Local adaptive receptive field self-organizing map for image color segmentation

Image and Vision Computing 27 (2009) 1229–1239

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Image and Vision Computing

journal homepage: www.elsevier .com/locate / imavis

Review article

Local adaptive receptive field self-organizing map for image color segmentation

Aluizio R.F. Araújo *, Diogo C. CostaUniversidade Federal de Pernambuco, Centro de Informática – CIn, Departamento de Sistemas da Computação, Av. Professor Luís Freire, s/n, Cidade Universitária,50740-540 Recife, PE, Brazil

a r t i c l e i n f o

Article history:Received 18 July 2007Received in revised form 31 October 2008Accepted 30 November 2008

Keywords:Self-organizing mapColor segmentationAdaptive receptive-fieldImage processing

0262-8856/$ - see front matter � 2008 Elsevier B.V. Adoi:10.1016/j.imavis.2008.11.014

* Corresponding author. Tel.: +55 81 2126 8430; faE-mail addresses: aluizioa@cin.ufpe.br (A.R.F. Ar

Costa).

a b s t r a c t

A new self-organizing map with variable topology is introduced for image segmentation. The proposednetwork, called a Local Adaptive Receptive Field Self-organizing Map (LARFSOM), is a fast convergent net-work capable of color segmenting images satisfactorily, which has optimum self-adaptive topology andachieves good PSNR values. LARFSOM is compared to SOM, FS-SOM and GNG, self-organizing maps usedfor color segmentation. LARFSOM reached a higher color palette variance and a better 3D RGB color spacedistribution of learned data from the training images than the other models. LARFSOM was tested to seg-ment images with different degrees of complexity and has given promising results.

� 2008 Elsevier B.V. All rights reserved.

1. Introduction

Automated image recognition processes are usually divided intosmaller problems or steps [4,9,19] as shown in Fig. 1. There are fivesteps widely adopted to create an intelligent or automatic imagerecognition system, a typical computer vision problem.

Image acquisition is the step in which the images generated by animaging sensor are obtained. Image disturbance and noise are re-moved during the pre-processing step. Then, the segmentationstage separates objects or elements present in the data from thebackground. The Recognition and Interpretation step analyzes eachsegmented object in order to identify them. Finally, post-processingyields a report or other kind of diagnostic about the image acquired.

Segmentation is the process of dividing (segmenting) an imageinto objects or elements that are coherent under some criteria [4].Segmentation techniques are often based on two image features[3,9]: discontinuity and similarity. Discontinuities are found in im-age regions where there are abrupt color changes. Similarities arefound in image regions where there is little color change, if any.

Artificial neural network models were proposed to segmentimages directly from pixel similarity or discontinuity. More than200 neural networks used in image processing are presented bydeRidder and Handels [4] and a 2D taxonomy for image processingalgorithms is introduced. Cheng et al. [3] discuss many color imagesegmentation techniques such as histogram thresholding, charac-teristic feature clustering, edge detection, region-based methods,fuzzy methods, and neural networks.

ll rights reserved.

x: +55 81 2126 8438.aújo), dcc@cin.ufpe.br (D.C.

Color segmentation is successfully performed by Self-organiz-ing Maps (SOMs) and related networks in the following articles[5,17,21]. In [17], a two-stage strategy includes a fixed-size two-dimensional feature map (SOM) to capture the dominant colorsof an image in an unsupervised way, and then a second stage, com-bines a variable-sized one-dimensional feature map and colormerging to control the number of color clusters that are used forsegmentation. The model in [5] is based on a two-step neural net-work. In the first step, a SOM performs color reduction and then asimulated annealing step searches for the optimal clusters fromSOM prototypes. This task involves a procedure of hierarchical pro-totype learning (HPL) to generate different sizes of color prototypesfrom the sample of object colors.

A color segmentation algorithm should be adaptive with respectto the final number of selected colors/objects because non-adap-tive color algorithms often produce poor color segmentation re-sults. SmART [21] is characterized by a variable number of nodes,which grows as new prototypes are needed. The new nodes areconnected to two others under a triangle-shaped neighborhood. In-stead of using the topological map to implement lateral plasticitycontrol as a SOM does, the topological relations between nodeswork as an inhibitory function of adaptive learning upon the pro-totype vectors.

