WAVELET BASED EXTRACTION OF BLOOD VESSELS

Hammad Omer and Ali Hojjat

Medical Image Computing, KIMHS, University of Kent, Canterbury, CT27PD, U.K.

Keywords: Vessel segmentation, Wavelet coefficients, Image reconstruction, Image enhancement.

Abstract: An algorithm for the segmentation of blood vessels based on the correlation of different wavelet scales is

presented. First the wavelet coefficients are computed for a defined number of scales and then the

correlation between the corresponding coefficients of two consecutive scales is computed. The normalized

product is used as a reference threshold for retaining original wavelet coefficients. If the normalized product

is greater than the corresponding original wavelet coefficient, the original coefficient is retained for image

reconstruction by inverse wavelet transform, otherwise the coefficient is changed with zero value. Low

frequency wavelet coefficients matrix is not used in image reconstruction process as we want only the edge

information. The proposed algorithm is quite general and can be used for the extraction of any type of blood

vessels and provides very promising results.

1 INTRODUCTION

Blood vessel identification and extraction in medical

images is an important step in many medical image

analysis applications e.g. diagnosis of the vessel

stenosis, development of models to analyze different

medical conditions, multimodal image registration

etc. Many vessel extraction techniques have been

proposed in the past. Cemil and Francis (Cemil and

Francis, 2004) presented a very good review of

many such techniques developed in the recent past.

Some of the techniques are suitable for a particular

type of blood vessel extraction e.g. retinal blood

vessels, abdominal blood vessels etc. This limits the

use of these approaches to a particular type of

application only. The vessel segmentation

algorithms developed so far may be broadly

categorized into six main categories (Cemil and

Francis, 2004): 1) pattern recognition techniques, 2)

model-based approaches, 3) tracking based

approaches, 4) artificial intelligence based

approaches 5) neural network based approaches, 6)

tube-like object detection approaches. More details

of these approaches can be found in (Cemil and

Francis, 2004). The blood vessel segmentation

approach presented here is based on correlation of

wavelet coefficients and is based on the idea

presented by Xu (Xu et al., 1994). The approach is

quite general and can be applied to any type of blood

vessels quite confidently.

2 METHODOLOGY

Wavelets constitute a tool to decompose, analyze

and synthesize functions with an emphasis on time-

frequency localization (Omer et al.). Wavelets are

families of functions generated from a single base

wavelet by dilations and translations. The wavelet

coefficient at scale j and time k is calculated as:

∫

+∞

∞−

−= duukuekjWe

)()(),(

(Eq.1)

where

is the wavelet at scale j.

The wavelet transform W(s,t) gives us a scale-

space decomposition of signals and with simple

modifications, images. They help in breaking

complicated signals into simpler components and

can be used in the analysis of complex signals, in the

segmentation or detection of particular features, and

in compression as well as de-noising images. Infact,

wavelets decompose a signal into different

resolution scales.

In a one-level Fast Wavelet Transform (FWT), a

signal C

is split into an approximation part C

i+1

and

a detail part D

i+1.

In a multilevel FWT, each

subsequent C

is split into an approximation C

i+1

and

detail Di+1. For 2-D images, each C

is split into an

approximation C i+1 and three detail channels D

i+1,

i+1

for horizontally, vertically and

diagonally oriented details of the image,

529

Omer H. and Hojjat A. (2009).

WAVELET BASED EXTRACTION OF BLOOD VESSELS .

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing, pages 529-534

DOI: 10.5220/0001558005290534

 SciTePress

respectively. Figure 1 is an illustration of this

process. The inverse FWT (IFWT) reconstructs each

from C

i+1

and D

i+1

. This transform and its

inverse are called the Fast Wavelet Decomposition

(FWD) and Fast Wavelet Reconstruction (FWR),

respectively, see (Westenberg and Roderdink, 2000)

for more details.

Figure 1: Ordering of the approximation and detail

coefficients of a two-level 2-D non standard FWT.

