BOUNDARY POINT DETECTION FOR ULTRASOUND IMAGE

SEGMENTATION USING GUMBEL DISTRIBUTIONS

Brian Booth and Xiaobo Li

Department of Computing Science, 2-21 Athabasca Hall, University of Alberta, Edmonton AB, Canada, T6G 2E8

Keywords:

Ultrasound Image Processing, Boundary Point Detection, Gumbel Distribution, log-Wiebull Distribution, A-

Mode Ultrasound, Data Fitting, Segmentation.

Abstract:

Due to high noise, low contrast, and other imaging artifacts, region boundaries in ultrasound images often do

not conform to the assumptions of many image processing algorithms. Speciﬁcally, the beliefs that region

boundaries have a high gradient magnitude or a high intensity can break down in this context.

In this paper, we present an alternative way of detecting likely boundary points in ultrasound images by

decomposing the image into one-dimensional intensity scans. These intensity scans, mimicking traditional

A-Mode ultrasound, are modeled using Gumbel distributions. Results show that the relationship between the

modes of these distributions and regions boundaries is relatively strong.

1 INTRODUCTION

Ultrasound image processing, particularly the task of

segmentation, has gained support in both the medical

and agricultural ﬁelds. In the medical ﬁeld, computer

generated segmentation results are used to help diag-

nose heart disease as well as breast and prostate can-

cer (Noble and Boukerroui, 2006). Meanwhile, the

agricultural ﬁeld uses segmentation results to deter-

mine the size of various cuts of meat in live animals.

Current image segmentation algorithms applied in

this ﬁeld use assumptions about the appearance of a

region or its boundary that are common to general im-

age processing. One popular assumption used here is

that a region boundary is characterized by a strong

gradient. This is the foundation of many active con-

tour methods (Kass et al., 1987). Also popular is

the belief that a region boundary has a high intensity,

which has most notably been incorporated into Itti &

Koch’s saliency map algorithm and has a biological

basis (Itti and Koch, 2000). This assumption is of

particular interest in ultrasound image segmentation

as likely region boundaries tend to appear brighter in

ultrasound images than their surroundings (Middleton

et al., 2004).

Algorithms based on these two assumptions have

been used for ultrasound image segmentation with

some success. Gradient-based methods have achieved

good results on a limited subset of ultrasound im-

ages - particularly echocardiographs - where gradient

information is reliable boundary indicator (Yan and

Zhuang, 2003; Corsi et al., 2002). Intensity-based al-

gorithms have achieved mild success on both agricul-

tural and medical ultrasound images, but there is room

for improvement (Booth et al., 2006).

Unfortunately, these segmentation approaches are

limited due to the unique nature of ultrasound images.

These images are obtained in a different medium than

other real world images and have distinct types of

noise and imaging artifacts. Assumptions that have

held for the segmentation of other real world images,

particularly that regions boundaries have a high gra-

dient magnitude or high intensity, though appropriate

for some ultrasound images, generally do not hold.

As a result, it is important to return to the question:

What constitutes an edge in an ultrasound image?

In this paper, we present one approach for detect-

ing edge points in ultrasound images for the purpose

of segmentation. In this approach, a given ultrasound

image is decomposed into one-dimensional intensity

scans with the goal of replicating the original acous-

tical signals obtained by the ultrasound transducer as

179

Booth B. and Li X. (2007).

BOUNDARY POINT DETECTION FOR ULTRASOUND IMAGE SEGMENTATION USING GUMBEL DISTRIBUTIONS.

In Proceedings of the Second International Conference on Signal Processing and Multimedia Applications, pages 175-179

DOI: 10.5220/0002138701750179

 SciTePress

(a) A-Mode Ultrasound

(b) B-Mode Ultrasound

Figure 1: Ultrasound Imaging Types.

well as possible. These intensity scans are then mod-

eled as a probability distribution obtained from mul-

tiple independent Gumbel distributions, each distri-

bution representing a likely region boundary. Using

Expectation-Maximization, a predetermined number

of Gumbel density functions are ﬁtted to each inten-

sity scan. The modes of the ﬁtted distributions are

then taken as likely boundary points.

The algorithm was implemented and tested on 304

ultrasound images of in vivo pork loins and compared

with boundary point selection algorithms based solely

on intensity or gradient magnitude. Our results sug-

gest that there is a stronger relationship between the

modes of the ﬁtted Gumbel distributions and region

boundary points than there is with the other two meth-

ods.

2 METHOD

To recognize the content of ultrasound images, it be-

comes important to understand the process through

which these images are formed. Therefore, a brief in-

troduction to the physics behind ultrasound imaging

is presented here prior to introducing the boundary

point detection algorithm.

2.1 Ultrasound Basics

The most common ultrasound imaging technique is

known as pulse-echo ultrasound. A simpliﬁed exam-

ple of this ultrasound technique is presented in Fig-

ure 2.

A single sound pulse, whose primary direction is

shown as T1, leaves the ultrasound transducer and

proceeds to enter the subject being scanned. As the

sound pulse continues outward, the density of the

medium through which the pulse travels will change.