Some color quantization implementations using neural networkarchitectures were proposed in [1,2,18,20,22]. Chang et al. [2] pro-posed a modified SOM called a Frequency Sensitive Self-organizingMap (FS-SOM). Chang et al. [2] claim that although the SOMreaches good results in color quantization, its performance is sen-sitive to optimal parameter selection in the training stage. In thisparticular point, the FS-SOM is indeed more robust than the SOMat selecting parameters due to two major differences between

Fig. 1. Automated image recognition processing steps.

1230 A.R.F. Araújo, D.C. Costa / Image and Vision Computing 27 (2009) 1229–1239

FS-SOM and SOM. In the former, the learning rate is a function ofthe number of times a node is triggered (the winning frequency):learning is inversely proportional to the number of victories. FS-SOM has a re-initialization step of weight vectors associated withnon-winning nodes, in order to raise their chances of winning inthe future.

Atsalakis and Papamarkos [1] proposed a new method for colorreduction called Self-Growing and Self-Organized Neural Gas(SGONG). This technique combines the characteristics of the Grow-ing Neural Gas (GNG) and the SOM. From the GNG, the growingnumber of nodes mechanism is used, and from the SOM, the learn-ing mechanism is used. A new method for Estimation of the MostImportant Classes (EMIC) is also introduced to reduce the numberof final classes, thus leading to a very small number of final colors.The color reduction technique proposed in [18] uses a tree cluster-ing procedure. In each node of the tree, a neural network cluster(NNC) is fed by image color values and additional local spatial fea-tures. The clusters consist of a Principal Component Analyzer and aKohonen SOM. The output neurons of the NNC define the colorclasses for each node.

Another color quantization model called Sample-Size AdaptiveSOM (SA-SOM) is presented in [20]. The main goal of this modelis to adapt to the variations of network parameters and trainingsample size. The SA-SOM, which shares many characteristics withthe FS-SOM, achieved higher PSNR rates than FS-SOM and requiredmany fewer training samples, resulting in a faster training time. In[22], a hybrid neuro-fuzzy technique based on a two stage processis proposed by Zagoris et al. Initially a SOM produces a predefinednumber of image colors and then the Gustafson–Kessel Fuzzy Clas-sifier (GKFC) is used to reduce the final number of colors.

We propose the LARFSOM, a neural model which aims to colorsegment images based on their color distribution. LARFSOM isself-adaptive with respect to the number of final colors, a suitablefeature for color segmentation, as opposed to both the fixed colorquantization models [2,4,18,20,22] and also to the color segmenta-tion model [17] with an initial fixed-size map. LARFSOM does notuse supervised learning as [5] does, thus incremental learning is via-ble. Unlike SmART [21], LARFSOM does not place a restriction on tri-angular-shaped neighborhoods for new nodes, which limit nodes toa maximum of four neighbors. The LARFSOM topology freely growsand modifies itself during training. Therefore, nodes may have asmany neighbor nodes as necessary to yield an n-dimensional map.

For test purposes, the SOM [13], the FS-SOM [2] and the Grow-ing Neural Gas [6,7] networks were also implemented and used forcolor segmentation. The SOM and FS-SOM have a fixed topologyand a pre-defined number of nodes, an undesired feature for imagesegmentation. GNG has a free topological structure which varies inpre-defined intervals and adjusts the topology to the training pat-terns. However, GNG grows periodically and indefinitely unless aconvergence criterion is met. LARFSOM grows only when it is nec-essary and has fast convergence.

The remainder of this paper is organized as follows. Section 2describes the color segmentation algorithms for the SOM, FS-SOM and GNG networks. Section 3 introduces the LARFSOM thatit is proposed to use for color segmentation. Section 4 shows theLARFSOM segmentation results, discusses and compares them to

the SOM, FS-SOM, GNG and other models. Finally, Section 5 drawsconclusions and suggests future studies.

2. Self-organizing maps and color segmentation

The color quantization process can be characterized by twosteps: (i) autonomous selection of the most representative colorsfrom all colors present in the original image to form the color pal-ette; and (ii) mapping each color in the original image to the near-est color in the palette. The final image must have only the selectedcolors and should be as similar as possible to the original one.

In fact, color quantization and color segmentation are based onthe same process of reducing the number of image colors. The maindifference is that color quantization usually results in a pre-definedfinal number of colors and the larger the number of final colors, thebetter is the resultant image. However, in color segmentation, eachfinal color in the resultant image represents an object. Thereforeonly a few colors are desired, otherwise, many objects or subpartsof objects will be detected. Hence, in color segmentation only a fewdistinct and dominant colors are desired.

