Visual Evaluation of 3D Image Enhancement

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Institutionen för Medicinsk teknik

Department of Biomedical Engineering

Examensarbete

Visual Evaluation of 3

D

Image Enhancement

Examensarbete utfört i Medicinsk teknik vid Tekniska högskolan i Linköping

av

Karin Adolfsson

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

Linköping 2006

Department of Biomedical Engineering Linköpings tekniska högskola

Linköpings universitet Linköpings universitet

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Visual Evaluation of 3

D

Image Enhancement

Examensarbete utfört i Medicinsk teknik

vid Tekniska högskolan i Linköping

av

Karin Adolfsson

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

Handledare: Björn Svensson

imt, Linköpings universitet

Mats Andersson

Henrik Einarsson

contextvision

Martin Hedlund

contextvision

Examinator: Hans Knutsson

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Avdelning, Institution

Division, Department

Division of Medical Informatics Department of Biomedical Engineering Linköpings universitet

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

Serietitel och serienummer

Title of series, numbering

ISSN

—

Titel

Title

Visuell utvärdering av tredimensionell bildförbättring

Visual Evaluation of 3DImage Enhancement

Författare

Author

Karin Adolfsson

Sammanfattning

Abstract

Technologies in image acquisition have developed and often provide image

volumes in more than two dimensions. Computer tomography and magnet

resonance imaging provide image volumes in three spatial dimensions. The image enhancement methods have developed as well and in this thesis work 3D image enhancement with filter networks is evaluated.

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

The results of this work are;

• a parameter setting tool that makes the initial parameter setting much easier and

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

Nyckelord

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

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Abstract

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

The aims of this work are; to find a method which makes the initial parameter settings in the 3D image enhancement processing easier, to compare 2D and 3D processed image volumes visualized with different visualization techniques and to give 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 easier and

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

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Acknowledgments

First of all I would like to thank all the employees at Contextvision AB, for help-ing me with various thhelp-ings and for the friendly and inspirhelp-ing atmosphere. Special thanks 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, answering questions and for guidance of the work.

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

Thanks also to my opponent Henrik Brodin for reading my report and giving valuable 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 Adolfsson Linköping, 8 december, 2006

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Introduction

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

1.1 Background

The developed method of 3D filters can perform fast processing of 3D signals. How the effect of this enhancement should be visualized to give a high clinical value needs however to be evaluated. This might seem straightforward but the visual result 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 the algorithm.

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

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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). Slices are used to get a quick overview of status, revealing hemorrhages or tumors. MPR is used to examine 3D CT and MRI images and gives an apprehension about the anatomy in different projections, since coronal, sagittal and axial projections are shown simultaneously. Prevalence of tumors or hemorrhages is exposed with this technique. To examine angiographies MIP is used, both with CT and MRI images, with or without contrast media (MRI). Volume rendering methods except MIP are not frequently used in the daily work, but have a growing potential with new faster techniques. It is however used when examining angiography images where MIP images don’t show underlying structures. In most clinics the visualization system are integrated in the manufacturer’s apparatuses, but there are a number of commercial visualization systems on the market. The goal with visualization in medicine is to give accurate anatomy and function mapping, enhanced diagnosis and 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 different techniques 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.

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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 be created to make the initial parameter setting easier.

The effects that the 3D enhancement processing has on different visualization techniques has not yet been studied. This thesis work will give a first indication of how the visualization methods affects the 3D processing. The results will be given visualized with different visualization methods.

1.3 Thesis outline

This thesis work is divided into two parts. The first part, covers the theory of local adaptive filtering and the result of the parameter setting tool. In chapter 2, image orientation, calculation of the control tensor i.e. the mapping functions and generation of the adaptive filter is explained. Chapter 3 gives a description of the parameter setting tool and shows results in test volumes and clinical image volumes.

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 of 3D enhancement including both test volumes and clinical images.

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Part I

Local adaptive filtering

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Chapter 2

Local adaptive filtering

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

W(u) = H

2_(u)

H2_{(u) + η}2_(u) (2.1)

where H2_{(u) is the spectrum of the signal and η}2_{(u) is the spectrum of the}

noise. The problem with Wiener filters is that they work well on stationary signals and an image or an image volume is highly non-stationary. To solve this problem the spectrum in equation (2.1) is made local instead of global. The result is an adaptive, 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 is too high. Instead we will use a steerable filter that has many desirable features of the local Wiener filter. The basis for control of the adaptive filter is the informa-tion contained in an orientainforma-tion 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 steps will be given in this chapter. The theory of local adaptive filtering is valid for multidimensional signals, [10].

