Visual Evaluation of 3D Image Enhancement

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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.

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.
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.

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.

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) (2.1)
H 2(u) + η2 (u)
where H 2(u) is the spectrum of the signal and η2 (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 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 steps will be given in this chapter. The theory of local adaptive filtering is valid for multidimensional signals, [10].

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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 magnitude 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.

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 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 T = 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 magnitude of 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−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: T 2 ≡ tij2 =λn2 (2.8) ij n

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].

Table of contents :

1 Introduction 
1.1 Background
1.1.1 Visualization techniques in clinical use
1.2 Objectives
1.3 Thesis outline
I Local adaptive filtering 
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
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
II Visualization techniques 
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
5 Results visualization techniques 
5.1 Visualization with slices
5.1.1 3D enhancement in test volume
5.2 Visualization with MIP
5.2.1 Evaluation of test volume
5.2.2 Evaluation of MRA renal arteries
5.2.3 Evaluation of MRA cerebral arteries
5.3 Visualization with volume rendering
5.3.1 Evaluation of MRA renal arteries
5.3.2 Evaluation of MRA cerebral arteries
5.4 Conclusions
6 Discussion 
6.1 Future work
Bibliography 

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