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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 58, NO. 3, MARCH 2011 567

Boundary Detection in Medical Images Using EdgeFollowing Algorithm Based on Intensity Gradient

and Texture Gradient FeaturesKrit Somkantha, Nipon Theera-Umpon*, Senior Member, IEEE,

and Sansanee Auephanwiriyakul, Senior Member, IEEE

AbstractFinding the correct boundary in noisy images is stilla difficult task. This paper introduces a new edge following tech-nique for boundary detection in noisy images. Utilization of theproposed technique is exhibited via its application to various typesof medical images. Our proposed technique can detect the bound-aries of objects in noisy images using the information from theintensity gradient via the vector image model and the texture gra-dient via the edge map. The performance and robustness of thetechnique have been tested to segment objects in synthetic noisyimages and medical images including prostates in ultrasound im-ages, left ventricles in cardiac magnetic resonance (MR) images,aortas in cardiovascular MR images, and knee joints in computer-ized tomography images. We compare the proposed segmentationtechnique with the active contour models (ACM), geodesic activecontour models, active contours without edges, gradient vector flowsnake models, and ACMs based on vector field convolution, by us-ing the skilled doctors opinions as the ground truths. The resultsshow that our technique performs very well and yields better per-formance than the classical contour models. The proposed methodis robust and applicable on various kinds of noisy images withoutprior knowledge of noise properties.

IndexTermsBoundary extraction, edge detection, edge follow-ing, image segmentation, vector field model.

I. INTRODUCTION

IMAGE segmentation is an initial step before performing

high-level tasks such as object recognition and understand-

ing. Image segmentation is typically used to locate objects and

boundaries in images. In medical imaging, segmentation is im-

portant for feature extraction, image measurements, and im-

Manuscript received June 22, 2010; revised October 3, 2010 and October 28,2010; accepted October 29, 2010. Date of publication November 9, 2010; dateof current version February 18, 2011. This work was supported in part by agrant under the program Strategic Scholarships for Frontier Research Networkfor Ph.D. Program Thai Doctoral degree from the Commission on Higher Edu-cation, Thailand. Asterisk indicates corresponding author.

K. Somkantha is with the Department of Electrical Engineering, Facultyof Engineering, Chiang Mai University, Chiang Mai 50200, Thailand (e-mail:[email protected]).

*N. Theera-Umpon is with the Department of Electrical Engineering, Facultyof Engineering, and the Biomedical Engineering Center, Chiang Mai University,Chiang Mai 50200, Thailand (e-mail: [email protected]).

S. Auephanwiriyakul is with the Department of Computer Engineering, Fac-ulty of Engineering, and the Biomedical Engineering Center, Chiang Mai Uni-versity, Chiang Mai 50200, Thailand (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TBME.2010.2091129

age display. In some applications it may be useful to extract

boundaries of objects of interest from ultrasound images [1],

[2], microscopic images [3][5], magnetic resonance (MR) im-

ages [6][8], or computerized tomography (CT) images [9],

[10]. Segmentation techniques can be divided into classes in

many ways, depending on the classification scheme. The most

commonly used segmentation techniques can be categorized

into two classes, i.e., edge-based approaches and region-basedapproaches. The strategy of edge-based approaches is to de-

tect the object boundaries by using an edge detection operator

and then extract boundaries by using the edge information. The

problem of edge detection is the presence of noise that results

in random variation in level from pixel to pixel. Therefore, the

ideal edges are never encountered in real images [11], [12]. A

great diversity of edge detection algorithms have been devised

with differences in their mathematical and algorithmic proper-

ties such as Roberts, Sobel, Prewitt, Laplacian, and Canny, all of

which are based on the difference of gray levels [13][16]. The

difference of gray levels can be used to detect the discontinu-

ity of gray levels. On the other hand, region-based approaches

are based on similarity of regional image data. Some of the

more widely used approaches are thresholding, clustering, re-

gion growing, and splitting and merging [17]. However, the

performance evaluation of image segmentation results is still a

challenging problem as they fail to extract the correct boundaries

of objects in noisy images.

