Segmentation Ensemble

A Knowledge Reuse for Model Order Selection using Case-based Reasoning

Pakaket Wattuya

and Ekkawut Rojsattarat

Department of Computer Science, Faculty of Science, Kasetsart University, Bangkok, Thailand

Department of Computer Science, Faculty of Science at Si-Racha,

Kasetsart University Si-Racha Campus, Chonburi, Thailand

Keywords:

Image Segmentation Ensemble, Case-based Reasoning, Model Order Selection.

Abstract:

Cluster ensemble has emerged as a powerful technique for improving robustness, stability, and accuracy of

clustering solutions, however, automatic estimating the appropriate number of clusters in the ﬁnal combined

results remains unsolved. In this paper we present a new approach based on a case-based reasoning to handle

this difﬁcult task. The key success of our approach is a novel use of cluster ensemble in a different role from

the past. Each ensemble component is viewed as an expert domain for building a case base. Having beneﬁted

from the information extracted from cluster ensemble, a case-based reasoning is able to settle efﬁciently the

appropriate number of clusters underlying a clustering ensemble. Our approach is simple, fast and effective.

Three simulations with different state-of-the-art segmentation algorithms are presented to illustrate the efﬁ-

cacy of the proposed approach. We extensively evaluate our approach on a large dataset in comparison with

recent approaches for determining the number of regions in segmentation combination framework. Exper-

iments demonstrate that our approach can substantially reduce computational time required by the existing

methods, more importantly, without the loss of segmentation combination accuracy. This contribution makes

the segmentation ensemble combination concept more feasible in real-world applications.

1 INTRODUCTION

Cluster ensemble has emerged as a powerful tech-

nique for dealing with several difﬁculties in clustering

problems. Thus far, it has been used for dealing with

1) instability of clustering algorithms (Topchy et al.,

2005; Franek et al., 2012); 2) sensitivity to noise,

outliers or sample variations (Nguyen and Caruana,

2007); and 3) inaccuracy of individual clustering

algorithms (Vega-pons and Ruiz-shulcloper, 2011;

Strehl and Ghosh, 2002). Within this role, cluster

ensemble integrates solutions from multiple different

clusterings into a single better solution, normally, be-

yond what a single clustering algorithm can achieve.

In addition to the beneﬁts outlined above, we

present a novel use of cluster ensemble to handle

another most difﬁcult problem in data clustering,

namely, a model order selection - the problem of es-

timating the optimal number of clusters in data. Over

the years, numerous approaches have been proposed

to this problem. A comprehensive survey of meth-

ods for estimating the number of clusters is given in

(Hardy, 1996; Milligan and Cooper, 1985), as well

as references therein. There have also been several

researches devoted to this issue known as the cluster

validation problem, whose comprehensive survey can

be found in (Halkidi et al., 2001; Dubes, 1993). How-

ever, many of such statistical and model-based ap-

proaches often require high computation which is not

suitable for large data (such as images) and real-time

applications, for example, a real-time image segmen-

tation problem. The goal of this paper is to provide a

learning procedure to deal with model order selection

in an image segmentation ensemble problem.

Image segmentation ensemble combination has

emerged in a similar manner as cluster problems,

namely, in order to improve the robustness, stabil-

ity, and accuracy of segmentation results. In general,

the desired number of regions is not known in ad-

vance and is often speciﬁed by a human user. Most

segmentation ensemble approaches assume a known

number of regions (Jiang and Zhou, 2004; Rohlﬁng

et al., 2004; Fischer and Buhmann, 2003). The ap-

proaches for automatically estimating the number of

regions are mostly based on a validity index where the

optimal combination solution with a desired number

287

Wattuya P. and Rojsattarat E..

Segmentation Ensemble - A Knowledge Reuse for Model Order Selection using Case-based Reasoning.

DOI: 10.5220/0004830102870295

In Proceedings of the 3rd International Conference on Pattern Recognition Applications and Methods (ICPRAM-2014), pages 287-295

ISBN: 978-989-758-018-5

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

of regions is found from a series of candidate combi-

nation solutions under a different number of regions.

Rabinovich et al. (Rabinovich et al., 2006) proposed a

validity index based on the concept of cluster stability

and used it to ﬁnd a shortlist of most stable segmen-

tations from a large number of possible segmentation

solutions. Wattuya et al. (Wattuya et al., 2008) pro-

posed a validity index based on the concepts of gen-

eralized median and mutual information. Their seg-

mentation validation criterion demonstrated promis-

ing results. More details of this method will be given

in the experiment section as we will use it in compar-

ison with our proposed method. The main drawback

of these approaches is their high computation time re-

quired for computing a series of candidate combina-

tion solutions and for validating them.