This occurs most signiﬁcantly at boundaries between

transducer

Figure 2: The Reﬂection and Refraction of Sound Waves

from an Ultrasonic Scanner. As in (Muzzolini, 1996).

two tissues of different densities. When the pulse

reaches these types of acoustical boundaries, a portion

of the pulse reﬂects back towards the transducer while

a now weakened pulse refracts further into the sub-

ject. Once the reﬂected portion of the sound wave, re-

ferred to as an echo, returns to the transducer, its am-

plitude is recorded and using the formula distance =

2 ∗ velocity ∗ time, the depth at which the echo was

produced can be determined (Muzzolini, 1996).

Using a single transducer, the best we can do is

a one-dimensional scan known as an A-Mode (am-

plitude mode) scan. An example of such a scan is

presented in Figure 1(a). To create a two-dimensional

image, known as a B-Mode (brightness mode) scan,

an array of transducers are used. As a result, an ul-

trasound image is often considered as an array of A-

Mode ultrasound scans. An example of B-Mode ultra-

sound is shown in Figure 1(b). Pixel intensity in an ul-

trasound image corresponds directly to the amplitude

of the echoes received by the associated transducer.

In an ultrasound image, the transducer array can be

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180

pictured as being at the top with each column of the

image representing an A-Mode ultrasound scan.

This form of image acquisition is susceptible to

noise for many reasons. First, most of our internal

tissues do not have a homogeneous density, result-

ing in echoes being recorded that are not near tissue

boundaries. The superposition of echoes that origi-

nated from different transducers also adds a particular

type of high intensity noise known as speckle noise.

However, the most problematic issue with ultrasound

in terms of noise is movement of the subject. Sim-

ply breathing can move tissue boundaries in ways that

distort the image (Middleton et al., 2004).

There are also many imaging artifacts common to

ultrasound, of which we mention two of particular in-

terest. First, note in Figure 2 that the strength of the

echoes recorded by the transducer will depend on the

angle at which the sound pulse meets a tissue bound-

ary. As a result, the amplitude of an echo, and in

turn the pixel intensity in an ultrasound image, will

be lower the less perpendicular a tissue boundary is to

the incident sound pulse.

Secondly, as an echo returns to the transducer, it

is common for a portion of the echo to reﬂect off the

transducer surface and reverberate between the trans-

ducer and the skin of the subject. This results is a

decay in amplitude after a strong echo is received in-

stead of a sharp drop-off (Muzzolini, 1996).

These two artifacts, combined with the amount of

noise common in ultrasound images, are the key rea-

sons why gradient magnitude and intensity may not,

on their own, be able to detect region boundaries. Fur-

thermore, the two imaging artifacts mentioned here

produce a distinctive pattern of echo responses for

a likely tissue boundary. In particular, the orienta-

tion dependence of the echoes results in a gradual rise

and fall in echo intensity around the depth of the tis-

sue boundary, while the reverberation of these echoes

leads to a decay in echo intensity following the tis-

sue boundary. This phenomenon can be seen in Fig-

ure 1(a).

2.2 Algorithm Description

The goal of the algorithm presented herein is to ob-

tain boundary points in ultrasound images by taking

advantage of the aforementioned physical properties

of ultrasound imaging. To achieve this goal, we de-

compose the given ultrasound images into its separate

columns and treat these columns as A-Mode ultra-

sound scans. Despite losing some spatial information

through this decomposition, we hope to gain an ad-

vantage by mimicking the original acoustical signal as

much as possible. Henceforth, we will be considering

one-dimensional scans similar to the one presented in

Figure 1(a).

By visual inspection, we note that the echo pat-

tern for a likely tissue boundary in an A-Mode scan

is similar in shape to the Gumbel probability distri-

bution, which is given by the following probability

density function:

f(x;µ, β) =

−

x−µ

−e

−

x−µ

(1)

The parameters, µ and β, represent the mode and

the spread of the density function respectively. A

graph of a sample Gumbel probability density func-

tion is presented in Figure 3.

Figure 3: A Sample Gumbel Distribution (µ = 0, β = 1).

Due to the similarities in shape, we model the in-

tensity distribution for the echoes from a potential

tissue boundary as a Gumbel distribution. An inde-

pendent collection of Gumbel distributions are ﬁtted

to each A-Mode ultrasound scan using Expectation-

Maximization. Though it is clear that the echoes cre-

ated from deeper tissue boundaries are not indepen-

dent of the echoes from earlier tissue boundaries, the

intensity distributions from these echoes still retain

the same shape.

To use Expectation-Maximization, the number of

Gumbel distributions to ﬁt to - and thereby the num-

ber of tissue boundaries in - each A-Mode scan must

be known ahead of time. The following algorithm is

used to estimate this number:

for i = 1:20,

- Fit a polynomial of degree i

to the A-Mode scan

- err[i] = average error between

the fitted polynomial and the

A-Mode scan

endfor

minDeg = i, where err[i] == min(err);

numGD = ceil(minDeg / 2);

Polynomials of various degrees are ﬁtted to each

A-Mode scan using the Least Mean Squared algo-

BOUNDARY POINT DETECTION FOR ULTRASOUND IMAGE SEGMENTATION USING GUMBEL

DISTRIBUTIONS

181

Table 1: Results for ﬁve different boundary point selection algorithms over 304 ultrasound images of in vivo pork loins.