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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 these structures can be a combination of lines, edges, planes or isotropic regions. These local structures have different orientations which can be used for image enhance-ment using adaptive filtering. To estimate the local structures or local orientations in 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 magmag-nitude of the different filters gives a tensor description of the local structures. The local structure is valid for simple signals, which means that 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 the signals dimensionality will determine the size of the tensor. In three dimensions the tensor has nine components, see equation (2.3), [11, 10]. Figure 2.2 and 2.3 illustrate different orientations in two images. The colors correspond to different orientations, this representation of orientations is only valid for 2D images.

T_{(ξ) =}   t1 t4 t5 t4 t2 t6 t5 t6 t3  =   x2 1 x1x2 x1x3 x1x2 x22 x2x3 x1x3 x2x3 x23  = ˆxˆxT (2.3)

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2.1 Image orientation 11

Figure 2.2. Orientations in 2D testvolume. To the left the original image and to the right 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 the right 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 separability requirement. 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 a rotation of 180 degrees gives the same orientation [6].

T_{(x) = T(−x)} _(2.4)

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

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

kδTk = c kδxk_r=const. (2.5)

where r = kxk 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 magnitude of the original vector x does not depend on the vector angle, see equation (2.6), [6].

kTk = f (kxk) (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}−1_xxT (2.7)

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

kTk2≡X ij t2ij = X n λ2n _(2.8)

2.1.2 Interpretation of the orientation tensor

Simple neighborhoods are represented by tensors of rank 1. Acquired data from the physical world are seldom simple and in higher dimensional data there exists structured neighborhoods that are not simple. The rank of the tensor will reflect the complexity of the neighborhood. The distribution of eigenvalues and the corre-sponding tensor representations will be given for three different cases of T in three dimensions. The eigenvalues of T are λ1≥ λ2 ≥ λ3≥ 0 and ˆei is the eigenvector

corresponding to λi, [11].

In the plane case, a simple neighborhood, λ1≫ λ2≈ λ3is

T_{≈ λ}₁ˆe₁ˆeT₁ _(2.9)

and this case corresponds to a neighborhood that is approximately constant on planes in a given orientation. The orientation of the planes is given by ˆe1.

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

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2.2 Calculation of the control tensor 13

and this case corresponds to a neighborhood that approximately constant on lines. The orientation of the lines is given by the eigenvector corresponding to the smallest eigenvalue, ˆe3.

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

is

T_{≈ λ}₁_(ê₁êT₁ _{+ ˆ}e₂êT₂ _{+ ˆ}e₃êT₃₎ _(2.11) and this case corresponds to an approximately isotropic neighborhood, which means that there exists energy in the neighborhood but no typical orientation, as in 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 the} adaptive filter is slowly varying between the neighborhoods, the orientation tensor is low-pass filtered. This is important since the filters are shift-variant (the kernel coefficients are dependent of the filter’s spatial position). The output from the low-pass filter T describes the variation of events in the neighborhood (2.12) [3].

T_{= h}_lp_{∗ T}₀ _(2.12)

After low-pass filtering the local structure tensor the eigenvalues of T are remapped with two mapping functions, the m-function and the µ-function which gives the control tensor, C. The control tensor’s largest eigenvalue γ1 controls

the 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 are

calculated 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 with two mapping functions, it is the eigenvalues of the local structure tensor that are mapped see equation (2.13).

T₌X i λiêiêTi C₌X i γiêiêTi (2.13)

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

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m(x, σ ; α, β, j) = xβ xβ+α_{+ σ}β 1/j (2.14) The variable x is position dependent and equals kTk = pλ2

1+ λ22+ λ23 and

corresponds to the local energy in the image with the maximum value one. The estimated local noise level answers to σ and can be seen as a threshold between noise and signal. The σ value is supposed to be so close to the local noise level as possible, to get the best filtering result. The parameter α is used to compress the signal this will equalize the local signal amplitude in all regions where the signal is above the noise. The parameter α should be used with care in signals with high local noise levels. Variable j equals the number of iterations. To adjust the slope between 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 the

adaptive 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 1 0 0.5 1 1.5 2 2.5 0 0.2 0.4 0.6 0.8 1 0 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). To the right α = 0.3 and different values of σ; 0.1, 0.2, 0.3, 0.4 and 0.5 (bottom curve).