In recent years, there have been several new methods to

solve the problem of boundary detection, e.g., active contour

model (ACM), geodesic active contour (GAC) model, active

contours without edges (ACWE), gradient vector flow (GVF)

snake model, vector field convolution (VFC) snake model, etc.

The snake models have become popular especially in bound-

ary detection where the problem is more challenging due to thepoor quality of the images. The ACMs also known as snakes

are curves defined within an image domain that can be moved

under the influence of the internal energy and external en-

ergy [18][20]. The internal energy is designed to keep the

model smooth during deformation. The external energy is de-

signed to move the model toward an object boundary or other

desired features within an image. However, the snake has weak-

nesses and limitations of small capture range and difficulties

progressing into concave boundary regions. The GAC model is

an extension of the ACM by taking into account of the geo-

metric information of an image [21]. An ACM based on curve

evolution and level sets, namely the ACWE, can detect objects

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568 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 58, NO. 3, MARCH 2011

boundaries that are not necessarily defined by gradient [22]. The

GVF is an ACM with a new external energy [23], [24]. This new

external energy is computed as a diffusion of gray-level gradient

vector of a binary edge map derived from the image. The resul-

tant field has a large capture range and forces active contours

into concave regions. VCF was applied as a new external energy

of an ACM and proved to be better than the existing snake mod-els [25]. However, when an image is highly noisy and possesses

a complex background, determining the correct boundaries of

objects from the gradients is not easy. Most of the methods of

snake models require a very accurate initial contour estimate

of the object. The contour of snake models can converge to a

wrong boundary if the initial contour is not close enough to the

desired boundary.

Though many algorithms for boundary detection have been

developed to achieve good performance in field of image pro-

cessing, most algorithms for detecting the correct boundaries

of objects have difficulties in medical images in which ill-

defined edges are encountered [26][28]. Medical images are

often noisy and too complex to expect local, low level opera-tions to generate perfect primitives. The complexity of medical

images renders the correct boundary detection very difficult.

To remedy the problem, we propose a new technique for

boundary detection for ill-defined edges in noisy images using a

novel edge following. The proposed edge following technique is

based on the vector image model and the edge map. The vector

image model provides a more complete description of an image

by considering both directions and magnitudes of image edges.

From the vector image model, a derivative-based edge operator

is applied to yield the edge field [29]. The proposed edge vector

field is generated by averaging magnitudes and directions in

the vector image. The edge map is derived from Laws texturefeature [30] andthe Canny edge detection[31]. Thevector image

model and the edge map are applied to select the best edges.

This paper is organized as follows. Section II describes the

proposed boundary detection technique. In section III, we show

the experimental results on the synthetic noisy images, prostate

ultrasound images, left ventricle in cardiac MR images, aorta in

cardiovascular MR images, and knee joints in CT images. The

results of our technique are compared with that of five snake

models by using the opinions of skilled doctors as the ground

truth. Section IV concludes this paper.

II. BOUNDARY EXTRACTION ALGORITHM

A. Average Edge Vector Field Model

We exploit the edge vector field to devise a new boundary

extraction algorithm [29]. Given an image f(x, y), the edge

vector field is calculated according to the following equations:

e(i, j) =1

k(Mx (i, j)i + My (i, j)j) (1)

e(i, j) 1k

f(x, y)

yi f(x, y)

xj

(2)

k = maxi, j

Mx (i, j)2

+ My (i, j)2

. (3)

Fig. 1. (a) Original unclear image. (b) Result from the edge vector field andzoomed-in image. (c) Result from the proposed average edge vector field andzoomed-in image.

Each component is the convolution between the image and the

corresponding difference mask, i.e.,

Mx (i, j) = Gy f(x, y) f(x, y)y

(4)

My (i, j) = Gx f(x, y) f(x, y)x

(5)

where Gx and Gy are the difference masks of the Gaussian

weighted image moment vector operator in the x and y direc-

tions, respectively, [29]

Gx (x, y) =12

x

x2 + y2

exp

x

2 + y2

22

(6)

Gy (x, y) =1

2 y

x2 + y2

expx

2 + y2

22

. (7)

Edge vectors of an image indicate the magnitudes and directions

of edges which form a vector stream flowing around an object.

However, in an unclear image, the vectors derived from the edge

vector field may distribute randomly in magnitude and direction.