Signals and noise behave very differently in

wavelet transform domain. Singularities are more

regular than noise(Xu et al., 1994). The evolution of

singularities and noise across wavelet scales were

analyzed by Mallat et al (Mallat and Hwang, 1992),

(Mallat and Zhong, 1992) and reiterated by Paul Bao

et al (Bao and Zhang, 2003).

As shown in the Figure 2, the edges in a signal

(or image) are represented by large wavelet

coefficients at the corresponding spatial locations

and tend to propagate through the scales. Using a

simple low pass filter would introduce heavy

blurring due to the cutoff of useful components at

the finer scales (at higher frequencies). To retain the

useful high frequency image features as well, it is

very important to distinguish between the high

frequency contributions from the actual signal and

those from the noise. Infact, most of the signal

features contributing to high frequencies also

contribute to low frequencies at the same spatial

locations. Hence there will be correlation between

wavelet coefficients of the useful image signal (such

as edges and spikes) at different scales. In the case

of noise, the correlation is much smaller. For this

reason, the correlation across scales is used to

distinguish between noise contribution and signal

features at high frequencies.

So, wavelets are used for subband decomposition

of a signal (or image). The approach has been to

detect edges directly on the wavelet transform data

algorithm, such as those introduced in (Witkin,

1983), (Fu et al., 2008). Xu(Xu et al., 1994) adopted

the direct multiplication of wavelet transform data

(sub-band decompositions of an image) at adjacent

scales to distinguish important edges from noise and

accomplish the task of removing noise from signals.

In practice, it is sufficient to implement the

multiplication at two adjacent scales. So, the DWT

scale products can be calculated as:

f(x)=W

f(x).W

f(x) (Eq.2)

Similarly, for 2D images, the multiscale products

have two components:

f(x,y)=W

f(x,y) W

f(x,y) (Eq.3)

f(x,y)=W

f(x,y) . W

f(x,y) (Eq.4)

Figure 3 shows the DWT and multi-scale products

of a noisy test signal f where

ൌ݃൅߳

(Eq.5)

Figure 2: a) DWT of a test signal g at the first four scales. b) The DWT of a sequence of Gaussian white noise at the first

four scales (Bao and Zhang, 2003).

BIOSIGNALS 2009 - International Conference on Bio-inspired Systems and Signal Processing

530

Figure 3: The DWT and multi-scale products of a noisy test signal at the first three scales (Bao and Zhang, 2003).

Although the wavelet transform coefficients of

the original signal ‘g’ are immersed into noise ‘ε’ at

fine scales, they are enhanced in the scale products

f. The significant features of ‘g’ are more

distinguishable in P

f than in W

f (Bao and Zhang,

2003).

We calculate the correlation of the wavelet

coefficient across consecutive scales starting from

the first scale to the last. Since there is no down

sampling, the j

scale has the same number of

coefficients as the first scale. We also estimate the

noise power at each level by observing the wavelet

transform of a small region of interest corresponding

to background signal. We assume the background

signal contains the same noise components as the

image. The position at which Corr

is smaller or

equal to that relative to the estimated noise (taken as

threshold value), the coefficient is changed to zero.

Thus the filtering process consists of, first,

calculating the wavelet decomposition and

correlation between different levels and then, if the

correlation value is lower than a threshold value, the

wavelet coefficient to which it refers is assigned a

value of zero, otherwise it is left unchanged (Bao

and Zhang, 2003). The technique can be considered

as a spatially dependant filter (it can be

demonstrated as a spatially dependant mask); it

spatially selects which part of the data is to be kept

(the edges) and which part of the data to eliminate

(noise); the signal is passed where the wavelet

transform is highly correlated across scales and

suppressed elsewhere. (Xu et al., 1994)

The absence of edges or other significant

features in a localized region of the signal allows the

noisy background to be removed. The thresholding

in wavelet domain over several scales sharpens the

image which results in enhancement of major edges

while suppressing noise. This also improves the

accuracy of locating important edges in images. This

method is simple and performs well on MRA images

of the head.

3 ALGORITHM

The proposed algorithm is based on the

identification of important vessel edges by

correlation between different scales of Wavelets.