The color quantization process using self-organizing maps has a3D input vector (red, blue, and green values) to compose colors forevery pixel of an image, according to the RGB standard. Each pixelis given as an input to a SOM network. Therefore the weight vec-tors are also 3D. The RGB standard values, ranging from 0 to 255,are normalized (0–1) before being input to the network.

2.1. Self-organizing map (SOM)

The SOM [13] is an one-layer neural network in which an inputvector X = [x1,x2, . . .,xn]T is fed into the network, often geometricallyarranged. All nodes are connected to some others, often in an one ortwo-dimensional structure and each node i is associated with aweight vector Wi = [wi1,wi2, . . ., win]T with the same dimension ofthe input vector. Through unsupervised learning, the output nodesare tuned and organized, i.e., the information presented is topolog-ically encoded. SOM networks are used for data clustering, datasegmentation, pattern detection, and feature extraction. There areseven processing steps required when SOM networks are used forcolor quantization [2]:

Step 1: Initialize the neighborhood variance, r0; the learningrate, g0; the neighborhood function, H0; the time iteration,t = 0; and the number of nodes, N, to determine the numberof colors in the quantized image:

wi ¼ ½randð0; 0:2Þ; randð0;0:2Þ; randð0; 0:2Þ�T ; 8i 2 N ð1Þ

The initialization in (1) produces random numbers, ranging from 0to 0.2, that do not induce any initial topological order to SOM, thusallowing it to arrange itself in the training stage. An example of arandomized initial map is shown in Fig. 2.

Step 2: Present a randomly chosen image pixel, x(t) = [r(t),g(t),b(t)]T, as input data, to the network.Step 3: Calculate the Euclidian distance between the input vec-tor, x(t), and the weight vectors wi, as follows:

kxðtÞ �wiðtÞk ¼ ðrðtÞ �wirðtÞÞ2 þ ðgðtÞ �wigðtÞÞ2 þ bðtÞ �wibðtÞð Þ2

ð2Þ

where x(t) is the input data pixel vector whose RGB values are r(t),g(t), b(t), and wi(t) is the weight vector of the current node, i. Thesmallest distance between the input vector and the weight vectorsof all nodes determines the best matching unit (BMU).

Step 4: Update the weight vector of the BMU and its neighbors:

wiðt þ 1Þ ¼ wiðtÞ þ gðtÞHðtÞðxðtÞ �wiðtÞÞ ð3Þ

Fig. 2. An 8 � 8 SOM random initialized map.

A.R.F. Araújo, D.C. Costa / Image and Vision Computing 27 (2009) 1229–1239 1231

where H(t) is the neighborhood function given by:

HðtÞ ¼ exp � dist2r2ðtÞ

� �ð4Þ

where dist is defined as the distance between the weight vectors ofBMU and the current node.

Step 5: Add 1 to the time iteration, t, and update the neighbor-hood radius, r(t), and learning rate, g(t):

gðtÞ ¼ g0 exp � tk

� �ð5Þ

r ¼ r0 exp � tk

� �ð6Þ

where k is a constant related to the maximum number of iterationsand the size of the initial neighborhood:

k ¼ max iterations= logðr0Þ ð7Þ

Steps 2 to 5 are repeated until the maximum number of iterationsor the convergence criterion (8) is met:

e ¼ 1N

XN�1

i¼0

kwiðtÞ �wiðt þ 1Þk26 emin ¼ 10�4 ð8Þ

Step 6: After the training process, assign a color represented bya node weight vector to each color in the palette.Step 7: In the image, replace each original pixel color by itsnearest one in the color palette.