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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 content in 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. the shape 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−1for which the µ-function

is 0.5 and the parameter β determines the slope in the transition area. In figure 2.5 two plots display the µ-function for different values of α and β [3].

0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 mu−func a=0.9 b=2.0 j=1.0 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 mu−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 the left β = 2 and different values of α; 0.1, 0.3, 0.5, 0.7 and 0.9 (curve to the right). To the right 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 them more or less isotropic. In 2D the tensors can be seen as ellipses and the eigenvalues of the tensors controls the isotropy of them, see figure 2.6.

0 0.2 0.4 0.6 0.8 1 0 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 1 0 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 1 0 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 a simple neighborhood, in the middle a tensor representing an approximately simple neigh-borhood and the the right a tensor representing an isotropic neighneigh-borhood (illustration of 2D tensors)

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In three dimensions the µ-function is used twice to calculate γ2 and γ3 see

equation (2.17). γn = γ1 n Y j=2 µj (2.17)

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

C_{= γ}₁e_ˆ₁_ˆeT

1 + γ2ê2ê2T + γ3ê3êT3

C_{= γ}₁_ê₁_êT₁ _{+ µ}₂_ê₂_êT₂ _{+ µ}₃_ê₃_êT₃ (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 pass filter, 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 is

close to zero, since in this regions the high pass content is low and it is supposed to 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 control

tensor. The ahp can amplify the high-pass part of the filter. It is initially set to

unity, but can be increased during the processing. The ahp value can be thought

of as a magnification factor to the m-function.

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

Fhp(u, C) =

X

k

ckFk(u) _(2.20)

where ckis the weighting coefficients which are signal-dependent and calculated

by the scalar product between the control tensor and the filter associated dual tensors M_ki.e. ck= C • Mk. For calculation of Mk see equation (2.21).

M_k_{= α ˆ}n_k ˆnT

k − β I (2.21)

In three dimensions α is 5 4, β is

1

4, ˆnk is the direction of filter k and I is the

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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 and β regulate the enhancement of different local energy levels in the volume. The optimal choice of the parameters may differ between volumes depending on noise level, 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 done by optimizing the parameters of the µ-functions. To facilitate the initial settings of the parameters in the m- and µ-functions a tool that depends on the local characteristics 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 through a number of steps to calculate the parameters, see figure 3.1 for illustration. It starts 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 regions are then collected and an average of these values are used for calculation of nine representative tensors, three for regions containing noise, three for regions with low contrast and three for regions with high contrast. These nine tensors are then displayed in the initial m-function to get an idea of the volume properties. It is possible to set the desired γ1 values for the different types of regions. In this step

you are able to enhance some characteristics and reduce others. The tool then calculates the new parameter values using a least square solution and finally the new m-function is displayed.

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18 Enhancement parameter setting tool, T-morph

Select characteristic regions ?

Calculate T in the neighborhood ?

mean ( T) in the neighborhood ?

Display kTk values ?

Set desired γ1 values

?

min P (m( kTk; 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, depending on the characteristics of the volume. The manual part of the tool is to select regions with noise, low contrast and high contrast. The user can decide what γ1 values

that are desired for these regions, but a default value is initially set. See figure 3.2 for illustration.

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

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

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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 single voxel with the desired characteristics is hard, therefore an average of the nearest neighborhood is used. The neighborhood consists of a region that is 5 × 5 × 5 voxels in size.

Figure 3.3.Illustration of the initial m-function with displayed kTk values, red is regions with 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-function for the selected volumes uses a least square solution, see equation (3.1).

arg min

3

X

k=1

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

The function mdesired defines the desired γ1 value for each type of region and

krepresents the different regions. When the new σ, α, and β values are calculated the suggested m-function is displayed, see figure 3.4.

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

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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 desired values for µ, the desired value for µ is set to 0 or 1 depending on if it is λ2

λ1 or

λ3

λ2 and depending on if it is the plane or the line case. The algorithm starts with

a selection of volumes containing planes and lines, see the µ- function parameter setting 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 P (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 three points in the image containing planes and three points containing lines. The collected regions are 3 × 3 × 3 in size. The tensor information in these regions is then collected and λn / λn−1 is calculated. The average value of P λn / P λn−1

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

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3.2 Initial parameter setting of the µ- function 21

Figure 3.7. Illustration of λn/ λ_n−1, µ- functions. There are two µ-functions, one for

the plane case and one for the line case.

