EVALUATION AND IMPROVEMENTS OF THE LEVEL SET

METHOD FOR RM IMAGES SEGMENTATION

Donatello Conte, Pasquale Foggia, Francesco Tufano and Mario Vento

Dipartimento di Ingegneria dell’Informazione e Ingegneria Elettrica

Universit

a degli Studi di Salerno, Via Ponte Don Melillo, 1 - 84084 Fisciano(SA), Italy

Keywords:

Medical Image, Level Set, Image Segmentation.

Abstract:

We present a novel algorithm for the segmentation of bony tissues in MR images. Our approach is based on the

level set algorithm. We introduce some pre-processing phases that improve image quality and segmentation

performance. The technique requires no training and operates semi-automatically, requiring only the entry of

a single seed point within the tissue to be segmented. The proposed approach is more robust than the other

approaches present in the literature, with respect to the position of the initial seed point. The quantitative

analysis of the results on a signiﬁcant number of images demonstrate the effectiveness of our approach.

1 INTRODUCTION

Despite much effort and signiﬁcant progress in re-

cent years, image segmentation remains a notoriously

challenging computer vision problem. In particular,

segmentation of medical images is difﬁcult because of

several factors: the complexity of the images; the lack

of anatomical models that fully capture all possible

shape variations for each structure; poor image con-

trast, noise, and missing or diffuse boundaries. Fur-

thermore segmentation of medical images is typically

a semi-automatic process: human interaction intro-

duces an instability in the results because the solu-

tion of most approaches depends considerably on the

choices made by the user at the start of the process.

One of the most widely used methods for image and

shape segmentation in medical images (as we will

show in the next section) is based on curve or bound-

ary evolution. Even though this approach presents ef-

fective solutions in terms of quality of the segmenta-

tion, it has some drawbacks that complicate its prac-

tical employment.

In this paper we present a new algorithm based on the

level set approach that overcomes some of the well

known problems of this kind of algorithms. In partic-

ular the proposed algorithm produces a solution that

is more robust with respect to human interaction: the

results of our algorithm are largely independent of the

initial seed points.

The paper is organized as follows: in section 2 a re-

view of the most used approaches for segmenting MR

images is shown; the proposed algorithm is presented

in section 3 while in section 4 the experimental phase

together with the analysis of the results are described.

Section 5 summarizes the conclusions obtained from

our work.

2 RELATED WORKS

In medical imaging classical segmentation methods,

like Thresholding or Region Growing, have been

substituted with more effective approaches. A well

known approach is to use some classiﬁers (k-nearest-

neighbor (Vrooman et al., 2007), Bayes classiﬁers

(Banga et al., 1992)) to segment an image. The pro-

cess of segmentation with classiﬁers is computation-

ally less expensive than the other approaches. How-

ever there are some drawbacks in the use of this ap-

proach: the ﬁrst is that it is difﬁcult to take into

account spatial information in the features used for

the classiﬁcation; the second drawback is that this

approach requires a supervised training phase. For

this reason, some clustering algorithms (unsupervised

classiﬁers) have been proposed for segmenting the

images: the three most used algorithms are K-means

((Vemuri et al., 1995)), fuzzy c-means ((Ardizzone

et al., 2007), (Foggia et al., 2006)) and expectation-

maximization ((Clark et al., 1994)). One of the main

disadvantage of standard clustering algorithms is that

they depend solely on the intensities of the image

210

Conte D., Foggia P., Tufano F. and Vento M. (2009).

EVALUATION AND IMPROVEMENTS OF THE LEVEL SET METHOD FOR RM IMAGES SEGMENTATION.

In Proceedings of the Fourth International Conference on Computer Vision Theory and Applications, pages 210-215

DOI: 10.5220/0001804102100215

 SciTePress

and do not consider spatial context. Furthermore,

these algorithms assume that the intensities of each

class are stationary. This assumption is often incor-

rect in many images due to the intrinsic heterogeneity

of a class, nonuniform illumination, or other imag-

ing artifacts. To take into account spatial information,

Markov Random Field (MRF) Models are often incor-

porated in this kind of algorithms (see (Pappas, 1992),

(Krause et al., 1997)). MRF are very suitable for med-

ical images analysis because in most cases the pixels

belong to the same class of adjacent pixels; in fact,

rarely, anatomical parts are composed by one pixel.