2.2. Frequency sensitive self-organizing map (FS-SOM)

Chang et al. [2] proposed a modified version of the SOM called aFS-SOM based on Frequency Sensitive Competitive Learning (FSCL)[14]. In this paper, FS-SOM is an adapted version of the original FS-SOM [2]. The main differences between the original and the mod-ified FS-SOM are: (1) the weight vector initialization proposed byChang et al. [2] was uniform, and now it is random; (2) the originalinput selection, a butterfly permutation, was changed to a simplerandomized selection; (3) the neighborhood influence functionwas replaced by the SOM’s (4) neighborhood function; and (4)the periodic node weight re-initialization process was replacedby a one-time-only re-initialization. The frequency-sensitive learn-ing rate remains the same. Such modifications aimed to diminishthe computational effort increasing the response speed at the ex-pense of losing PSNR accuracy. This is justified because, for imagecolor segmentation, only a few final colors are desired, the domi-nant ones. The original FS-SOM was applied to handle color quan-tization of images when many colors are present in the final image.In addition, the FS-SOM needs 80% of pixel presentations to achievegood results [2,1], which leads to a long time being needed for

training which is not suitable for a low number of final colors. Afaster training FS-SOM would be more appropriate for color seg-mentation. The modified FS-SOM algorithm for color quantizationhas several differences from the SOM algorithm, as shown below.

Step 1: The FS-SOM uses a counter, ui, of the number of victoriesof each node, initialized as ui = 1.Step 3:The FS-SOM determines the winning node based on theEuclidian distance, as the SOM does. Its neighbor’s weights areupdated by (9). However, the SOM learning rate, g(t), a functionof time (5), is replaced by a frequency sensitive learning rate,G(ui), related to the winning frequency for each neuron:

wiðt þ 1Þ ¼ wiðtÞ þ GðuiÞHðtÞðxðtÞ �wiðtÞÞ ð9ÞGðuiÞ ¼ u�0:5

i ð10Þ

where ui is the winning counter of each neuron:

uiðt þ 1Þ ¼ uiðtÞ þ HðtÞ ð11Þ

where G(ui) is a monotonic decreasing function of ui. The H(t)neighborhood influence function is the same (4).

After a predefined time iteration, suggested to be t = N*20 (N isthe number of nodes), the nodes that have never won, ui = 1, arereinitialized, and have their weights assigned to represent the colorof a randomly selected pixel of the original image. The reinitializednode has a greater chance of winning. All other steps are identicalto those for the SOM.

2.3. Growing neural gas (GNG)

GNG, proposed by Fritzke [6,7], determines its own number ofnodes and topology based on the stochastic distribution of trainingpatterns. This is different from SOM and FS-SOM, whose number ofnodes and connections are defined before training. Hence, GNG ismore suitable for image segmentation as the final number of colorsis not pre-defined. The GNG algorithm for color quantization is de-scribed below:

Step 1: Initialize the set N of nodes with two units N = {c0,c1}whose weights are copied from the RGB values of two randomlychosen image pixels. Initialize the set C of edges with the con-nection (a,b), and the set I, that references the ages of the edgesas performed in [6,7] and set age(a,b) = 0:

C ¼ fða; bÞg ð12ÞI ¼ fageða;bÞg ð13Þ

Step 2: Present a randomly chosen image pixel n = [r g b]T to thenetwork as input data.Step 3: Calculate the Euclidian distance between the sample n

and the weight vectors (wis) as follows:

dðn;wiÞ ¼ kn�wik2 ð14Þkn�wik2 ¼ ðr �wirÞ2 þ ðg �wigÞ2 þ ðb�wibÞ2 ð15Þ

Calculate the shortest distance between the input and all weightvectors to find the best matching unit (BMU):

dðws1 ; nÞ 6 dðws2 ; nÞ 6 dðwi; nÞ; 8i 2 N ð16Þ

where N is the all-node set.Step 4: Insert a new connection between s1 and s2if it does notexist. Set the age of the link s1 � s2 to zero:

ageðs1;s2Þ ¼ 0 ð17Þ

Step 5: Add the Euclidian distance from n to weight vector ws1,to the error variable of s1:

1232 A.R.F. Araújo, D.C. Costa / Image and Vision Computing 27 (2009) 1229–1239

DEs1 ¼ kn�ws1k2 ð18Þ

Step 6: Update the weight vectors of the winner and its directtopological neighbors Ns1 , by fractions eb and en, respectively,of the total distance to the input signal, n:

Dws1 ¼ ebðn�ws0Þ ð19ÞDwi ¼ enðn�wiÞ; 8i 2 Ns1 ð20Þ

Step 7: Increment the age of all edges emanating from s1:

ageðs1; iÞ ¼ ageðs1; iÞ þ 1; 8i 2 Ns1 ð21Þ

Step 8: Remove the edges with ages greater than amax. Removeunits which no longer have emanating edges.Step 9: If the current iteration is an integer multiple of a param-eter k, insert a new unit as follows:� Find the unit q with the maximum accumulated error:

q ¼ arg maxc2N

Ec ð22Þ

� Find the neighbor f of q with the maximum accumulatederror:

f ¼ arg maxc2Nq

Ec ð23Þ

� Insert a new unit r to the network and interpolate its weightvector from q and f.