Therefore, we extend the capability of the previous edge vector

field by applying a local averaging operation where the value of

each vector is replaced by the average of all the values in the

local neighborhood, i.e.,

M(i, j) =1

Mr (i, j )N

Mx (i, j)2 + My (i, j)2 (8)

D(i, j) =1

Mr

(i, j )N

tan1

My (i, j)

Mx (i, j)

(9)

where Mr is the total number of pixels in the neighborhood N.

We apply a 3 3 window as the neighborhood N throughoutour research.

An example of the edge vector field and average edge vector

field is displayed in Fig. 1. Fig. 1(b) and (c) shows the results

of the edge vector field and average edge vector field of the

original image in Fig. 1(a). From the result, we can see that

our proposed edge vector field yields more descriptive vectors

along the object edge than that of the original edge vector field.

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SOMKANTHA et al.: BOUNDARY DETECTION IN MEDICAL IMAGES USING EDGE FOLLOWING ALGORITHM 569

Fig. 2. (a) Synthetic noisy image. (b) Left ventricle in the MR image.(c) Prostate ultrasound image. (d)(f) Corresponding edge maps derived fromLaws texture and Canny edge detection.

This idea is exploited for the boundary extraction algorithm of

objects in unclear images.

B. Edge Map

Edge map is edges of objects in an image derived from Laws

texture and Canny edge detection. It gives important information

of the boundary of objects in the image that is exploited in a

decision for edge following.

1) Laws Texture: The texture feature images of Laws tex-

ture are computed by convolving an input image with each of the

masks. Given a column vector L = (1,4,6,4,1) T , the 2-D maskl(i, j) used for texture discrimination in this research is gener-

ated by L

LT . The output image is obtained by convolving

the input image with the texture mask.2) Canny Edge Detection: The Canny approach to edge de-

tection is optimal for step edges corrupted by white Gaussian

noise. This edge detector is assumed to be the output of a filter

that reduces the noise and locates the edges. The first step of

Canny edge detection is to convolve the output image obtained

from the aforementioned Laws texture t(i, j) with a Gaussian

filter. The second step is to calculate the magnitude and direc-

tion of the gradient. The third step is nonmaximal suppression

to identify edges. The broad ridges in the magnitude must be

thinned so that only the magnitudes at the points of the greatest

local change remain. The last step is the thresholding algorithm

to detect and link edges. The double threshold algorithm is usedto detect and link edges.

Edge map shows some important information of edge. This

idea is exploited for extracting objects boundaries in unclear

images. Examples of the edge maps are shown in Fig. 2.

C. Edge Following Technique

The edge following technique is performed to find the bound-

ary of an object. Most edge following algorithms take into

account the edge magnitude as primary information for edge

following. However, the edge magnitude information is not ef-

ficient enough for searching the correct boundary of objects in

noisy images because it can be very weak in some contour areas.

Fig. 3. Edge masks used for detecting of image edges (normal directionconstraint).

This is exactly the reason why many edge following techniques

fail to extract the correct boundary of objects in noisy images. To

remedy the problem, we propose an edge following technique

by using information from the average edge vector field and

edge map. It gives more information for searching the boundary

of objects and increases the probability of searching the correct

boundary. The magnitude and direction of the average edge vec-

tor field give information of the boundary which flows around

an object. In addition, the edge map gives information of edgewhich may be a part of object boundary. Hence, both average

edge vector field and edge map are exploited in the decision of

the edge following technique. At the position (i, j) of an image,

the successive positions of the edges are then calculated by a

3 3 matrix

Lij (r, c) = Mij (r, c) + Dij (r, c) + Eij (r, c)

0 r 2, 0 c 2 (10)

where , , and are the weight parameters that control the

edge to flow around an object. The larger value of an element in

Lij

indicates the stronger edge in the corresponding direction.

The 3 3 matrices Mij , Dij and Eij are calculated as follows:

Mij (r, c) =M(i + r 1, j + c 1)

maxi, j M(i, j)(11)

Dij (r, c) = 1 |D(i, j) D(i + r 1, j + c 1)|

(12)

Eij (r, c) = E(i + r 1, j + c 1), 0 r 2,0 c 2 (13)

where M(i, j) and D(i, j) are the proposed average magnitude

and direction of edge vector fields as shown in (8) and (9).