Two critical points of MRF approach are the compu-

tational burden (due to the required iterative optimiza-

tion schemes) and the sensitivity of the results to the

model parameters.

The most used approach in segmentation of medi-

cal images is the level set method ((Cremers et al.,

2005)). Level set is an optimization based method.

A segmentation of the image plane Ω is computed

by locally minimizing an appropriate energy func-

tional E(C) by evolving the contour C of the region

to be segmented starting from an initial contour. In

general, method based on this approach may use ei-

ther an explicit (parametric) or implicit representa-

tion of the contours. In explicit representations ((Leit-

ner and Cinquin, 1991), (McInerney and Terzopoulos,

1995)) – such as splines or polygons – a contour is

deﬁned as a mapping from an interval to the image

domain: C : [0, 1] → Ω. In implicit contour represen-

tations ((Dervieux and Thomasset, 1979), (Osher and

Sethian, 1988)), contours are represented as the (zero)

level line of some embedding function φ : Ω → ℜ:

C = {x ∈ Ω|φ(x) = 0}.

In the original level set algorithm, only gradient infor-

mation is taken into account in the energy term E(C).

Some authors ((Osher and Santosa, 2001), (Chan and

Vese, 2001), (Russon and Paragios, 2002)) have pro-

posed improvements of the classical algorithm by in-

troducing some priors information (e.g. shape, color

or motion information).

Level set algorithms are widely used in medical im-

ages segmentation because they are very effective.

However they present some drawbacks:

• The segmentations obtained by a local optimiza-

tion method are strongly dependent to the initial-

ization. For many realistic images, the segmenta-

tion algorithm tends to get stuck in undesired local

minima (especially in the presence of noise) forc-

ing the user to try with several seed points before

obtaining a satisfactory solution.

• This approach lacks a meaningful probabilistic in-

terpretation. Extensions to other segmentation cri-

teria such as color, texture or motion are not

straight-forward.

• This algorithm has a problem in ﬁnding correct

contours of the regions when the region bound-

aries have corners or other singularities.

In this paper we present a novel algorithm based on

level set that overcomes the ﬁrst of the considered

problems.

3 THE PROPOSED METHOD

To reduce the limits of level set standard algorithm

we propose the follow improvements for the segmen-

tation:

• an image smoothing ﬁlter is used to reduce the

noise;

• an image pre-segmentation is performed to make

the results independent of the chosen seed points;

• the ﬁnal segmentation is based on the Laplacian

level set, to enhance the contour of the tissue of

interest.

In the following subsections, each of these steps is

discussed in more detail.

3.1 Smoothing Filter

One of the main problems in MR image processing

is the noise. To reduce this problem a 3D Gaussian

ﬁlter, with a 3x3x3 kernel, is applied to the image be-

fore the segmentation step. The coefﬁcients of the

convolution mask are obtained according to the clas-

sical Gaussian distribution function. The size of the

mask and σ have been empirically chosen. The lat-

ter value has been chosen by performing the mean of

the variances among all the 3x3x3 sub images within

a bone region of a set of training images. After this

phase the resulting image is:

(x, y, z) =

[I(x, y, z) ∗G

(x, y, z)] =

∑

i=−1

∑

j=−1

∑

k=−1

I(x, y, z)G

(i, j, k)

where λ =

∑

i=−1

∑

j=−1

∑

k=−1

(i, j, k).

The smoothing ﬁlter has two positive effects: it re-

duces the image noise and the corners are less evident.

3.2 Image Pre-segmentation

The base level set algorithm strongly depends on the

choice of the seed point. The reasons of this prob-

lem depend from the minimization of the energy func-

tional; in fact it is possible to stop the process in a

EVALUATION AND IMPROVEMENTS OF THE LEVEL SET METHOD FOR RM IMAGES SEGMENTATION

211

Figure 1: The effect of the seed point on the segmentation:

a) Energy function diagram showing the energy of the seed

point A and of the found (local) minimum B (the diagram is

a 2D projection of the actual 3D diagram); b) Segmentation

result.

local minimum distant from a global minimum. The

process start from a initial condition; in our applica-

tion the segmentation with the base level set algorithm

can evolve to very different solutions from different,

but very close, seed points.