When the average value of the λ- quotients are calculated a least square solution yields the parameters to fit the selected regions. In the first µ- function, the plane case, λ1 >> λ2 ≈ λ3, the desired value for λ_λ2₁ is zero and the desired value for

λ3

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 λ_λ2₁ is one and the

desired value for λ3

λ2 is zero, this gives a µ2 value close to one. When the least

square solution is calculated the new µ- function is displayed with a dashed line in the original µ- function, see figure 3.8.

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3.3 Result of the parameter setting tool

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

SN R= 20hSDEV (signal)_{SDEV (noise)}i.

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

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3.4 Conclusions 23

The third test is done on a part of a MRI-brain volume. The reason for not choosing a whole MRI volume is a limitation in computer memory. The size of the tested volume is 128 × 128 × 72 voxels. The desired γ- value for noise is set to 0.4, 0 stands for an almost total suppression of noise and 1 stands for neither suppression nor enhancement of noise, see figure 3.11 for result. The T values of real volumes are overall lower then the test volume’s, this makes it important to select 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 settings in the 3D enhancement processing easier. The developed parameter setting tool makes it much easier to set the initial parameters and the time it takes to reach wanted enhancement effects is much shorter. Often only small manual adjustments from the suggested values of the parameters is needed. One drawback with the method is that it is not optimized considering the time it takes find the values of the parameters, another is that the selection of voxels in clinical image volume must be done carefully to get the desired result. Despite of these drawbacks the parameter setting tool gives an easier initial parameter setting.

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Part II

Visualization techniques

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Chapter 4

Visualization techniques

Visualization is any method that operates on multidimensional data to produce an image. 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 extracting meaningful information from volumetric data using interactive graphics and imag-ing, [5]. 3D images can be viewed interactively using a number of 3D visualization techniques. The optimal choice of the rendering technique is generally determined by the clinical application. The goal with visualization in medicine is to give accu-rate anatomy and function mapping, enhanced diagnosis and accuaccu-rate treatment planning and the goal with developing visualization techniques is improvement in speed, an improved access to the data through interactive, intuitive manipulation and measurement of the data. The visualization techniques in clinical applications include both 2D and 3D display techniques some of them will be described in this chapter. [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 select single or multiple planes to be displayed on the screen. Often three perpendicular planes are displayed simultaneously, with screen cues to their relative orientation and intersection. This method presents familiar 2D images for the operator and allows the operator to orient the planes optimally for examination,[2].

In the second approach, 3D images are presented as a polyhedron representing the boundaries of the reconstructed volume. The faces of the polyhedron can be moved 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. At each new location of the face, the image is mapped in real time. In this way the operator always has 3D image-based cues relating the plane being manipulated to the rest of the anatomy, [2].

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28 Visualization techniques

4.2 Image-order volume rendering

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

Figure 4.1. Image-order volume rendering

In visualization the scalar values of the intensity are placed at the vertexes on each voxel. Each ray intersects the volume along a series of voxels, which are weighted and summed to achieve the desired rendering result according to the ray casting function. The rays that intersects the volume can be parallel to the view direction 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 average gray value along the ray and convert it to a gray scale pixel value on the image plane, [9].

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

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

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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 to what is behind the object. Transmissivity is the amount of light that is transmitted through the object and represents by 1−As. The equation involves that a different

order of the objects will give a different resulting color, [9].

To get a better interpretation of the image plane a 2D shading technique can be implied to the image. The simplest 2D shading technique makes the intensity value in the output image inversely proportional to the depth of the corresponding input voxel. This makes features far from the image plane darker and features close to the image plane brighter. One drawback with this technique is that details like surface discontinuities and object boundaries are lost. Better results can be obtained with a 3D shading operation at the intersection point, called gray-level shading. If (x, y, z) is the intersection point in the data, the gray-level gradient at that 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, Dyand Dzare the distances

between the neighboring voxels in the x, y and z directions. The vector that contains 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 shading calculation is finished when the first opaque voxel is reached along the ray path.

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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 ray and displays it on the image plane. This technique is suitable for visualization of blood vessels and other small bright objects. The advantage of MIP is that segmentation and shading are not needed for these objects. One disadvantage is that 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 view planes simultaneously,[8].

4.3 Object-order volume rendering

In object-order volume rendering the input volume is sampled along the rows and columns of the 3D array and each voxel is processed to determine its contribution to the image. When an alpha composition method is used, the voxels must be traversed in a back-to-front or front-to-back ordering to avoid that one voxel that projects to a pixel later than another will prevail, even if it is farther away from the image 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 the volume reaches opaque alpha values to avoid unnecessary processing, [9].