N@N [ frg; wr ¼ ðwq þwf Þ=2 ð24Þ

� Add the edges (r,q) and (r,f) and remove the edge (q,f) fromthe edges set C.

� Decrease the error variables of q and f by a fraction a:

DEq ¼ �aEq; DEf ¼ �aEf ð25Þ

� Interpolate the error variable of r from q and f

Er ¼ ðEq þ Ef Þ=2 ð26Þ

Step 10: Decrease the error variables of all units by b

DEc ¼ �bEc; 8c 2 N ð27Þ

Step 11: Update the number of iterations t = t + 1 and repeatfrom Step 2 unless the stop criterion (8) is reached.Step 12: After the training process, assign each color repre-sented by a weight vector to a color in the palette.Step 13: Replace each original pixel color in the image by itsclosest one in the color palette.

3. Local adaptive receptive field self-organizing map (LARFSOM)

LARFSOM presents a new node insertion strategy based on thesimilarity between an input pattern and the existing prototypes.The similarity is determined by means of an activation thresholdvalue, calculated with respect to a local neighborhood receptivefield value. As new nodes are added to the network, the topologyis modified by creating and deleting edges, and nodes are free tohave as many neighbors as necessary.

The LARFSOM takes advantage of some elegant characteristicsof SOM [13] and Grow When Required (GWR) [15] networks. Thecompetitive-learning and clustering capabilities of SOM are pre-served as is the topological distribution of data learned amongthe map neighbor nodes. Analogous to GWR, LARFSOM grows onlywhen new nodes are required, based on an activation threshold.However, LARFSOM is simpler than GWR in the sense that thenode-winning counter is simpler to calculate and only the bestmatching unit has its connections updated. Unlike GNG [6,7],LARFSOM grows only when the activation value of a prototype isnot satisfactory according to a threshold and not at fixed iterationintervals. In addition it has faster convergence.

LARFSOM receives an input pattern and then calculates theclosest node by Euclidian distance. A new connection betweenthe two best matching (closest to the input pattern) units is cre-ated. By an activation criterion, the BMU is tested to verify if itscurrent prototype is sufficiently similar to the input pattern. Ifthe activation value is satisfactory, the BMU is trained to improveits ability to respond to similar future stimuli. Otherwise, a newnode is created to represent a new prototype for the current inputand the two shortest connections among the new node and the twoBMUs are created. The main difference between the GWR andLARFSOM activation criteria is the usage of a receptive field, whichinfluences the activation value. The receptive field works as inRadial Basis Functions Networks [10] limiting the influence of pro-totype clusters. At the end of the training process, disconnectedunits are removed.

3.1. LARFSOM algorithm

The LARFSOM algorithm has 11 steps: (1) parameter initializa-tion; (2) selection of input pattern (a particular pixel); (3) searchfor best matching unit (BMU); (4) connection insertion betweenthe two best units; (5) calculation of the BMU local receptivefield; (6) calculation of BMU activity based on the receptive field;(7) possible insertion of a new node or updating of BMU weights;(8) verification of convergence criterion; (9) elimination of dis-connect nodes; (10) construction of the color palette; and (11)construction of the color segmented image. These steps are de-tailed as follows.

Step 1: Initialize the parameters: final learning rate (qf), learningrate modulator (e), activity threshold (aT), number of wins of nodei (di = 0), maximum number of victories of each node (dm), thetime iteration (t = 0), the minimum error (emin), and the initialnumber of connected nodes (N = 2), the weights of which are cop-ied from the RGB values of two randomly chosen image pixels.Step 2: Present a randomly chosen image pixel n = [r g b]T to thenetwork as input data.Step 3: Calculate the Euclidian distance between the sample n

and the weight vectors (wis) as follows:

dðn;wiÞ ¼ kn�wik2 ð28Þkn�wik2 ¼ ðr �wirÞ2 þ ðg �wigÞ2 þ ðb�wibÞ2 ð29Þ

Calculate the shortest distance between the input and all weightvectors to find the best matching unit (BMU):

dðws1 ; nÞ 6 dðws2 ; nÞ 6 dðwi; nÞ; 8i 2 N ð30Þ

where N is the all-node set. Increment the wins counter of BMU:dS1 ¼ dS1 þ 1.