In a general data clustering ensemble, Fred and

Jain (Fred and Jain, 2005) proposed a thresholding

criterion for estimating the true number of clusters

called a lifetime criterion. The k - cluster lifetime is

deﬁned as the range of threshold values on the den-

drogram that lead to the identiﬁcation of k clusters.

The optimal number of clusters is determined as the

one with the highest lifetime value. The important

drawback of this criterion is that it does not work well

with complex data (i.e. not well separated and a non-

spherical cluster shape). It requires a large size of en-

semble (e.g. 200 clusterings per ensemble) in order

to ensure convergence of the method. This is quite

infeasible in practice for an image segmentation com-

bination approach.

In this work, we propose a case-based reasoning

(CBR) approach to handle this task. CBR is suitable

for handling our problem in many aspects (will be dis-

cussed in Section 3). A knowledge domain for build-

ing a case base is derived from the segmentation en-

semble in a framework of knowledge reuse. Once a

case base is built, the solution (i.e. the number of re-

gions) of a new problem is derived by adapting the

solutions of the previous cases retrieved from the case

base. The approach is designed to be applicable to

practically any image segmentation method and im-

age segmentation combination framework. The main

advantages of our approach over the existing methods

are that i) it requires signiﬁcantly less computation

time, i.e. no time required for computing a series of

candidate combination solutions and no time required

for searching a large set of candicate solutions for the

optimal combination solutions; ii) it can work well

with a small size of segmentation ensemble. These

advantages make the concept of image segmentation

combination more feasible in real-world applications.

In fact, the idea of the use of segmentation ensem-

ble in model order selection is partly motivated by the

problem of image segmentation ensemble combina-

tion. In a frameworkof image segmentation combina-

tion, a segmentation ensemble needs to be generated

for combination process. Thus, instead of only us-

ing it for a combination purpose, we propose to use it

for determining the number of regions in a ﬁnal com-

bined result, as well. Hence, no additional work for

generating a segmentation ensemble is required in this

approach.

We extensively evaluate our approach on a large

dataset. Recent approaches for determining the num-

ber of regions based on the median concept (Wattuya

et al., 2008) and minimum description length prin-

ciple (Rao et al., 2009) are described in Section 4

where they are compared with our method. Three

simulations with different state-of-the-art segmenta-

tion algorithms are presented to illustrate the efﬁcacy

of the proposed approach. Each segmentation algo-

rithm simulates different characteristics of experts to

build the case base. The experiments show promising

results. Our CBR approach can signiﬁcantly reduce

the computational time required by the existing model

order selection methods without the loss of segmen-

tation combination accuracy.

The paper is organized as follows. We begin with

a review of using CBR on image segmentation prob-

lem. Then, our proposed CBR approach is described

in Section 3. Experimental results are described in

Section 4. Finally, future work is discussed to con-

clude the paper.

2 RELATED WORK

The concept of CBR as a problem-solving technique

has been used in a wide range of application areas in-

cluding computer vision applications. CBR has been

successfully applied not only in low-level tasks in

computer vision, such as image segmentation (Perner,

1999; Frucci et al., 2008), but also in high-level tasks,

such as image interpretation (Perner et al., 2003) and

medical image understanding (Grimnes and Aamodt,

1996). The works (Perner, 1999; Frucci et al., 2008)

used CBR for solving a parameter selection problem

which differs from our task. They used CBR to ﬁnd an

appropriate parameter setting for each individual im-

age to ensure that good segmentation results are ob-

tained even if the segmentation algorithm is applied

to images with different characteristics. However, the

problem of parameter selection seems to be less com-

plicated than our problem of determining an appropri-

ate number of clusters. For a particular segmentation

algorithm, solutions of parameter selection problem

of images with similar characteristics tend to be the

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same, while solutions of model order selection prob-

lem may be totally different. In the next section, we

will describe how we use segmentation ensemble as

an expert domain to cope with this difﬁculty.

3 OUR PROPOSED CBR

CBR is a problem-solving technique that uses previ-

ous cases or past experiences to solve new problems

(Kolodner, 1993; Leake, 1996). CBR is suitable for

dealing with our problem for two reasons. Firstly,

the problem of image segmentation is ill-deﬁned. It

is hardly possible to explicitly express it in terms of

rules or models. However, these rules/models are not

required by CBR. Secondly, CBR can learn for itself

to solve future problems in an automatic way.

Segmentation ensemble is a key component for

building our CBR. We use it as a knowledge domain

for generating a case base. Each segmentation so-

lution in an ensemble (computed from different seg-

menters) can be viewed as a judgment from individ-

ual experts on the input image. Having beneﬁted from

this information, the CBR will be able to settle natu-

rally the appropriate number of regions underlying a

segmentation ensemble. In this section, we describe

the details of building our case base. We begin by

describing the way we extract knowledge from a seg-

mentation ensemble and the way we represent it as a

case in a case base. Then we describe how we retrieve

similar cases from the case base, and ﬁnally, how we

adapt them to the new problem.