Shading effects in object-order volume rendering can be done with the 2D shading technique discussed earlier. One better way is to use gradient information in the shading technique. This method evaluates the gradient at each (x, y) voxel location in the input image where z = D(x, y) is the depth. The estimated gradient vector 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 combincast-ing different techniques and are therefore more used ,[8, 9].

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Chapter 5

Results visualization

techniques

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

5.1 Visualization with slices

Slices are used in clinics to examine the anatomy in the body. The aim with these examinations is to give a correct diagnosis and an accurate treatment plan. In this chapter the results of the two and three dimensional filtering will be presented. The hypothesis is that if volumes are filtered with a three dimensional technique more information is used and therefore the result will be better. The test volume is filtered in both two and three dimensions, noise is added so that the signal is hardly 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 diagonals of a dodecahedron, see figure 5.1 for illustration.

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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 to the right with noise added.

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

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

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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 is shown 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 slice with added noise.

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

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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 investigations for vessel anomalies in about 95 percent of the cases. To evaluate the enhancement effects with 3D filtering visualized with MIP one test volume and two different angiographies 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 orientations as possible and has noise added for evaluation of the enhancement effects in 3D compared to 2D, see figure 5.6.

0 20 40 60 80 0 10 20 30 40 50 60 70 20 30 40

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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 that the noise is almost totally suppressed in the 3D filtered volume while in the 2D filtered volume more noise is preserved.

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

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5.2.2 Evaluation of MRA renal arteries

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

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

The result of the second evaluation showed that the 3D processed volume gave a more correct estimation of the stenosis degree than the unprocessed volume. The 3D processed volume’s stenosis degree was in accordance with the degree of stenosis in the unprocessed slices, while the unprocessed volume gave an overestimation of the stenosis, see figure 5.10. The stenosis degree were later measured in the slice and compared to the MIP visualization of unprocessed, 2D processed and 3D processed angiographies, see table 5.1. The measurements were made with GIMP’s1_{measurement tool and the diameter over a particular intensity level was}

used for the calculation.

Data set Stenosis degree (%)

Axial slice 31

Unprocessed MIP 45

2D processed MIP 42

3D processed MIP 32

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

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Figure 5.10.To the left, 2D processed volume of renal artery stenosis. To the right the 3D processed volume of the stenosis visualized with MIP.

In the third evaluation, the second angiography examination a dataset with low noise level and stenosis degree were used. Two axial slices are shown in figure 5.11. The artery is bending perpendicular to the image plane why two slices must be examined to display the whole diameter.

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

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

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Axial slice 15

Unprocessed MIP 24

2D processed MIP 21

3D processed MIP 17

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 the 3D 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 one MRA of cerebral arteries is used. This angiography gives a good apprehension about how small brain vessels that are visible, figure 5.13 shows the unprocessed and the 3D processed volumes visualized with MIP.

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

To evaluate the enhancement effects of images with less good quality, white noise were added to the volume of the cerebral angiography MRI. A frontal MIP of 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 the 2D processed volume and to the right 3D processed volume

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

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The result of the 2D and 3D processing were studied in other view directions as well. In the axial MIP of the volume the difference between the 2D and 3D processed volume were even more pronounced. Top image in 5.15 shows a part of the 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 added visualized with MIP, to the left the 2D processed volume and to the right 3D processed volume

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

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5.3 Visualization with volume rendering 41

5.3 Visualization with volume rendering

Volume rendering is not frequently used to examine angiography images, but it may be in the future as the technique develops. Volume rendering has advantages compared to MIP in image volumes where structures of low intensities is hidden by structures of higher intensities.

5.3.1 Evaluation of MRA renal arteries

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

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

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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 5.3 and the result from the second MRA is shown in table 5.4.

Axial slice 31

Unprocessed MIP 36

2D processed MIP 36

3D processed MIP 33

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

Axial slice 15

Unprocessed MIP 12

2D processed MIP 15

3D processed MIP 17

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

The results of the measurements of the degree of the stenosis does not show any particular advantage for the 3D processed volume. This might depend on that the transfer functions is not set properly or that the algorithm of the volume rendering 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 rendering a MRA of the cerebral arteries with noise added is used. This is the same data set used in the evaluation of visualization with MIP. The unprocessed volume is shown on top in figure 5.17. The result of the 2D and 3D processed volumes visualized with volume rendering is presented in the bottom of figure 5.17. The transfer functions is set to suppress the noise but there is a limit where the vessels gets suppressed too. In the result it is clear that the 3D processed image volume shows more small vessels and that the noise is more suppressed than in the 2D processed volume. The extra information that the 3D processing gives, even gives a result in the visualization.

