y, z − 1)

2Dz

(4.2)

where (Gx, Gy, Gz) is the gradient vector and Dx, Dy and Dz are the distancesbetween the neighboring voxels in the x, y and z directions. The vector thatcontains the gradients is then used as a normal vector for the shading calculation.The intensity value from the shading is then stored in the image. The shadingcalculation is finished when the first opaque voxel is reached along the ray path.

main: 2006-12-21 8:52 — 30(42)

30 Visualization techniques

4.2.1 Maximum intensity projection

Maximum intensity projection (MIP) images are image-order volume rendered,where the ray casting function collects the maximum gray value along the rayand displays it on the image plane. This technique is suitable for visualizationof blood vessels and other small bright objects. The advantage of MIP is thatsegmentation and shading are not needed for these objects. One disadvantage isthat light reflections is ignored which gives a low sensibility for depth in the image.This disadvantage can be improved by rotating the object or look at different viewplanes simultaneously,[8].

4.3 Object-order volume rendering

In object-order volume rendering the input volume is sampled along the rows andcolumns of the 3D array and each voxel is processed to determine its contributionto the image. When an alpha composition method is used, the voxels must betraversed in a back-to-front or front-to-back ordering to avoid that one voxel thatprojects to a pixel later than another will prevail, even if it is farther away from theimage plane than the earlier voxel. Figure 4.3 illustrates back-to-front scanning.If you traverse the voxels in a front-to-back order you can stop scanning when thevolume reaches opaque alpha values to avoid unnecessary processing, [9].

Shading effects in object-order volume rendering can be done with the 2Dshading technique discussed earlier. One better way is to use gradient informationin the shading technique. This method evaluates the gradient at each (x, y) voxellocation in the input image where z = D(x, y) is the depth. The estimated gradientvector at each pixel is then used as a normal vector for the shading, [5].

Volume rendering techniques that use object-order are available but ray cast-ing techniques offers more flexibility in combining different techniques and aretherefore more used ,[8, 9].

Figure 4.3. Object-order volume rendering

main: 2006-12-21 8:52 — 31(43)

Chapter 5

Results visualization

techniques

This chapter will present the results of the evaluation of the 3D processed imagevolumes in different visualization techniques. The result contains evaluations ofboth test volumes and real clinical data sets visualized with slices, maximumintensity projection and volume rendering.

5.1 Visualization with slices

Slices are used in clinics to examine the anatomy in the body. The aim with theseexaminations is to give a correct diagnosis and an accurate treatment plan. In thischapter the results of the two and three dimensional filtering will be presented.The hypothesis is that if volumes are filtered with a three dimensional techniquemore information is used and therefore the result will be better. The test volumeis filtered in both two and three dimensions, noise is added so that the signal ishardly visible in the unprocessed volume.

5.1.1 3D enhancement in test volume

The test volume is from [4] chapter 7. The lines corresponds to the space diagonalsof a dodecahedron, see figure 5.1 for illustration.

31

main: 2006-12-21 8:52 — 32(44)

32 Results visualization techniques

0 20 40 60 80 100 120 140

0

100

200

0

20

40

60

80

100

120

140

Figure 5.1. Test volume for studying noise reduction.

Noise is added to the test volume and the signal is hardly visible in the noise.In figure 5.2 one slice from the volume is shown, to the left without noise and tothe right with noise added.

Figure 5.2. To the left, one slice of the original volume. To the right the original slicewith noise added.

In figure 5.3 the same slice is shown. To the left the slice is filtered with a 2Dfiltering technique and to the right the whole volume is filtered in tree dimensionsand the slice is extracted and displayed. In the 3D filtered slice the signal is distinctdespite considerable noise reduction while in the 2D case the signal is invisible.

main: 2006-12-21 8:52 — 33(45)

5.1 Visualization with slices 33

Figure 5.3. To the left, the slice 2D filtered. To the right, slice of 3D filtered volume.