3.1 Knowledge Extraction

The ﬁrst task of building a case base is to determine

the problem features that make up a case. These fea-

tures should deﬁne our problem well. Thus, we ﬁrst

investigate the connection between image features, in-

formation provided by a segmentation ensemble, and

a true number of regions (k

∗

) in an image.

Supposition I: Image Features vs. k

∗

The ﬁrst intuitive assumption is about the relation be-

tween low-level image features and a number of re-

gions in an image. However, it is not easy to model

or deﬁne a correlation between them. It is typical that

two or more images happen to have similar feature

values but different number of regions and it is often

that two or more images with different feature values

have similar number of regions.

Supposition II: Median of k

of Ensemble vs. k

∗

The second conjecture was made based on the as-

sumption that the number of regions of segmentations

in an ensemble (will be denoted as k

- a number of re-

gions of the ith segmentations in an ensemble) could

be used to imply k

∗

. Thus, simple statistical measures

such as the mean and the median of k

have been in-

vestigated in (Wattuya et al., 2012). The work pre-

sented in (Wattuya et al., 2012) is our ﬁrst attempt

to develop our idea of using CBR for model order

selection. In that work we used both low-level fea-

tures and the median of k

to represent a case in a case

base (we applied the fuzzy c-means algorithm to han-

dle the ambiguity of low-level features). The experi-

ments showed good results, however, we later found

out that the median of k

works well when the values

of k

is in a normal range (e.g. k ∈ [2, 60]). For ex-

ample, if an image segmentation algorithm used for

generating segmentation ensembles tends to produce

over-segmentation results (e.g.

k > 50, the median of

would be less appropriate for implying a true num-

ber of regions. This is true for the mean of k

. In our

experments, this situation is simulated and the exper-

imental results show the inefﬁectiveness of using the

meadian and the mean alone.

Supposition III: Segmentation Quality vs. k

∗

The assumption we used in the proposed approach is

based on the quality of segmentations in an ensemble.

Thus, two pieces of information are extracted from

each segmentation solution in an ensemble. For each

segmentation S

, the ﬁrst piece of information is the

number of regions k

and the second piece is the qual-

ity q

. The ﬁrst piece of information can be viewed as

the decision of an expert on the k

∗

of a given image,

while the second piece reﬂects the expertise of that

expert.

Let us ﬁrst consider good quality segmentations

in an ensemble. What do they tell us? Good quality

segmentations, whose q

is relatively high, tell us that

their corresponding k

are reliable and very likely to

be k

∗

. Based on this assumption, we can further im-

ply that segmentations with similar values of q

and

similar values of k

tend to have similar values of k

∗

On the other hand, segmentations with similar values

of q

but different values of k

should have different

values of k

∗

. Bad quality segmentations are not abso-

lutely useless. They can be used to help estimate k

∗

We consider three situations:

• Low k

∗

: q

of high k

would be low. The further

the k

is away from k

∗

, the lower the value of q

is.

This implies that the value of k

∗

is not high.

• High k

∗

: q

of low k

would be low. This implies

that the value of k

∗

of this image is not low.

• Moderate k

∗

: q

of too low or too high k

would

be low. This implies that the value of k

∗

of this

image is not too low or too high.

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It is possible that some bad segmentations may

not follow the above assumption, since the bad seg-

mentations are arbitrarily bad in their own way. How-

ever,in our experiments we observed that the majority

of them act in the above manner since we used ex-

pert segmentation algorithms, not arbitrary ones (e.g.

k-means). Nonetheless, we manage handle this un-

certainty in two ways. The ﬁrst way is to exclude

a few of the worst segmentations in each ensemble

from consideration. The second way is to general-

ize a case base. We will discuss how to evaluate the

quality of segmentations in an ensemble later in this

section. In the rest of the paper, we will call q

and k

extracted from segmentations in an ensemble ensem-

ble features.

We claim that ensemble features are higher related

to k

∗

than low-level image features. We test this hy-

pothesis by clustering 300 images from BSDS dataset

into C clusters using ensemble features and low-level

image features, separately. Image features are con-

trast, correlation, homogeneity, and entropy (Haralick

et al., 1973). For each cluster, we compute the stan-

dard deviation of k of images within the same cluster.

Small standard deviation of k indicates that all im-

ages in the same cluster have k close to each other.