E(i, j) is the edge map from Laws texture and Canny edge

detection. It should be noted that the value of each element in

the matrices Mij , Dij, and Eij are ranged between 0 and 1.

Let Ck , k = 1, 2, . . . , 8, be the constraint masks of edgefollowing to the next direction in object boundary as shown

in Fig. 3. The constraint mask is selected by considering the

direction of the vector model at a position (i,j). The mask which

hasa similarity in directionof vector is selected to suit thechosen

constraint of edge following. The value of each element in each

mask dictates the corresponding direction. At the position (i,j),

the next direction of the edge following technique is selected as

the direction that gives the maximum value of the element-wise

multiplication results between Lij and Ck . The next direction

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Fig. 4. (a) Edge map [E(i, j)]. (b) Results of counting the connected pixels[C(i, j)]. (c) Density of edge length [L(i, j)].

can be calculated by

Dij,opt = arg maxk

2r =0

2c= 0

Lij (r, c)Ck (r, c) (14)

where k = 1,2, . . ., 8 denotes the eight directions as indicated bythe arrows at the center of the masks shown in Fig. 3. The edge

following is started from the initial position to end position.

D. Initial Position

In this section, we present a technique for determining a

good initial position of edge following that can be used for

the boundary detection. The initial position problem is very

important in the classical contour models. Snake models can

converge to a wrong boundary if the initial position is not close

enough to the desired boundary. Finding the initial position of

the classical contour models is still difficult and time consuming

[32], [33]. In this proposed technique, the initial position of edge

following is determined by the following steps.

The first step is to calculate the average magnitude [M(i, j)]using (8). The position with high magnitude should be a good

candidate of strong edges on the image. The second step is to

calculate the density of edge length for each pixel from an edge

map. An edge map [E(i, j)], as a binary image, is obtained

by Laws texture and Canny edge detection. The idea of using

density is to obtain measurement of the edge length. The density

of edge length [L(i, j)] in each pixel can be calculated from

L(i, j) =C(i, j)

maxi, j C(i, j)(15)

where C(i,j) is the number of connected pixels at each position

of pixel. An example of counting the number of connected pixelsis shown in Fig. 4(a) and (b). The density of edge length from

the example is shown in Fig. 4(c). The third step is to calculate

the initial position map P(i, j) from summation of average

magnitude and density of edge length, i.e.,

P(i, j) =1

2(M(i, j) + L(i, j)). (16)

The last step is the thresholding of the initial position map. We

have to threshold the map in order to detect the initial position

of edge following. IfP(i, j) > Tm ax , then P(i, j) is the initial

position of edge following. We obtained the initial position by

setting Tm ax to 95% of the maximum value. Theinitial positions

from our method are positions that are close to the edges of

Fig. 5. (a) Aorta in cardiovascular MR image. (b) Averaged magnitude[M(i, j)]. (c) Density of length edge [L(i, j)]. (d) Initial position map [P(i, j)]and initial position of edge following derived by thresholding Tm ax = 0.95.

interested areas. An example of the initial position derived from

our method is shown in Fig. 5 to illustrate that the method can

be applied to ill-defined edges in medical images.

We can see that any one of the white circle points in the initial

position map is a good candidate to be the initial position for our

edge following technique. However, the maximum value of the

white circle points is used in this research. After determining

the suitable initial position, the proposed technique will follow

edges along the object boundary until the closed loop contour

is achieved. This causes a limitation of the technique, i.e., theboundary must be closed loop.

III. EXPERIMENTAL RESULTS

We tested the performance of the proposed method by com-

paring its results with the results from five classical contour

models. We also computed the probability of error in bound-

ary detection and the Hausdorff distance of the six methods by

comparing their results with the opinion from expert medical

doctors. Finally, we tested the efficiency of time consumption

by comparing running times of the six methods. Each input

image was preprocessed by a 3

3 median filter prior to the

application of each method.

