Robust Object Segmentation using Split and Merge - East West ...

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Addressing the performance abilities and shortcomings ofthe aforementioned modified SM algorithm mentioned inSection 2, a new algorithm namely robust objectsegmentation based on split and merge (ROSSM) isproposed in this paper. The proposed ROSSM algorithmuses the concept of multistage SM technique discussed insection 2.3 to be robust in segmenting objects in an imagedynamically. It uses T-test for both splitting and mergingregions. Besides, it considers intra-region varianceminimization and intra-region variance maximizationthroughout the merging process to maintain the objectsidentity. It also takes into account the human visualperception limitation to maintain the realistic shapes of theidentified objects. These concepts are highlighted in thenext sections.3.1. Region Stability TestThere are many theorems to identify region stability such asZ-test, T-test and Chi-square test [16]. Among them, T-testis considered in this paper because of its universalacceptance and well recognition as statistical theorem toidentify the stability of a sample space from its samplevalues. Let S be a sample space and s be a set of samplessuch that s ∈ S . Applying T-test, it can be identifiedwhether the sample set s is stable within its sample space Sor not [16]. For large sample set (over 30 samples), the95% fiducial limits of population mean are given byX ± t0.05SEand 99% fiducial limits of population meanare given by ± t SE where the standard error of meanSE XX0. 01with0. 05σn= (1)t =1.96 and t0. 01=2.58 [16].For small sample set (less than 30 samples), the decisiondepends on the value of t which is given by the followingequation:X − µt = n(2)Swhere X = mean of the sample, µ = mean of thepopulation, n = size of the sample, and S = StandardDeviation of the sample. The 95% fiducial limits ofSpopulation mean are given by X ± t 0. 05while then99% fiducial limits of population mean are given byX ±Snt 0.01. Depending on the degree of freedom, thevalue of t0.05varies from 12.71 to 2.04 and for t0.01from63.66 to 2.75 while the degree of freedom for small sampleis given by n-1 and for large sample it is infinity [16]. Thistheorem is used to compute the feature values in theROSSM algorithm for both split and merge stages. Thistheorem solves the problem of feature selection anomaliesof the SM algorithm as T-test ensures the region stability interms of any features such as pixel intensity.3.2. Intra-variance and Inter-variance TestThe optimization of the proposed ROSSM algorithm leadsto produce regions having less intra-variance and moreinter variances. Hence, the global solution can be achievedif the intra-and inter-variance test is applied.In the image segmentation domain, the number of clustersis not given a priori. Since, the number of clusters insegmentation algorithm is neither fixed nor manuallyprovided, the minimization of the intra-region variabilityand the maximization of the inter-region variability in theunion of two regions are considered [11]. However, boththe straight minimization of the intra-region variability andthe maximization of the inter-region variability lead toundesirable trivial solutions being N regions or 1 regionrespectively. ROSSM minimizes the intra- regionvariability while at the same time constraining the interregionvariability in the union of two regions. The regionbehind such condition is - if two regions belong to singleobject, their intensities should be similar and as a resulttheir combined variability should be minimal. On the otherhand, when one of nearly intensified region disappears dueto merging, the verity of variance is increased while thenumber of the regions is decreased. This leads tomaximization of intra-region variability. Because of thisinterrelationship, the features perform well. In this way, theinter-region variability constraint defines the scale at whichtwo regions can be differentiated from each other. Tominimize the intra- region variability, the sum-of-squarederrorcriterion is used such that it fits better to the model.Further, it implements the joint intra-region variabilityconstraint as a minimum variance for the union of twoclusters. At the same time, joining two clusters maximizesthe inter-cluster variability. This leads to the followingregion growing model:min ∑RR i ∈ Rn Var(R )where niis the number of pixels in region i, Var(R i ) is thevariance of the region isubject to:1Var(Y) = ∑ || x −Y∀Ri, Rj, i ≠ j;MaxVar(R −{R , R } ∪ ( Rwhere MaxVar(R)=Var(Var(R k ))ijiii