On the other hand, large standard deviation of k indi-

cates that the number of k within a cluster are highly

varied. Therefore, we expect to have a low standard

deviation of k for each cluster. The numbers of k used

in this test are taken from human segmentations of

BSDS dataset. Since one image has multiple human

segmentations, the average of them are used. For en-

semble features, we generated three sets of features

which are based on three different image segmenta-

tion algorithms (which will be described later in Sec-

tion 4). For each set of features, we conducted a se-

ries of experiments with several clustering algorithms

with C ∈ [30,40,50,60,70] clusters. The three clus-

tering algorithms with the largest Silhouette index and

Calinski-Harabasz index values (i.e. complete link-

age, average linkage, and k-means) show that the av-

erage of standard deviations of k of clusterings using

ensemble features is smaller than the average of stan-

dard deviations of k of clusterings using low-level im-

age features. This indicates that ensemble features are

more related to k

∗

than low-level features.

3.2 Building a Case Base

3.2.1 Case Description

Given a segmentation ensemble S = {S

,...,S

} of

N segmentations of the same image, each segmen-

tation can be produced by using different algorithms

or with the same algorithm but different parameter

values. Let K = {k

,·· · , k

} be a set of the num-

ber of regions in the segmentations in S. As we dis-

cussed earlier, a case is described as a feature vector

x = {hk

i,··· , hk

i}. k

and q

are the number

of regions and the quality value of the ith segmenta-

tion in an ensemble. r = [1, N] is the number of seg-

mentations to be used.

Since in practice the ground truth data is not avail-

able for evaluating the quality of segmentation solu-

tions, an unsupervised validation method has to be

used. In this work, we proposed to apply two different

concepts for evaluating the quality of segmentations.

The ﬁrst one is based on the concept of mutual infor-

mation, while the second one is based on the concept

of minimum description length (MDL) principle.

SNMI Quality Measure. The SNMI measure is ﬁrst

introduced by (Strehl and Ghosh, 2002) for design-

ing consensus functions. Given an ensemble E of

r clustering solutions denoted by E = C

,.. .,C

Strehl and Ghosh suggested that a good consensus

clustering should maximize the following criterion:

SNMI(C,E) =

∑

i=1

NMI(C,C

), where NMI is the

normalized mutual information which is used as simi-

larity measures in many contexts including image seg-

mentation (Fowlkes et al., 2003; Franek et al., 2012;

Wattuya et al., 2008). The NMI value is maximized

to be one if two clusterings deﬁne the same partition

of the data. In contrast, if two clusterings deﬁne com-

pletely independent partitions, the NMI value is 0. We

propose to apply SNMI as a quality index (q) and use

it for a case description. Higher SNMI value indicates

higher quality of segmentaiton that can capture more

information among other segmentations in an ensem-

ble.

MDL Quality Measure. The MDL principle can

be used to encode image information (e.g. texture,

boundary, color) and evaluated segmentation quality

based on a coding length function. It deﬁnes the best

ﬁtted segmentation as the one that produces the short-

est code length of the image. Hence, a low value of

MDL indicates a good segmentation result. In this

work we adapt the MDL criterion used for image seg-

mentation as proposed in (Rao et al., 2009). For ad-

ditional details the readers are referred to (Rao et al.,

2009). Since the range of values of k

and q

is rela-

tively large, all values are normalized into a range of

0 to 10.

Note that the main advantages of SNMI-based

measure over MDL-based measure are that it is fast

computation and requires no original image data in

computation process. This is very useful when the

original data are not available.

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3.2.2 Case Solution

A case solution is deﬁned as an approximate num-

ber of regions,

k, in a ﬁnal segmentation combina-

tion result. We estimate the number of

k through the

framework of image segmentation combination. The

random walker-based segmentation combination al-

gorithm (Wattuya et al., 2008) is used to produce a

series of combination results with different number of

k ∈ [k

min

max

]. Once candidate results are obtained

by a combination algorithm, the next step is to eval-

uate the combination solutions to determine an opti-

mal one.

k is then deﬁned as the number of regions

of the optimal combination result. The accuracy of

depends on a segmentation validation index. In this

work we proposed two validity criteria for choosing

the optimal combination result. The ﬁrst criterion is

based on the NMI concept and the second criterion is

based on the MDL principle.

NMI-based Validity Criterion. This criterion follows

the concept of mutual information mentioned above.

The best combined segmentation result should share

the largest amount of information with all correspond-

ing human segmentations. The candidate combina-

tion result with the highest NMI value is chosen as

the optimal combination result. This criterion is a su-

pervised method and requires ground-truth segmenta-

tion. However, the human segmentations is only used

for computing the case solutions in a training process.

Thus, the on-line process of our approach is still fully

automatic and requires no human intervention. We

will call this approach CBR-NMI.