A. Boundary Extraction in Synthetic Noisy Images

and Medical Images

The proposed method was first implemented on synthetic im-

ages. The synthetic images were generated from the original

binary image by corrupting them with additive white Gaussian

noise. We did this to make sure that the ground truths of the

boundaries were known. Several synthetic images were tested

and the intuitive results were achieved, i.e., the boundary de-

tection results from the images with higher signal-to-noise ratio

were better than that with lower ratio. We further tested our

method to detect object boundaries in some types of medical

images including prostates in ultrasound images, left ventricles

in cardiac MR images, aortas in cardiovascular MR images, and

knee joints in CT images. The prostate ultrasound images were

obtained from the CIMI Labs website of the Nanyang Techno-

logical University [34] and UW image computing systems lab

[35]. The cardiac MR images of left ventricles were obtained

from York University [36] and Medical School, Chiang Mai

University (CMU.) The cardiovascular MR images of aortas

were obtained from Imaging Consult website [37] and Medi-

cal School, CMU. The CT images of knee joints were obtained

from Learning Radiology website [38] and Medical School,

CMU. The total numbers of synthetic, prostate ultrasound, left

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TABLE IERRORS IN IMAGE SEGMENTATION AND HAUSDORFF DISTANCE BETWEEN TWO

SKILLED DOCTORS ON EACH TYPE OF MEDICAL IMAGES

ventricle MR, aorta MR, and knee join CT images are 20, 10,

20, 30, and 22, respectively. The object boundaries of these or-

gans are very useful in the diagnoses and treatment planning

for the corresponding diseases. For comparison, we tried to ap-

ply the traditional edge following technique [39], [40] in this

research but it did not perform well. Therefore, we turned to

five conventional edge detection methods, i.e., the ACM, GAC,

ACWE, GVF, and VFC snake models that are normally applied

to solve the problem of boundary detection. To make the com-parison fair, the initial contours of the five snake models were

selected manually to make them close to the object boundary.

We adjusted the weight parameters , , , and of the ACM,

GAC, ACWE, GVF, and VFC snake models between 0.1 and

0.5 with 0.1 increment. The results of the five snake models

were selected from the best experimental results of all parame-

ter settings. For the weight parameters of the proposed method,

we used just three settings: = 0.6, = 0.2, = 0.2; =0.5, = 0.2, = 0.3; and = 0.4, = 0.3, = 0.3 for allimages. The results of our method were selected from the best

experimental results of the three parameter settings.

B. Boundary Detection Evaluation Measures

To further evaluate the efficiency of the proposed method

in addition to the visual inspection, we evaluate our boundary

detection method numerically using the Hausdorff distance and

the probability of error in image segmentation

PE = P(O)P(B|O) + P(B)P(O|B) (17)

where P(O) and P(B) are a priori probabilities of objects and

background in images. P(B|O) is the probability of error inclassifying objects as background and vice versa [41]. The ob-

jects surrounded by the contours obtained using the five snake

models and the proposed method are compared with that man-

ually drawn by skilled doctors from the Medical School, CMU.

Figs. 69 show segmentation results in medical images from the

six methods comparing with the skilled doctors opinions. The

results from our proposed method are visually better than that

from the five snake models. It yields the contours that are very

close to the experts opinions.

It should be noted that each of the medical images was de-

lineated by two experts. This leads us to the investigation of

the variation among the experts opinions. Table I shows the

PEs and the Hausdorff distances between the experts. The re-

sults showing disagreements among them confirm that the object

segmentation is subjective among the experts.

Fig. 6. Prostate ultrasound images. (a) Original image. (b) Doctors delin-eation. Results of (c) ACM, (d) GAC, (e) ACWE, (f) GVF, (g) VFC, and (h) theproposed technique.

Fig. 7. Left ventricle in cardiac MR images. (a) Original image. (b) Doctorsdelineation. Results of (c) ACM, (d) GAC, (e) ACWE, (f) GVF, (g) VFC, and(h) the proposed technique.

Fig. 8. Aorta in cardiovascular MR Images. (a) Original image. (b) Doctorsdelineation. Results of (c) ACM, (d) GAC, (e) ACWE, (f) GVF, (g) VFC, and(h) the proposed technique.