In ﬁgure 1 the point A indicates the initial condition of

the energy function when we choose the seed in ﬁgure

1b , while the point B indicate the result of the min-

imization of the energy function. The point A and B

in ﬁgure 2a have the same meaning for seed in ﬁgure

2b. We can note that choosing two close seed points

we have two very different results of the segmentation

process.

To reduce this dependence we introduce a pre-

segmentation phase using a fast but not much effec-

tive algorithm which does not depend on the energy

function. In this way we will use a larger region in-

stead a single point for the initial condition. The cre-

ated seed region produces an initial value of the en-

ergy function that is close to the global minimum in-

dependently from the point chosen by the user (see

ﬁgure 3).

We tried two different algorithms for this phase: re-

gion growing (Adams and Bischof, 1994) and fast

marching (Zhang et al., 2007). The results of both

Figure 2: The segmentation obtained on the same image

of ﬁg. 1, starting from a different seed: a) Energy function

diagram showing the energy of the seed point A and of the

found (local) minimum B (the diagram is a 2D projection

of the actual 3D diagram); b) Segmentation result.

algorithms are similar, so we have chosen the ﬁrst be-

cause of its minor computational cost. Moreover it

has a small number of parameters with respect of fast

marching algorithm.

In this phase, in order to avoid merging between re-

gions of different tissues, the pre-segmentation algo-

rithm parameters must be tuned so as to prefer over-

segmentation to under-segmentation.

3.3 Laplacian Level Set

The smoothing ﬁlter reduces the corner problems, but

at the same time it reduces the contrast of the im-

age causing the loss of information for the contour of

the tissue of interest. This effect generates the classic

under-segmentation problem.

To avoid the under-segmentation problems a deriva-

tive ﬁlter is applied at the image to evidence the con-

tours of the bone. The used ﬁlter is the Laplacian so

deﬁned:

∇

f (x, y, z) =

f (x, y, z)

δx

f (x, y, z)

δy

f (x, y, z)

δz

The ﬁltered image enhances the contours (see Fig. 4)

and becomes the input image of the level set algo-

VISAPP 2009 - International Conference on Computer Vision Theory and Applications

212

Figure 3: Minimum with pre-segmentation: a) Energy func-

tion diagram b) Segmentation result.

Figure 4: Output image of the Laplacian operator.

rithm. After the application of the ﬁlter, the energy

term E(C) to minimize (see Section 2) becomes the

follow:

E(C) =

inside

(u(x, y, z) −µ

inside

)

dxdydz +

outside

(u(x, y, z) −µ

outside

)

dxdydz

where u(x, y, z) is the intensity of the ﬁltered image.

4 EXPERIMENTAL RESULTS

To evaluate the results of the proposed algorithm we

used the precision and recall index so deﬁned:

precision =

T P

T P + FP

recall =

T P

T P + FN

where TP is the number of correctly detected objects

of interest, FP is the number of wrongly detected ob-

jects of interest and FN is the number of missed ob-

jects of interest. These indexes are directly usable

for applications where the objects of interest are ei-

ther completely detected or completely missed. In

our application, instead, the objects of interest are not

atomic regions, so we need to consider also partial

recognition of the tissue of interest. For this reason

TP, FP and FN are so deﬁned:

T P =

g ∩ d

g ∪ d

FP =

−

d ∩ g

FN =

−

d ∩ g

where g is the set of voxels actually belonging to the

region of interest (ground truth), d is the set of vox-

els detected by the algorithm and

denotes the car-

dinality of a set. It is simple to show that when the

object of interest is perfectly detected precision = 1

and recall = 1; instead when the detection is totally

incorrect precision = 0, and recall = 0.

The algorithm has been tested on 11 MRI of wrists

acquired at low ﬁeld for a total of 762 bi-dimensional

slices. The ground truth has been manually traced by

medical experts.