The result in the slices where the lines is more parallel to the image plane isshown in figure 5.5. The signal with and without noise is displayed in figure 5.4.

Figure 5.4. To the left, one slice of the original volume. To the right the original slicewith added noise.

As expected the signal that is parallel to the image plane is more preserved inthe 2D filtered image, but a lot of noise is preserved as well. In the 3D filteredslice the signal is distinct and almost all noise is removed. The small structuresin the center is preserved in the 3D filtered image but not in the image that isfiltered in two dimensions.

main: 2006-12-21 8:52 — 34(46)


Figure 5.5. To the left, the slice 2D filtered. To the right, slice of 3D filtered volume.

5.2 Visualization with MIP

Maximum intensity projection, MIP, is used to examine angiography investigationsfor vessel anomalies in about 95 percent of the cases. To evaluate the enhancementeffects with 3D filtering visualized with MIP one test volume and two differentangiographies are visualized, filtered with 2D and 3D respectively.

5.2.1 Evaluation of test volume

The test volume is a spiral bended to a circle to receive as many orientationsas possible and has noise added for evaluation of the enhancement effects in 3Dcompared to 2D, see figure 5.6.

0

20

40

60

80

0

10

20

30

40

50

60

7020

30

40

Figure 5.6. Test volume for studying image enhancement visualized with MIP

main: 2006-12-21 8:52 — 35(47)

5.2 Visualization with MIP 35

Figure 5.7. Test volume with noise added visualized with MIP

The result of the 2D and 3D filtering is displayed in figure 5.8 and shows thatthe noise is almost totally suppressed in the 3D filtered volume while in the 2Dfiltered volume more noise is preserved.

Figure 5.8. To the left, 2D filtered test volume and to the right 3D filtered test volumevisualized with MIP.

main: 2006-12-21 8:52 — 36(48)


5.2.2 Evaluation of MRA renal arteries

In the second and third evaluation two different MRI angiographies, MRA, wereexamined by a radiologist. The examination contained an estimation of the degreeof the stenosis in renal arteries in unprocessed and 3D processed angiographyvolumes, visualized with MIP. The volumes were compared to unprocessed slicesfrom the same angiography to evaluate the similarity. The unprocessed slicesare as close to ground-truth as possible and are often used for comparison. Theangiography volumes have different degree of stenosis and different noise levels.The first angiography has a quite high noise level and a stenosis degree about 50percent, see figure 5.9 for illustration.

Figure 5.9. To the left, an axial slice of renal artery stenosis and to the right theunprocessed volume visualized with MIP.

The result of the second evaluation showed that the 3D processed volume gavea more correct estimation of the stenosis degree than the unprocessed volume. The3D processed volume’s stenosis degree was in accordance with the degree of stenosisin the unprocessed slices, while the unprocessed volume gave an overestimationof the stenosis, see figure 5.10. The stenosis degree were later measured in theslice and compared to the MIP visualization of unprocessed, 2D processed and3D processed angiographies, see table 5.1. The measurements were made withGIMP’s 1measurement tool and the diameter over a particular intensity level wasused for the calculation.

Data set Stenosis degree (%)Axial slice 31

Unprocessed MIP 452D processed MIP 423D processed MIP 32

Table 5.1. Measured degree of stenosis in MRA 1 renal arteries.

1http://www.gimp.org/.

main: 2006-12-21 8:52 — 37(49)


Figure 5.10. To the left, 2D processed volume of renal artery stenosis. To the right the3D processed volume of the stenosis visualized with MIP.

In the third evaluation, the second angiography examination a dataset withlow noise level and stenosis degree were used. Two axial slices are shown in figure5.11. The artery is bending perpendicular to the image plane why two slices mustbe examined to display the whole diameter.

Figure 5.11. To the left, axial slice of the suspected renal artery stenosis and to theright the the next slice of the renal artery.