MDL-based Validity Criterion. The MDL we used

here is the same as the one we use for evaluating the

quality of segmentations described above. The MDL

criterion deﬁnes the optimal combination solution as

the one that minimizes its total coding length. This

criterion is an unsupervised method and requires no

human segmentation data. However, the accuracy of

k would not be as accurate as the supervised method.

We will call this approach CBR-MDL.

A case in a case base is thus deﬁned as a problem-

solution pair c = (x,

k), where

k is a solution corre-

sponding to a problem feature vector x deﬁned above.

3.3 Case Retrieval

Case retrieval is a process of ﬁnding the cases that

are closest to the new problem. The cases with the

highest similarity values will be chosen and their as-

sociated solutions will be adapted to the new prob-

lem. Because our case description is extracted from

a segmentation ensemble, its accuracy depends di-

rectly on the performance of image segmentation al-

gorithm that we use to generate a segmentation en-

semble. Practically, a segmentation ensemble typi-

cally contains incorrect segmentations. The informa-

tion about k∗ extracted from them is not absolutely

accurate. Hence, it would be more beneﬁcial to com-

pensate their errors by generalizing the cases in a case

base and use a case prototype as a case representative,

instead of using each individual case on its own.

For this purpose, we apply a k-means clustering

algorithm to cluster the cases into c clusters. The

cases with similar case descriptions will be clustered

together. The c cluster centers are used as case repre-

sentatives of the whole cases in the case base and their

solutions are deﬁned as the average of the solutions

of the cases in the same cluster. It is not unusual that

the solutions of the cases in the same cluster are not

exactly the same, however, a small difference among

them is observed. Actually, the averaging of the case

solutions is a good concept for error compensation of

individual case solutions.

It is interesting to note that k-means clustering

used in our approach not only beneﬁts for a case base

generalization but also for decreasing the number of

cases required for matching in the retrieval step. In-

stead of matching all the original cases in the entire

case base, the task of case matching boils down to

matching the new case with the c new case represen-

tatives only. Since our case is represented as a real-

value feature vector, the simple Euclidean distance is

used in a case matching process.

We note here that in our previous work (Wattuya

et al., 2012) we used the fuzzy c-means algorithm for

a case base generalization since we needed it to han-

dle uncertainty in both case descriptions (as discussed

earlier) and case solutions. In that work a case solu-

tion was also derived from a segmentation ensemble.

Hence, it is more uncertain and more inaccurate than

the case solution deﬁned in this work.

3.4 Cases Adaptation

According to our case description, it is impossible that

a new case will exactly match any case in a case base.

Thus, the case that is closest to the new case will be

retrieved, and the solution of a retrieved case will be

applied directly to the new case. However, there is

a situation where the new case is close to more than

one case in a case base. For example, the difference

among the distances between the new case and those

cases is very small (i.e. less than 0.005). In this sit-

uation, a group of cases that are closest to the new

case will be retrieved. The solution for the new case

is then derived by averaging the solutions of the re-

trieved cases.

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4 EXPERIMENTS

4.1 Segmentation Ensemble Generation

We tested our approach on 300 natural images of

size 481 × 321 from the BSDS dataset (Martin et al.,

2001), each having multiple manual segmentations.

We apply NMI to quantitatively evaluate the segmen-

tation quality against the ground truth. One segmen-

tation result is compared to all manual segmentations

and the average NMI (ANMI) is reported. Larger

ANMI values indicate better combination results that

share more information with the ground truths.

In the experiments, three state-of-the-art segmen-

tation algorithms were used as baseline segmentation

algorithms for generating a set of initial segmenta-

tions to be combined. The three segmentation algo-

rithms are the graph-based algorithm (FH) (Felzen-

szwalb and Huttenlocher, 2004), the mean shift-based

algorithm (MS) (Comaniciu and Meer, 2002), and the

region growing-based algorithm (JSEG) (Deng and

Manjunath, 2001). These algorithms were chosen be-

cause of their good performance, computational efﬁ-

ciency and different segmentation behavior.

A segmentation ensemble is obtained by varying

the parameter values of the same segmentation algo-

rithm in an appropriate range as summarized in Ta-

ble 1. The total number of parameter combinations

for each algorithm is equal to 24 combinations. For

each combination of parameters, the segmentation al-

gorithms are run over the complete set of 300 images

from the BSDS dataset to form three sets of segmenta-

tion ensembles (with 24 segmentations per ensemble).

We call the set of 300 segmentation ensembles pro-

duced by FH, MS, and JSEG algorithms as ’FH en-

sembles’,’MS ensembles’, and ’JSEG ensemble’, re-

spectively.