Step 4: Insert a new connection between s1 and s2 if it does notexist.Step 5: Calculate the receptive field of s1:

rs1 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðws1r �ws2rÞ2 þ ðws1g �ws2gÞ2 þ ðws1b �ws2bÞ2

qð31Þ

Step 6: Calculate the activity of s1:

as1 ¼expð�kn�ws1kÞ

rs1

ð32Þ

Step 7: Insert a new node if BMU activation is below a threshold(aT), or else update the BMU weight vector:If as1 < aT

� Add a new node with weight vector wn = n

� Update the number of nodes N = N + 1� Remove the connection between s1 and s2

� Calculate the distances

A.R.F. Araújo, D.C. Costa / Image and Vision Computing 27 (2009) 1229–1239 1233

dðwn;ws1 Þ;dðwn;ws2 Þ;dðws1 ;ws2 Þ

� Insert connections between nodes with the two smallestdistances.

Else Dws1 ¼ q� ðn�ws1 Þ ð33Þ

where q ¼ e� qðdi=dmÞf ; di 6 dm

e� qf ; di > dm

(

Step 8: Update the number of iterations t = t + 1 and repeatfrom Step 2 unless the stop criterion (8) is reached.

Step 9: Remove disconnected nodes.Step 10: After the training process, assign each color repre-

sented by a weight vector to a color in the palette.Step 11: Replace each original pixel color in the image by its

closest one in the color palette.The number of nodes after the training process definesthe number of palette colors. To use them to recon-struct an image, an interpolation method is proposedto generate more colors based on those in the palette.Thus, a network with few nodes is suitable for colorsegmentation of full color images, so reducing thetraining time significantly. To do color interpolation,Step 11 is replaced by Step 12.

1 House, LDatabase: ht

Fig. 3. The original images used to test the proposed algorithm: (a) house, (b)

Step 12: Replace each original pixel color in the imageby a weighted mean of the three best BMUs of the cur-rent input. For instance, for the red component of theimage, the interpolation is given by:

pepper, (c) Lena and (d) baboon.

� nÞPi2fs1 ;s2 ;s3gdðwsi

� nÞ ð34Þ

where RjGjBj is the new color for the actual image pixel and mir isthe color closest to the stimulus in the palette. The number of win-ners was determined using tests with different winner numbers.Three nodes were shown to be satisfactory, fast and precise forthe interpolation.

4. Results and discussion

In this section, the results achieved by LARFSOM are presentedand discussed. The performance is shown in Section 4.1 where fourreal world images widely adopted in the image processing litera-ture (house, pepper, Lena and baboon) are color segmented. In Sec-tion 4.2, LARFSOM is compared with SOM, FS-SOM and GNG for thesegmentation task. In Section 4.3, the color palette distribution ofLARFSOM compared to SOM, FS-SOM and GNG is presented anddiscussed. Finally, in Section 4.4, the LARFSOM CPU time is dis-cussed and its PSNR values compared to other image processingmodels.

4.1. LARFSOM color segmentation

This section initially presents the results of the proposed seg-mentation technique which has been tested by means of four realworld images:1 house, pepper, Lena and baboon, shown in Fig. 3(a)–(d), respectively. These images have increasing color segmentationcomplexities. The house (256 � 256 pixels) is the simplest one andhas 33,925 colors but few dominant and contrasting colors. Pepper(512 � 512) has183,525 colors and more prevailing colors. However,the objects’ borders are clearly defined by color contrasts. Lena(512 � 512) has148,279 colors and few dominant and similar colors,so color segmentation is harder than in the previous cases. Finally,baboon (512 � 512) has 230,427 colors and plenty of soft and abrupt

ena, pepper and baboon images were collected at the USC–SIPI Imagetp://sipi.usc.edu/database/.

color changes. Hence, this is the hardest color segmentation toperform.