neighbor and merging any two regions R i and R j decreasesthe inter-variance of the image. After application of this test,the stable regions that have minimum variance withinthemselves are obtained. At the same time, their inter-regionvariances are maximized. This test allows finding a globalsolution where the threshold is dynamically updated therebyto eliminate the problems of result anomalies due tothreshold change. However, there are some rare situations inwhich individual cluster can violate these constraints [11].3.3. Concept of Human PerceptionIf the change of any object or feature is less than or equal to0.5dB, human perception is unable to detect the change[17]. Now, let the larger region be R l and the smaller regionbe R s . Presence of R s collocated to R l creates distortion. Theregions R s with R l will be merged considering them belongsto the same object if they satisfy the following equation:Rl0.5=20logRs0.5⇒ anti-log( )20Rl⇒ 1.059=R( )=sRlRs⇒ R l =1.059R s (4)Referring (4), it can then be said that for any twoneighboring regions, if the size of one region is less than orequal to 6% of another one, human perception cannotdifferentiate these two regions. This concept can be used toallow the SM to identify any non-patterned shaped objectaccurately without any distortion.4. Proposed ModelTo enhance the performance of segmentation process and toaddress the drawbacks of the SM algorithm mentioned inSection 2, this section presents a newly developed robustobject segmentation based on split and merge (ROSSM)algorithm based on the basic idea of the SM algorithm. Themain two constituent parts of the ROSSM algorithm are: (i)split stage, and (ii) merge stage. Since the splitting is thefirst step of the proposed ROSSM algorithm, it is detailed inthe next section.4.1. Split StageIn the split stage, it recursively subdivides a larger regioninto almost equally four sub-regions based on the thresholdvalue which is calculated applying T-test and its 95%fiducially limit. This fiducially limit ensures the regionstability. Let R i be a larger region at any instant of splitstage. If the P(R i )=FALSE as mentioned in Section 2, itsub-divides the region R i into four almost equal sub-regionR j where j=1,2, …,4. The idea behind this method is thatsplit stage of it partitions the whole image into numeroussmall regions. The main characteristics of each splittedregion are that they are individually stable in nature asmentioned in Section 3. They may either be a full object ora small part of a full object (i.e. a leaf of 3 intensity levelmay be represented as 3 regions in this stage). In this stagean image is spitted into number of sub-regions, for exampleas shown in the Figure 3. After splitting the image into alarge number of smaller regions, it needs to merge thesplitted regions to form final segmented regions and themerge stage is detailed in the next section.(a)(b)Figure 3: (a) Original image, (b) Splitted regions of (a)4.2. Merge StageThe merge stage of the proposed ROSSM algorithmcontains three main constituent parts which are applied onlyon the connected regions and that are: (i) merging on thebasis of T-test, (ii) merging for inter-variance maximizationand intra-variance minimization, and (iii) merging regionsconsidering human perception. Since the merging of regionson the basis of region stability is the first step of theproposed ROSSM algorithm, it is detailed in the nextsection.4.2.1. Merging on the basis of stability testAny two connected regions are qualified to be merged ifthey are both stable i.e., these two regions are within the99% fiducially limit of T-test. The idea behind this mergingis to combine those parts of an object which wereunexpectedly separated due to hard partitioning in the splitstage. Moreover, if two connected regions having aminimum combined intra variance are chosen for mergingto form a larger region, the merging would be more fruitful.This issue is already discussed in section 3.2. This processwill continue until any region satisfies to be merged underthe criteria of T-test. After completion of merging on thebasis of T-test, regions obtained are stable in nature. Theymay either be a full object or a stable part of an object. Atthis stage, there may exist some stable parts of objectswhich are not still merged. To merge these components ofobjects, the following technique is applied.4.2.2. Merging for Inter-variance Maximization andIntra-variance Minimization
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