The three segmentation algorithms have different

segmentation behavior, resulting in the difference of

segmentation ensemble characteristics as illustrated

in Figure 1. The x-axis is the quality of segmenta-

tions q (high value of q indicates good segmentation

quality) and the y-axis is the number of region k. FH

algorithm tends to produce segmentation results with

a normal range of k ∈ [1, 40]. Thus, it has nearly uni-

form distribution over the full range (as shown in the

ﬁrst plot). MS and JSEG algorithms tends to produce

segmentation results with a much wider range of k.

The dense distribution in the upper left area of the

plots correspond to the highly over-segmentation be-

havior of the segmentation algorithms. Notice that

segmentations with overly high k have very low q

(close to 0). Our experiments demonstrate that our

CBR approach can work well for all data distribution.

Table 1: Segmentation algorithms and their parameters.

Algos. Parameter values

FH σ = {.4,.5,· ·· ,.9}, K = {150,300,500,700},M = 1500

MS h

= {8,16},h

= {7,11,15}, M = {100,500, 1000,1500}

JSEG l = {1,2,3},q = {300, 600}, m = {0.2,0.4,0.6,0.8}

0 5 10

FH ensemble

normalized k

normalized q

0 5 10

MS ensemble

normalized k

normalized q

0 5 10

JSEG ensemble

normalized k

normalized q

Figure 1: The distribution of three sets of ensembles after

normalized into a range [0, 10].

4.2 Model Order Selection Methods

Four methods for determining the number of regions

in a ﬁnal combination results are used for compari-

son: the generalized median-based validation method

(GM) (Wattuya et al., 2008), the MDL-based valida-

tion method (MDL) (adapted from (Rao et al., 2009)),

and two statistical methods based on the mean and the

median of a number of regions in an ensemble.

For the ﬁrst two methods, the random walker-

based segmentation combination algorithm (Wat-

tuya et al., 2008) is applied to generate a series

of candidate combination results with different k ∈

min

max

]. Then, an optimal segmentation com-

bination result is chosen as the one that optimized

the validity criterion. The generalized median-based

method selects an optimal solution as the one with the

minimal average NMI distance (i.e. 1- NMI) among

all individual segmentations in an ensemble. This ap-

proach is regarded as an approximation of the GM

segmentation of the input ensemble by investigating

a subspace of U, which consists of the combination

segmentations for the considered range of k only. For

the MDL-based method, a similar MDL function used

for building a case base is used. The optimal segmen-

tation combination result is the one with the shortest

coding length. For the last two statistical measures,

the mean and the median of a number of regions in an

ensemble are ﬁrst computed. Then, the combination

algorithm is applied to generate a combination result

with k equals the mean/median of a number of regions

in an ensemble.

4.3 Experimental Results

Comparison of Model Oder Selection Approaches

For our CBR approach, the 300-image dataset is ran-

domly partitioned into a 200-image training set and

a 100-image test set. Three non-overlapping test set

are generated. For each test set we run the k-means

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Table 2: Average performance overall three test sets.

Ensemble Model order selection method

MDL quality measure SNMI quality measure

GM MDL Average Median CBR-NMI CBR-MDL CBR-NMI CBR-MDL

FH 0.6179 0.6167 0.6097 0.6077 0.6162 0.6151 0.6149 0.6127

MS 0.6267 0.6252 0.6072 0.6147 0.6296 0.6291 0.6281 0.6293

JSEG 0.5911 0.5946 0.5889 0.5873 0.5967 0.5914 0.5953 0.5937

Table 3: Model order selection methods, their computational requirements, and their actual computation time (in second).

Approach Number of Number of MDL Number of NMI Number of Euclidean Total time

combination computationI computation distance computation

GM |k| (20.9757) - |k|N (5.8490) - (26.8247)

MDL |k| (20.9757) |k| (48.4283) - - (69.4040)

CBR (MDL measure) 1 (1.1832) N (21.2152) - c (0.0001) (22.3985)

CBR (SNMI measure) 1 (1.1832) - N(N − 1)/2 (1.4083) c (0.0001) (2.5916)

algorithm 100 times and retain only the best results.

Note that a small variance of ANMI over 100 runs

is observed. The CBR performance reported in Ta-

ble 2 is the average performance over all three test

sets. For all experiments we set the number of en-

semble members (r) to 20 and the number of clusters

our method on the r and c by varying their values in

a proper range. No signiﬁcant change in the perfor-

mance is observed.

As expected, the mean and median approach ob-

tained the worst performance in all scenarios. As we

discussed earlier, the number of regions in an ensem-

ble depends heavily on the behavior of segmentation

algorithm used and has a weak correlation to the k

∗

It is not surprising that the performance of CBR-NMI

is better than that of CBR-MDL because the case

solutions of CBR-NMI are computed based on hu-

man segmentations, while the case solutions of CBR-

MDL are computed based on the MDL-based objec-

tive function. The solutions of CBR-NMI should be

closer to the k

∗

than the solution of CBR-MDL. Even

though the CBR based on SNMI acheived slightly

lower performance than the CBR based on MDL, it

has two dominant advantages, namely, it performs

much faster and requires no original image data in the

computation.