The difference in the ocular examination between the un-, 2D- and 3D-processedangiographies were not as pronounced as in test two. But the measurements ofthe diameters did show a much better similarity between the 3D processed volumeand the axial slices than the un- and 2D processed, see table 5.2.

main: 2006-12-21 8:52 — 38(50)




Table 5.2. Measured degree of stenosis degree in MRA 2 renal arteries.

Figure 5.12. To the left, 2D processed volume of renal artery stenosis. To the right the3D processed volume of the stenosis visualized with MIP

5.2.3 Evaluation of MRA cerebral arteries

For evaluation of the image quality regarding the visibility of small structures oneMRA of cerebral arteries is used. This angiography gives a good apprehensionabout how small brain vessels that are visible, figure 5.13 shows the unprocessedand the 3D processed volumes visualized with MIP.

Figure 5.13. To the left the unprocessed volume and to the right 3D processed volume

main: 2006-12-21 8:52 — 39(51)


The result of the 3D enhancement processing does in this case only show aminor enhancement in noise reduction. The cause of this is that the noise level inthe unprocessed volume is low, i.e. the image quality of this volume is from thebeginning very good.

To evaluate the enhancement effects of images with less good quality, whitenoise were added to the volume of the cerebral angiography MRI. A frontal MIPof the unprocessed volume is shown on top in figure 5.14.

Figure 5.14. On top the unprocessed volume added with white noise, to the left the2D processed volume and to the right 3D processed volume

The MRA of cerebral arteries with white noise added were processed in 2Dand 3D. The 2D processing is made of the slices from front to back. The problemwith the unprocessed volume is that the noise conceal small vessels. In the frontalMIP this problem is reduced in the 2D processed volume and even more reducedin the 3D processed volume. See figure 5.14 for the result.

main: 2006-12-21 8:52 — 40(52)


The result of the 2D and 3D processing were studied in other view directionsas well. In the axial MIP of the volume the difference between the 2D and 3Dprocessed volume were even more pronounced. Top image in 5.15 shows a part ofthe unprocessed volume in axial projection, very few small vessels is visible.

Figure 5.15. On top the unprocessed volume of cerebral arteries with white noise addedvisualized with MIP, to the left the 2D processed volume and to the right 3D processedvolume

To the left in figure 5.15 the same part of the volume is shown but here thevolume is 2D processed. More noise is suppressed here but the visibility of thesmall vessels is hardly better. To the right the result of the 3D processed volumeis shown. The noise is even more suppressed than in the 2D processed volumebut the major result is that the small vessels now is visible. It is a big differencecompared to the unprocessed and 2D processed volumes.

main: 2006-12-21 8:52 — 41(53)

5.3 Visualization with volume rendering 41

5.3 Visualization with volume rendering

Volume rendering is not frequently used to examine angiography images, but itmay be in the future as the technique develops. Volume rendering has advantagescompared to MIP in image volumes where structures of low intensities is hiddenby structures of higher intensities.

5.3.1 Evaluation of MRA renal arteries

The renal artery MRAs used to evaluate the 3D processing visualized with MIPis used to evaluate the visualization with volume rendering as well. The ocularexamination did not show a significant difference between the un-, 2D and 3Dprocessed volumes. See figure 5.16 for illustration.

Figure 5.16. On top the unprocessed volume, to the left the 2D processed volume andto the right 3D processed volume

main: 2006-12-21 8:52 — 42(54)


The same measurements of the degree of stenosis is made in the images visual-ized with volume rendering. The result of the first MRA is displayed in table 5.3and the result from the second MRA is shown in table 5.4.



Table 5.3. Measured degree of stenosis in MRA renal arteries visualized with volumerendering.



Table 5.4. Measured degree of stenosis degree in MRA 2 renal arteries visualized withvolume rendering.

The results of the measurements of the degree of the stenosis does not showany particular advantage for the 3D processed volume. This might depend onthat the transfer functions is not set properly or that the algorithm of the volumerendering have an influence on the result.