The average PEs of the results on the synthetic images using

the ACM, GAC, ACWE, GVF, VFC snake models, and the

proposed method are 15.67%, 11.17%, 8.32%, 8.37%, 7.56%,

and 7.10%, respectively. The average Hausdorff distances of the

results on the synthetic images using the six methods are 6.40,

4.71, 2.76, 2.71, 2.54, and 2.17 pixels, respectively. The PEs and

Hausdorff distances between the results using all six methods

and each of the two experts opinion on each type of the medical

images are shown in Tables II and III, respectively. The results

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TABLE IIAVERAGE RESULT ON ALL IMAGES BY MEAN OF PROBABILITY OF ERROR IN IMAGE SEGMENTATION (PE) (IN %)

TABLE IIIAVERAGE RESULTS ON ALL IMAGES BY MEAN OF HAUSDORFF DISTANCE (IN PIXELS)

Fig. 9. Knee jointsin CT images. (a) Original image.(b) Doctorsdelineation.

Results of(c) ACM,(d) GAC,(e) ACWE,(f) GVF, (g)VFC,and(h) theproposedtechnique.

shown in the tables are the average results of all images in each

type. We can see that the results from the proposed method

are much closer to the experts opinions than that from the

five snake models. The ACWE and GVF snake models provide

similar performances that are better than the ACM and GAC

models. The VFC model provides the best performance among

the five snake models.

C. Efficiency of Computation Cost

We compared the efficiency of time consumption between

the proposed method and the snake models on two synthetic

images, i.e., images containing an ellipse-shaped object and im-

ages containing a U-shaped object. The sizes of images used

in this experiment were varied from 64 64 pixels to 1024 1024 pixels. The maximum number of iterations of the five

snake models was set to 50 for all images. Fig. 10 shows the

results of the computation time for each method on the images

containing a U-shaped object. The times on the images contain-

ing an ellipse-shaped object are similar and are not shown here

to save space. From the figure, the five snake models require

huge computation cost. On the other hand, the proposed method

can achieve the contour much faster. The experimental results

Fig. 10. Calculation time comparison of the six methods in images containinga U-shaped object.

show that the proposed method provides much more efficient

computation time than the five snake models. The reason is that

it only considers a 3 3 neighborhood to follow the objectboundary while the other methods consider much larger neigh-

borhood for each iteration. This is another advantage of our

proposed method over the classical contour models to detect the

correct object boundary.

IV. CONCLUSION

We have designed a new edge following technique for bound-

ary detection and applied it to object segmentation problem in

medical images. Our edge following technique incorporates a

vector image model and the edge map information. The pro-

posed technique was applied to detect the object boundaries in

several types of noisy images where the ill-defined edges were

encountered. The proposed techniques performances on object

segmentation and computation time were evaluated by compar-

ing with five popular methods, i.e., the ACM, GAC, ACWE,

GVF, and VFC snake models. Several synthetic noisy images

were created and tested for the sake of the known ground truths.

The opinions of the skilled doctors were used as the ground

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truths of interesting objects in different types of medical im-

ages including prostates in ultrasound images, left ventricles in

cardiac MR images, aortas in cardiovascular MR images, and

knee joints in CT images. Besides the visual inspection, all six

methods were evaluated using the probability of error in image

segmentation and the Hausdorff distance. The results of detect-

ing the object boundaries in noisy imagesshow that the proposedtechnique is much better than the five contour models. The re-

sults of the running time on several sizes of images also show

that our method is more efficient than the five contour models.

We have successfully applied the edge following technique to

detect ill-defined object boundaries in medical images. The pro-

posed method can be applied not only for medical imaging, but

can also be applied to any image processing problems in which

ill-defined edge detection is encountered.

ACKNOWLEDGMENT

The authors would like to thank the following surgeons

for drawing the respective ground truths: Dr. J. Tanyanop-porn (prostates), Dr. W. Kultangwattana (left ventricles, aor-

tas, and knee joints), Dr. S. Arworn (prostates). They thank

Dr. J. Euathrongchit, a diagnostic radiologist who provided the

ground truths for left ventricles, aortas, and knee joints and

the images of aortas and knee joints. They are also grateful to

Dr. A. Phrommintikul for providing the images of left ventricles.

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Authors photograph and biography are not available at the time of publication.

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