For MS and JSEG ensembles, the performances

of both CBR-NMI and CBR-MDL are slightly bet-

ter than the performances of GM and MDL, while

the performance of CBR-NMI and CBR-MDL are

slightly worse than the performances of GM and

MDL for an FH ensemble. However, the standard de-

viation of the performance accuracy of our CBR ap-

proach is better than GM and MDL approaches in all

cases. This indicates that our approach is more stable

than the rest. Even though our CBR approach does

not show a signiﬁcant improvement over the other

methods, we argue that it does show the signiﬁcant

reduction of computation time, especially the CBR

approach based on SNMI quality measure. This con-

tribution would make the segmentation combination

framework more feasible in practical applications.

Comparison of Computation Time

We summarize the details of the four methods in com-

parison with the proposed CBR approach in Table 3

in terms of the four computation requirements: i) the

number of combination results to be computed; ii) the

number of segmentations that need to be evaluated us-

ing the MDL quality criterion; iii) the number of times

needed for computing a distance between two seg-

mentations based on NMI measure; and iv) the num-

ber of case matching using Euclidean distance used in

the CBR approach. We did not discuss about the time

spend on a generation of segmentation ensembles re-

quired by a segmentation algorithm because this step

is a preprocessing task needed by all approaches.

In the table |k| refers to a number of all possible

combination results with different number of regions

in [k

min

max

] and N refers to a number of segmen-

tations in an ensemble. In practice |k| is typically

larger than N. It is obvious that the MDL method re-

quires the highest computation time, while the CBR

approach requires the least computation time. In all

experiments conducted in this work, |k| is equal to 49,

where [k

min

max

] is [2, 50], and N is equal to 24.

The actual computation time (shown in parenthe-

sis) used to process one input image of each approach

implemented in MATLAB on an Intel Core i7, CPU

2.30GHz. The computation time reported in the ta-

ble are the average of computation times of 20 test

images. Experimental results show that the compu-

tation time of the CBR based on MDL quality mea-

sure is substantially less than that of MDL approach

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and slightly less than the GM approach. More inter-

estingly, the computation time of the CBR based on

SNMI quality measure is substantially less than both

MDL and GM approaches and without the loss of seg-

mentation combination accuracy. We are very posi-

tive about the potential of our proposed approach be-

cause the only computational burden of our approach

is just one step for evaluating quality of segmentations

in an ensemble. If a more effective segmentation val-

idation method is available, we can not only greatly

reduce the overall computation time, but also improve

the accuracy of the combinationation results. Unlike

GM and MDL approaches that have a ﬁx overhead of

computing a series of combination results.

5 CONCLUSIONS AND FUTURE

WORK

We proposed a new approach for automatically de-

termining the number of regions in a ﬁnal segmen-

tation combination result. We presented a novel use

of cluster ensemble concept to handle this difﬁcult

problem. We ﬁrst studied the correlation between a

segmentation ensemble and k

∗

of an image. The in-

formation about k

∗

is then extracted from an ensem-

ble and used as a knowledge domain for building a

case base. We represented the extracted knowledge

in terms of the number of regions of segmentations

in an ensemble and the qualities of them. The con-

cepts of NMI and MDL are used to evaluate the qual-

ity of ensemble members. By utilizing this informa-

tion, our case-based reasoning is able to settle the true

number of regions in the ﬁnal segmentation combi-

nation result as good as the more sophiticated meth-

ods. Even though our CBR approach does not show

any signiﬁcant improvement over the existing meth-

ods, it does show the signiﬁcant reduction of compu-

tational time without the loss of segmentation com-

bination accuracy. This contribution would make the

segmentation ensemble concept more feasible in real-

world applications. However, the results of our CBR

approach presented in this paper are one of our ﬁrst

attempts. There is room for improvement, actually, in

most steps of our approach. More effective and so-

phisticated methods should be very useful to improve

the performance of the proposed approach. It is also

interesting to apply our approach in different domains

or in a general data cluster ensemble application.

REFERENCES

Comaniciu, D. and Meer, P. (2002). Mean shift: A robust

approach toward feature space analysis. IEEE Trans.

Patt. Anal. Mach. Intel., 24:603–619.

Deng, Y. and Manjunath, B. (2001). Unsupervised segmen-

tation of color-texture regions in images and video.

IEEE Trans. Patt. Anal. Mach. Intel., 23(8):800–810.

Dubes, R. C. (1993). Cluster analysis and related issues.

Handbook of Pattern Recognition & Computer Vision,

pages 3–32.