5.3.2 Evaluation of MRA cerebral arteries

To evaluate the image quality of small structures visualized with volume renderinga MRA of the cerebral arteries with noise added is used. This is the same dataset used in the evaluation of visualization with MIP. The unprocessed volume isshown on top in figure 5.17. The result of the 2D and 3D processed volumesvisualized with volume rendering is presented in the bottom of figure 5.17. Thetransfer functions is set to suppress the noise but there is a limit where the vesselsgets suppressed too. In the result it is clear that the 3D processed image volumeshows more small vessels and that the noise is more suppressed than in the 2Dprocessed volume. The extra information that the 3D processing gives, even givesa result in the visualization.

main: 2006-12-21 8:52 — 43(55)

5.3 Visualization with volume rendering 43

Figure 5.17. On top the unprocessed volume of cerebral MRA visualized with volumerendering, to the left the 2D processed volume and to the right 3D processed volume

To see the small structures, a part of the MRA cerebral arteries is shown infigure 5.18, on top the unprocessed volume and in the bottom the 2D and 3Dprocessed volumes.

main: 2006-12-21 8:52 — 44(56)


Figure 5.18. On top the unprocessed volume of cerebral MRA visualized with volumerendering, to the left the 2D processed volume and to the right 3D processed volume

5.4 Conclusions

The aims of this second part was to compare 2D and 3D processed image volumesand to give an illustration of the benefits of 3D enhancement processing visualizedwith different visualization techniques. The results show that in image volumeswith a high noise level the 3D processed volumes gives a significant enhancedimage quality compared to the 2D processed volumes. These results are shown inslices, MIP and volume rendering. The differences are even more pronounced if thevolume is presented in a different view direction than the volume is 2D processedin. In volumes with lower noise levels the differences is not as marked.

The evaluation of the renal artery MRA showed that the 3D processed volumegave a more accurate estimation of the stenosis degree visualized with MIP, whileno improvement was shown when it was visualized with volume rendering. Theexplanation to why no improvement was seen in the volume visualized with volumerendering may be improperly set transfer functions or that the volume rendering

main: 2006-12-21 8:52 — 45(57)

5.4 Conclusions 45

process have an influence on the result. MIP on the other hand is very sensitiveto noise which can be the explanation to the good results on the estimations ofstenosis degree.

main: 2006-12-21 8:52 — 46(58)


main: 2006-12-21 8:52 — 47(59)

Chapter 6

Discussion

T-morph gives a suggestion of the parameter values depending on different char-acteristics in the image volume. The user select regions in the image that consistsof noise, structures with low contrast and structures with high contrast and canchoose how much to suppress or enhance these characteristics. The user also selectregions in the volume that consists of planes and lines to set the parameters ofthe µ- function. This tool gives an initial setting of the enhancement parameterswhich can be a starting point for further manual adjustments. Another positiveaspect of the tool is that one can get an idea of the image properties in differentareas because the T and the λn / λn−1 values are displayed in the m- and µ-functions. The share of anisotropic structures in clinical image volumes are muchlower than in the test volumes, this gives that the selection of regions must bedone carefully.

The results of the evaluation of processed volumes visualized with different vi-sualization techniques showed convincing results for the 3D processed volumes,best results were shown in image volumes with a quite high noise level. The clin-ical image volumes from modern equipment does not usually give this bad imagequality, but if the acquisition time is shortened or if the slice thickness is decreasedthe signal-to-noise ratio will decrease. Theses volumes could be enhanced with the3D processing, but this needs more evaluation. I think that shortening the ac-quisition time would have a clinical values for patients in an emergency state orpatients that have problems to lie still, for example patients in acute pain or chil-dren. Another aspect of advantages concerning shortening the acquisition timewould be the economic aspect. If the radiology department could perform moreexaminations a day this would give economic values. Decreasing the slice thicknesswould also give higher noise levels and a higher resolution. The clinical value ofhigher resolution would of cause be a possibility to see smaller structures in theimage.