The flow chart of the algorithm is shown in Figure 4

and can be discussed in the following steps:

1) The size of the input image is computed.

WAVELET BASED EXTRACTION OF BLOOD VESSELS

531

Figure 4: Flow-chart for proposed algorithm for Wavelet Based Vessel Edge Extraction.

2) Three masks are initialized with zero

values. The size of the masks is equal to

that of the original image.

3) The wavelet transform of the input image is

computed for a defined number of scales.

The output of this stage is a set of four

matrices (Low Frequency coefficients, High

Frequency Coefficients in horizontal

direction, High Frequency coefficients in

vertical direction and High Frequency

coefficients in diagonal direction) for each

scale.

BIOSIGNALS 2009 - International Conference on Bio-inspired Systems and Signal Processing

532

Figure 5: [Left] Time of Flight (TOF) MRA of the circle of Willis [Right] Edges enhanced image by the proposed

algorithm.

4) These wavelet coefficients are saved for

later retrieval.

5) The product of the two horizontal detail

coefficient matrices in two consecutive

scales is computed and the same process is

repeated for the vertical as well as diagonal

detail coefficients and for all resolution

levels/scales.

6) The product (i.e. Energy) computed in the

previous step is normalized to that of the

original wavelet coefficients. It enables us

to compare the power of the product to that

of the original wavelet coefficients.

7) A comparison is made between the

normalized product and the original

wavelet coefficients. If the Normalized

product is greater than the corresponding

original wavelet coefficient, the mask value

at the corresponding location is set to 1

otherwise it remains as zero.

8) The masks are multiplied with the original

wavelet and thus only the coefficients

related to edges are retained and others are

lost.

9) The inverse wavelet transform is computed

based on the processed wavelet

coefficients. At this stage, we use only the

processed detail coefficients (i.e.

Horizontal, Vertical and Diagonal) and do

not use the low frequency related wavelet

coefficients.

4 RESULTS AND DISCUSSION

The above algorithm was applied on MRA images

of Circle of Willis and the results obtained were very

good with improved boundaries about blood vessel

edges. The output image showed a clear suppression

of the noisy parts of the image. One important

observation was regarding the number of scales to

be used to find inter-scale correlation which is a

primary measure to identify which wavelet

coefficients belong to the actual signal and which

are representing noise. The use of more than two

scales, causes the loss of much of the edge related

information along with the noisy coefficients and the

reconstructed image does not give very clear

representation of the actual vessel edges. The best

results are obtained with two scales used as almost

all the edges are retained and are very clearly visible

in the resulting image.

Another advantage of this approach is that the

coefficients which are more likely related to noise

are removed during this process of correlation and in

this way, the result is containing noise free edge

information. Figure 5 presents the results of this

algorithm on an MRA image. The left hand side

shows the original MRA image and the image on the

right shows the enhanced image.

5 CONCLUSIONS

We propose a vessel extraction technique based on

normalized inter-scale energy in wavelet domain

which proves to be a very good tool to identify

vessel edges. The noise level in the image is also

WAVELET BASED EXTRACTION OF BLOOD VESSELS

533

reduced. The wavelet coefficients with small

information at the higher scales are removed as they

are more probably associated with noise. The image

reconstruction involves the computation of inverse

wavelet transformation of the processed detailed

coefficients and suppressed low frequency

coefficients. The resulting image contains only the

contours of the blood vessels. This algorithm makes

no assumption about the vessel shapes so it can be

applied to the vessels of any part of the body. The

future work may involve the optimization of the

proposed algorithm. This algorithm is applied onto

MIP (Maximum Intensity Projection) image of Time

of Flight MRI image in which 3D data is mapped on

a 2-D plane. During this process of image

projection, some important information is lost. If this

algorithm could be extended to 3D data, so that the

algorithm would not be applied on 2D projection

image but directly on the 3D image. It will improve

the quality of the reconstructed image. Furthermore,

since 3D involves huge quantity of data to be

processed, introduction of some parallel approach

may considerably reduce the computational time.

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