Felzenszwalb, P. and Huttenlocher, D. (2004). Efﬁcient

graph-based image segmentation. International Jour-

nal of Computer Vision, 59(2):167–181.

Fischer, B. and Buhmann, J. (2003). Bagging for path-

based clustering. IEEE Trans. Patt. Anal. Mach. Intel.,

25(11):14111415.

Fowlkes, C., Martin, D., and Malik, J. (2003). Learning

afﬁnity functions for image segmentation: Combining

patch-based and gradient-based approaches. In CVPR,

volume 2, pages 54–61.

Franek, L., Jiang, X., and Wattuya, P. (2012). Local in-

stability problem of image segmentation algorithms:

Systematic study and an ensemble-based solution.

IJPRAI, 26(5).

Fred, A. L. N. and Jain, A. K. (2005). Combining multiple

clusterings using evidence accumulation. IEEE Trans.

Patt. Anal. Mach. Intel., 27(6):835–850.

Frucci, M., Perner, P., and Sanniti, G. (2008). Case-based

reasoning for image segmentation. IJPRAI, 22:1–14.

Grimnes, M. and Aamodt, A. (1996). A two layer case-

based reasoning architecture for medical image un-

derstanding. In European Workshop on Advances in

Case-Based Reasoning, pages 164–178.

Halkidi, M., Batistakis, Y., and Vazirgiannis, M. (2001). On

clustering validation techniques. Journal of Intelligent

Information Systems, 17:107–145.

Haralick, R. M., Shanmugam, K., and Dinstein, I. (1973).

Textural features for image classiﬁcation. IEEE Trans.

Syst, Man, and Cyber, 3(11):610–630.

Hardy, A. (1996). On the number of clusters. Computa-

tional Statistics and Data Analysis, 23:83–96.

Jiang, Y. and Zhou, Z.-H. (2004). Som ensemble-based im-

age segmentation. 20(3):171–178.

Kolodner, J. (1993). Case-Based Reasoning. Morgan Kauf-

mann, San Mateo, CA.

Leake, D. (1996). Case-Based Reasoning: Experiences,

Lessons, and Future Directions. AAAI Press, CA.

Martin, D. R., Fowlkes, C., Tal, D., and Malik, J. (2001).

A database of human segmented natural images and

its application to evaluating segmentation algorithms

and measuring ecological statistics. In ICCV, pages

416–425.

Milligan, G. W. and Cooper, M. C. (1985). An examination

of procedures for determining the number of clusters

in a data set. Psychometrika, 50:159179.

Nguyen, N. and Caruana, R. (2007). Consensus clusterings.

In IEEE ICDM, pages 607 – 612.

Perner, P. (1999). An architecture for a cbr image segmen-

tation system. Journal on Engineering Applications in

Artiﬁcial Intelligence, 12(6):749–759.

ICPRAM2014-InternationalConferenceonPatternRecognitionApplicationsandMethods

294

Perner, P., Guether, T., and Perner, H. (2003). Airborne

fungi identiﬁcation by case-based reasoning. In Work-

shop on CBR in the Health Sciences.

Rabinovich, R., Belongie, S., Lange, T., and Buhmann,

J. M. (2006). Model order selection and cue combina-

tion for image segmentation. In CVPR, pages 1130–

1137.

Rao, S., Mobahi, H., Yang, A., Sastry, S., and Ma, Y.

(2009). Natural image segmentation with adaptive

texture and boundary encoding. In ACCV, pages 135–

146.

Rohlﬁng, T., Russakoff, D. B., and Jr., C. R. M.

(2004). Performance-based classiﬁer combination

in atlas-based image segmentation using expectation-

maximization parameter estimation. IEEE Trans.

Med. Imaging, 23(8).

Strehl, A. and Ghosh, J. (2002). Cluster ensembles - a

knowledge reuse framework for combining multiple

partitions. Machine Learning Research, 3:583–617.

Topchy, A. P., Jain, A. K., and Punch, W. F. (2005). Clus-

tering ensembles: Models of consensus and weak

partitions. IEEE Trans. Patt. Anal. Mach. Intel.,

27(12):1866–1881.

Vega-pons, S. and Ruiz-shulcloper, J. (2011). A survey of

clustering ensemble algorithms. IJPRAI, 25(3):337–

372.

Wattuya, P., Jiang, X., Prassni, J., and Rothaus, K. (2008).

A random walker based approach to combining mul-

tiple segmentations. In ICPR, pages 1–4.

Wattuya, P., Soonthornphisaj, N., and Jiang, X. (2012). Us-

ing soft case-based reasoning in model order selection

for image segmentation ensemble. In JSAI.

SegmentationEnsemble-AKnowledgeReuseforModelOrderSelectionusingCase-basedReasoning

295