The peak signal-to-noise ratio (PSNR) [2] is the metric used toassess the color segmentation in this paper. There is not a standardmetric for color segmentation and the segmented images are usu-ally evaluated by human supervisors. Despite the PSNR not beingan ideal metric for segmentation, it is often the metric chosen[1,2,12,20,21]. The PSNR shows how a segmented image is relatedto the original image. The PSNR is given by:

PSNR ¼ 10 log3� 2552

MSE

!ð35Þ

MSE ¼PNt�1

j¼0 ðXj � X0jÞ2

� �Nt

ð36Þ

where Xj and X 0j are the pixel values of the original and quantizedimage, and Nt is the total number of pixels. The higher the PSNR va-lue, the better is the image quality. Usually, PSNR > 30 is considereda good level of quality [2,12]. It is worth remembering that an imagewith a higher number of colors will have a higher PSNR due to itssimilarity to the original images. However, that does not ensure thisimage has had its objects better segmented. Thus, it is fair to com-pare the PSNR for a similar (or equal) number of segmented colors.

The LARFSOM parameters chosen were empirically selectedafter tests with different sets of parameters. The parameters whichwere chosen produced close quality for many different images. ForLARFSOM, the parameters were: e = 0.4, qf = 0.06, and dm = 100.The model was not highly sensitive to parameter modification, ex-cept for the activity threshold value (aT). Three activity thresholdvalues (aT) were used: 5.0, 3.0 and 1.25, and the color interpolationis illustrated for an image with aT = 3.0. Different parameter com-binations were tested on the four images (Fig. 3) with good resultsfor all four images.

Figs. 4–7 show the results of the color segmentation performedby LARFSOM. Tables 1–4 give further details such as threshold val-ues, the presence of interpolation (34) to reconstruct the image,

Fig. 4. LARFSOM color segmentation of the house image.

Fig. 5. LARFSOM color segmentation of the pepper image.

Fig. 6. LARFSOM color segmentation of the Lena image.

Fig. 7. LARFSOM color segmentation of the baboon image. The parameters are sownin Table 4.

1234 A.R.F. Araújo, D.C. Costa / Image and Vision Computing 27 (2009) 1229–1239

the total number of iterations, PSNR, the final number of nodes,and the final number of colors.

The results reported in Tables 1–4 show that LARFSOM tends toincrease in size and to take longer to converge when the complex-ity of the segmentation grows. LARFSOM did not need many train-ing iterations to capture the color distribution of the images.Pepper, Lena and baboon, for example, have 262,144 pixels butfor aT = 3.0, less than 20,000 pixel presentations were enough for

learning. Despite the fast convergence, LARFSOM determines themost significant colors.

The self-adaptive number of nodes is also an interesting feature.Table 1 shows five nodes (colors) were enough to finely representthe house image. Pepper was easily segmented due to its veryabrupt color contrast with six nodes. Also, four nodes segmentedmost of the objects in the Lena image, whereas the hardest colorsegmentation that of the baboon was also possible with six nodes.

Fig. 8. Images used in the LARFSOM comparison test with the SOM, FS-SOM andGNG networks: (a) flowers, (b) sailboat, (c) pens and (d) yacht.

Table 1LARFSOM color segmentation of the house image.

Image aT Interpolation Iterations PSNR Nodes Colors

(a) 5.0 No 2429 33.00 26 26(b) 3.0 No 2137 31.02 15 15(c) 3.0 Yes 2137 33.05 15 3580(d) 1.25 No 589 25.30 5 5

Table 2LARFSOM color segmentation for the pepper image.

Image aT Interpolation Iterations PSNR Nodes Colors

(a) 5.0 No 27,468 32.06 91 91(b) 3.0 No 16,784 28.97 33 33(c) 3.0 Yes 16,784 31.27 33 13,000(d) 1.25 No 330 22.75 6 6

Table 3Color segmentation of the Lena image by LARFSOM.

Image aT Interpolation Iterations PSNR Nodes Colors

(a) 5.0 No 2050 31.16 29 29(b) 3.0 No 1809 29.06 16 16(c) 3.0 Yes 1809 30.97 16 6446(d) 1.25 No 219 23.53 4 4

Table 4LARFSOM color segmentation of the baboon image.

Image aT Interpolation Iterations PSNR Nodes Colors

(a) 5.0 No 17,848 30.57 133 133(b) 3.0 No 5282 27.40 40 40(c) 3.0 Yes 5282 29.74 40 26,851(d) 1.25 No 271 20.75 6 6

A.R.F. Araújo, D.C. Costa / Image and Vision Computing 27 (2009) 1229–1239 1235

The PSNR values were also satisfactory in spite of the intense colorreduction during segmentation of the colors.