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5.3 Visualization with volume rendering 43

Figure 5.17. On top the unprocessed volume of cerebral MRA visualized with volume rendering, 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 in figure 5.18, on top the unprocessed volume and in the bottom the 2D and 3D processed volumes.

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Figure 5.18. On top the unprocessed volume of cerebral MRA visualized with volume rendering, 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 volumes and to give an illustration of the benefits of 3D enhancement processing visualized with different visualization techniques. The results show that in image volumes with a high noise level the 3D processed volumes gives a significant enhanced image quality compared to the 2D processed volumes. These results are shown in slices, MIP and volume rendering. The differences are even more pronounced if the volume is presented in a different view direction than the volume is 2D processed in. In volumes with lower noise levels the differences is not as marked.

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

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5.4 Conclusions 45

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

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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 consists of noise, structures with low contrast and structures with high contrast and can choose how much to suppress or enhance these characteristics. The user also select regions in the volume that consists of planes and lines to set the parameters of the µ- function. This tool gives an initial setting of the enhancement parameters which can be a starting point for further manual adjustments. Another positive aspect of the tool is that one can get an idea of the image properties in different areas 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 much lower than in the test volumes, this gives that the selection of regions must be done 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 image quality, but if the acquisition time is shortened or if the slice thickness is decreased the signal-to-noise ratio will decrease. Theses volumes could be enhanced with the 3D 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 or patients that have problems to lie still, for example patients in acute pain or chil-dren. Another aspect of advantages concerning shortening the acquisition time would be the economic aspect. If the radiology department could perform more examinations a day this would give economic values. Decreasing the slice thickness would also give higher noise levels and a higher resolution. The clinical value of higher resolution would of cause be a possibility to see smaller structures in the image.

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48 Discussion

6.1 Future work

The parameter setting tool is not optimized with respect to speed, i.e calculation of 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 use a 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 weight the characteristics due to the needs. For example if noise reduction is the most important task for one volume the weight function could increase the importance of 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 images with noise added. Next more quantitative studies of estimation of stenosis degree in renal arteries visualized with MIP is needed to get an objective evaluation of the 3D enhancement processing. It would also be interesting to let a reference group of radiologists evaluate the image quality in 3D processed images visualized with 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 shows as good results here.

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Bibliography

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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, Linköping University, Sweden, SE-581 83 Linköping, Sweden, October 1992. Dissertation No 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, June 1989. Report LiTH–ISY–I–1019, Computer Vision Laboratory, Linköping University, Sweden, 1989.

[7] R. A. Robb. Three-dimensional visualization in medicine and biology. In

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

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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.

Visual Evaluation of 3D Image Enhancement

Institutionen för Medicinsk teknik

Department of Biomedical Engineering

Examensarbete

Visual Evaluation of 3

Image Enhancement

Visual Evaluation of 3

Image Enhancement

Examensarbete utfört i Medicinsk teknik

vid Tekniska högskolan i Linköping

av

Abstract

Acknowledgments

Contents

I

Local adaptive filtering

7

II

Visualization techniques

25

List of Figures

List of Tables

Chapter 1

Introduction

1.1

Background

1.1.1

Visualization techniques in clinical use

1.2

Objectives

1.3

Thesis outline

Part I

Local adaptive filtering

Chapter 2

Local adaptive filtering

2.1

Image orientation

2.1.1

Mapping requirements

2.1.2

Interpretation of the orientation tensor

2.2

Calculation of the control tensor

2.2.1

The m-function

2.2.2

The µ-function

2.3

Generation of the adaptive filter

Chapter 3

Enhancement parameter

setting tool, T-morph

3.1

Initial parameter setting of the m-function

3.2

Initial parameter setting of the µ- function

3.3

Result of the parameter setting tool

3.4

Conclusions

Part II

Visualization techniques

Chapter 4

Visualization techniques

4.1

Multi-planar reformatting

4.2

Image-order volume rendering

4.2.1

Maximum intensity projection

4.3

Object-order volume rendering

Chapter 5

Results visualization

techniques

5.1

Visualization with slices

5.1.1

3D enhancement in test volume