47

main: 2006-12-21 8:52 — 48(60)

48 Discussion

6.1 Future work

The parameter setting tool is not optimized with respect to speed, i.e calculationof the tensor information and to find the values of the parameters is not instant.One improvement to speed up the calculations of the parameters could be to usea gradient descent algorithm instead of the least square solution. Another im-provement of the tool could be to have a weighting function where one can weightthe characteristics due to the needs. For example if noise reduction is the mostimportant task for one volume the weight function could increase the importanceof this in the tool.

More work needs to be done to evaluate the benefits of the 3D enhancement.First of all a study of clinical image volumes of lower image quality would be in-teresting, to see if the good results stands up to the good results from the imageswith noise added. Next more quantitative studies of estimation of stenosis degreein renal arteries visualized with MIP is needed to get an objective evaluation ofthe 3D enhancement processing. It would also be interesting to let a referencegroup of radiologists evaluate the image quality in 3D processed images visualizedwith MIP. Further studies of image quality of 3D processed volumes would be in-teresting in other modalities like ultrasound and CT to see if the processing showsas good results here.

main: 2006-12-21 8:52 — 49(61)

Bibliography

[1] H. Einarsson. Implementation and performance analysis of filternets. Master’sthesis, Linköping university, SE-581 83 Linköping, Sweden, January 2006.

[2] A. Fenster and D.B. Downey. Basic principles and applications of 3-d ultra-sound imaging. In Advanced Signal Processing Handbook. CRC Press LLC,2001.

[3] G. H. Granlund and H. Knutsson. Signal Processing for Computer Vision.Kluwer Academic Publishers, 1995. ISBN 0-7923-9530-1.

[4] L. Haglund. Adaptive Multidimensional Filtering. PhD thesis, LinköpingUniversity, Sweden, SE-581 83 Linköping, Sweden, October 1992. DissertationNo 284, ISBN 91-7870-988-1.

[5] A. E. Kaufman. Volume visualization in medicine. In Handbook of Medical

Imaging. Academic Press, 2000. ISBN 0-12-077790-8.

[6] H. Knutsson. Representing local structure using tensors. In The 6th Scan-

dinavian Conference on Image Analysis, pages 244–251, Oulu, Finland, June1989. Report LiTH–ISY–I–1019, Computer Vision Laboratory, LinköpingUniversity, Sweden, 1989.

[7] R. A. Robb. Three-dimensional visualization in medicine and biology. InHandbook of Medical Imaging. Academic Press, 2000. ISBN 0-12-077790-8.

[8] G. Sakas, G. Karangelis, and A. Pommert. Advanced applications of volumevisualization methods in medicine. In Advanced Signal Processing Handbook.CRC Press LLC, 2001.

[9] W. Schroeder, K. Martin, and B. Lorensen. The Visualization Toolkit. An

Object-Oriented Approach to 3D Graphics. Kitware, inc., 3 edition, 2002.ISBN 1-930934-07-6.

[10] B. Svensson. Fast multi-dimensional filter networks, design, optimizationand implementation. Lic. Thesis LiU-Tek-Lic-2006:26, Linköping University,Sweden, April 2006. Thesis No. 1245, ISBN 91-85523-92-5.

49

main: 2006-12-21 8:52 — 50(62)

50 Bibliography

[11] C-F. Westin. A Tensor Framework for Multidimensional Signal Processing.PhD thesis, Linköping University, Sweden, SE-581 83 Linköping, Sweden,1994. Dissertation No 348, ISBN 91-7871-421-4.

Department of Biomedical Engineering - DiVA portal22847/FULLTEXT01.pdfmain: 2006-12-21 8:52 — -1(1) Institutionen för Medicinsk teknik Department of Biomedical Engineering Examensarbete

Documents