Boundary Point Distance from Actual Boundary (in pixels) Percentage

Detection Algorithm Mean Std. Deviation Maximum Outliers

Gumbel Dist. Fitting 10.661± 2.329 7.356± 1.916 34.668± 8.661 87.768± 2.185

Intensity (equal number) 29.268± 8.844 27.823± 7.792 98.226± 23.406 87.270± 2.262

Gradient (equal number) 16.168± 5.964 15.374± 6.699 62.001± 23.034 88.837± 2.205

Intensity (top 13%) 3.922± 2.002 6.210± 3.235 28.209± 12.441 97.172± 0.252

Gradient (top 13%) 1.795± 0.581 2.155± 0.945 11.904± 4.891 97.350± 0.224

rithm. While these polynomials do not relate well

to the tissue boundaries represented in the scan, the

degree of the polynomial of best ﬁt can be related to

the number of Gumbel distributions to ﬁt to the scan.

The polynomial’s degree is divided by two on account

of the Gumbel distribution’s roughly parabolic shape.

An example of an A-Mode scan ﬁtted with Gumbel

distributions is shown in Figure 4.

Figure 4: An A-Mode Scan Fitted with Three Gumbel Dis-

tributions. The Gumbel Distributions are Scaled for View-

ing Purposes.

The modes of the ﬁtted Gumbel distributions are

taken as the most likely locations of the tissue bound-

aries the distributions represent.

3 EXPERIMENTAL RESULTS

The proposed boundary point detection algorithm was

implemented and tested on a set of 304 ultrasound

images of in vivo pork loins. The ultrasound im-

ages were recorded with an Aloka Flexus Model SSD-

1100 equipped with a 3.5MHz/127mm transducer Ul-

trasound system. The images are from between the

3rd and 4th ribs from the last rib and 7cm off the mid-

line of the pigs. This collection of images includes

the thirty-eight images used in (Booth et al., 2006).

For each image, we compare the detected bound-

ary points with a manually traced contour created

by an expert. The distance between each point on

the manually traced contour and the closest bound-

ary point is measured. The average, standard devia-

tion, and maximum values of these distances are cal-

culated for each image. Also calculated is the per-

centage of detected boundary points that are not the

closest boundary point for any of the points on the

manually traced contour.

The set of boundary points obtained by the pro-

posed algorithm are compared with those obtained by

thresholding based on intensity and gradient magni-

tude. Two thresholds are used: one which provides

an equal number of boundary points, and one that

gives thirteen percent of the image’s pixels as bound-

ary points. The second threshold is essentially the

same one used on intensity in (Booth et al., 2006).

Table 1 displays results for all ﬁve approaches.

Means and standard deviations for each measure are

provided over all images in the set.

Given an equal number of detected boundary

points, the intensity and gradient methods detect

points that have a much larger average distance to

the contour as well as a larger standard deviation than

the proposed approach, suggesting in those two cases

that large portions of the contour do not have any de-

tected boundary points nearby. Increasing the number

of likely boundary points in the intensity and gradi-

ent methods does seem to alleviate this problem, but

also introduces a signiﬁcant amount of outliers, which

suggests that the relationship between those measures

and the contour are not as strong as with the proposed

algorithm.

Visual inspection appears to conﬁrm that this is

in fact what is happening. Figure 5 shows the re-

sults from all ﬁve algorithms on an average case. De-

spite obvious outliers due to noise and other anatomi-

cal structures, boundary points are detected near large

portions of the contour using the presented approach.

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182

(a) Original Image with Contour

(b) Gumbel Distribution Fitting (c) Intensity (equal number)

(d) Gradient (equal number) (e) Intensity (13%)

(f) Gradient (13%)

Figure 5: Sample Boundary Point Detection Results from an Average Case for our Algorithm and Four Others. The Contour

is Displayed in Green while the Detected Boundary Points are Shown in White.

4 CONCLUSION

Given the different medium from which ultrasound

images are created, general assumptions about how

an edge is represented break down. Using knowledge

of how the images are acquired, we present a bound-

ary point detection algorithm that ﬁts Gumbel dis-

tributions to mimicked A-Mode scans obtained from

an ultrasound image. Results on 304 in vivo pork

loin ultrasound images show that the relationship be-

tween the modes of the Gumbel distributions and ac-

tual boundary points is stronger than methods based

on other general image processing assumptions.

ACKNOWLEDGEMENTS

We gratefully acknowledge Dr. Alan Tong of La-

combe Research Centre, Agriculture and Agri-Food

Canada for providing the ultrasound image data for

this study. Also, thanks to the Natural Sciences and

Engineering Research Council of Canada (NSERC)

and the Informatics Circle of Research Excellence

(iCORE) for funding this project.

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BOUNDARY POINT DETECTION FOR ULTRASOUND IMAGE SEGMENTATION USING GUMBEL

DISTRIBUTIONS

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