We compare the proposed algorithm (LLS) with basic

level set algorithm (BLS) and with basic level set with

pre-segmentation module (PLS). We also compare

our algorithm with another algorithm: Geodesic Ac-

tive Contours (see (Caselles et al., 1997) and (Yan and

Kassim, 2006)). Geodesic Active Contours (GAC)

based algorithms are similar to Level Set based al-

gorithms, but the ﬁrst are motivated by a curve evolu-

tion approach and not by an energy minimization one.

Comparison between GAC and our algorithm is more

suitable than comparison with only Level Set based

algorithms because GAC are less sensitive to initial

parameters. Also for GAC algorithm we present both

basic algorithm and algorithm with pre-segmentation

module (PGAC).

In the following table we report the results:

EVALUATION AND IMPROVEMENTS OF THE LEVEL SET METHOD FOR RM IMAGES SEGMENTATION

213

Table 1: Experimental Results.

Precision Recall

BLS 0.81 0.89

PLS 0.92 0.94

GAC 0.95 0.89

PGAC 0.99 0.90

LLS 0.99 0.94

For the algorithm BLS we have manually searched

the best seed point and we have often changed the

calibration parameters. The results shown in table 1

are performed considering the best segmentation ob-

tained for any image. It is important to note that we

are not sure that the chosen seed is really optimal in

the mathematical sense.

Even if the algorithm could in theory produce better

results, in practical use it is not possible to proceed

in this way because of the high effort in the calibra-

tion phase and because of an uncertainty factor on the

results. So we apply the pre-segmentation step also

to the BLS algorithm, to compare this latter with our

proposal independently of the chosen seed.

In conclusion it is important to remark that the idea

of the pre-segmentation phase is necessary for the re-

sult repeatability. Furthermore the Laplacian operator

improve the precision of the results (see table 1).

Under-segmentation problem is present in an algo-

rithm with a low value of precision. This is the case

of BLS: the basic algorithm is not able to recognize

blurred contours (often presents in RM images). With

our pre-segmentation module all algorithms improve

their results with respect of the precision index.

The algorithms with a low value of recall present

over-segmentation problems. Table 1 shows that

BLS, GAC and PGAC are over-segmenting.

We can conclude that Geodesic Active Contours

based approaches are very effective to ﬁnd tissues

contours, but they often present missing voxels within

the tissue: these approaches are very sensitive to

brightness variability. Level Set based approaches are

not able to ﬁnd blurred contours: in these approaches

local information give weak contribution to the ﬁnal

solution.

In any case, Table 1 shows that our approach is more

effective than all others. To have a visual idea of the

effectiveness of our proposed algorithm, in Fig. 5a

and Fig. 6a, Fig. 5b and 6b, Fig. 5c and Fig. 6c

results of the application of Basic Level Set with pre-

segmentation phase, Geodesic Active Contours with

pre-segmentation phase and Laplacian Level Set are

respectively shown. Note that the images result of

the PLS algorithm, obtained after a difﬁcult calibra-

tion phase, is not able to avoid the under-segmentation

Figure 5: a) Basic Level Set with pre-segmentation; b)

Geodesic Active Contours with pre-segmentation; c) Lapla-

cian Level Set.

Figure 6: a) Basic Level Set with pre-segmentation; b)

Geodesic Active Contours with pre-segmentation; c) Lapla-

cian Level Set.

problem and the images result of PGAC algorithm

presents some holes within the tissue.

VISAPP 2009 - International Conference on Computer Vision Theory and Applications

214

5 CONCLUSIONS

A new algorithm for segmenting MR images is pro-

posed. The algorithm is based on the level set ap-

proach and is conceived to overcome some of the dif-

ﬁculties of the original level set method: the solution

is repeatable as regard as changes in initial conditions

and the precision of the result is very high. This algo-

rithm can be used for many applications in the ﬁeld of

Computer Aided Diagnosis.

Currently we are working on the extension of the ex-

periments to assess the results. Then we will analyse

the new results to ﬁnd other improvements to the de-

scribed method.

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