A higher (aT) value induces the creation of more nodes in thetraining stage, leading to more colorful palettes and higher PSNRvalues. The higher thresholds cause worse segmentation quality,because too many objects (different colors) are present in the seg-mented images.

The interpolation of the palette colors generated a high numberof final colors making it harder for the color segmentation proce-dure. Despite adding difficulties to segmentation, the interpolationcapability may be very useful for image reconstruction. Interpola-tion makes it possible for small-sized palettes to reconstruct a finalimage with many more colors than those in the palette, improvingimage quality. The interpolation process occurs after LARFSOM hasconverged, so the number of training iterations is the same foreither case.

4.2. Comparing SOM, FS-SOM, GNG, and LARFSOM

LARFSOM is compared with SOM, FS-SOM and GNG for the seg-mentation task. The GNG algorithm was chosen for test compari-sons because it has been the SOM with variable topology, mostused for color quantization according to the literature [1,22]. Anal-ogously, the FS-SOM was chosen as the most used [2,20] frequencysensitive SOM model. Once more, four real-world images2 werechosen for the tests: Fig. 8(a)–(d). The images have an increasing

2 Flowers, sailboat, pens and yacht images were collected at the ImageProcessing/V i d e o C o d e c s / P r o g r a m m i n g w e b s i t e : h t t p : / / w w w . h l e v k i n . c o m /default.html#testimages.

level of difficulty of color segmentation. The image of the flowers(500 � 362 pixels) is the easiest task since it has 89,648 colors andmany dominant colors with different characteristics. The sailboatimage (512 � 512) has 168,627 colors and less dominant and lesscontrasting colors than the flowers. The color segmentation of pens(512 � 480) is harder than that for the sailboat. The Pens image has121,057 colors and few soft color changes in the pens. Finally, theyacht image (512 � 480) has 150,053 colors and many differentand contrasting dominant colors. The yacht’s complexity for colorsegmentation is the highest because in this image there are objectscontaining different colors and objects with similar colors.

The parameters were empirically chosen for each modelthrough parameter variations that lead to the best results. Formethods other than LAFRSOM, some parameters were constrainedto match those of LARFSOM:� LARFSOM: qf = 0.05, e = 0.3, dm = 100, and aT = 1.65 to force a

low final number of nodes.� SOM and FS-SOM: The number of nodes is the final number of

nodes of LARFSOM, r0 = 0.5, g0 = 0.2 and 0.1.� GNG: Any number of nodes or limited to the number of LARF-

SOM nodes, eb = 0.05, en = 0.0006, insertion node interval 1000,error decays a = 0.5 and b = 0.0005.

The results of the color segmentation of the LARFSOM, SOM, FS-SOM, and GNG for the images in Fig. 8 are shown in Figs. 9–12 andfurther details are given in Tables 5–8. The convergence criterionfor all networks is given by (8) and a maximum of 100,000 itera-tions was chosen.

LARFSOM showed fast convergence, suitable self-adaptation,and good PSNR values for the images. Tables 5–8 show that, inthe examples of this paper, 1.5% was the maximum percentage oftotal pixels per image, necessary for presentation to LARFSOM dur-ing the training stage. These results suggest LARFSOM demandsonly a low percentage of the total number of pixels of an imageto segment it.

SOM also achieved good PSNR rates but with a significantly lar-ger number of training iterations. The modified FS-SOM had fastconvergence. However, this led to the poorest PSNR results. GNGdid not converge in any experiment, and reached the maximum

Fig. 9. LARFSOM (a), SOM (b), FS-SOM (c) and GNG (d) results for the flowers imageaccording to Table 5.

Fig. 10. LARFSOM (a), SOM (b), FS-SOM (c) and GNG (d) results for the sailboatimage according to Table 6.

Fig. 11. LARFSOM (a), SOM (b), FS-SOM (c) and GNG (d) results for the pens imageaccording to Table 7.

Fig. 12. LARFSOM (a), SOM (b), FS-SOM (c) and GNG (d) results for the yacht imageaccording to Table 8.

Table 5Color segmentation of the flower image by LARFSOM, SOM, FS-SOM and GNG.

Network Image Parameters Nodes Iterations PSNR

LARFSOM (a) aT = 1.65 16 2636 24.82SOM (b) g0 = 0.2 16 34,522 25.03

– g0 = 0.1 16 18,064 21.95FS-SOM – g0 = 0.2 16 905 20.49

(c) g0 = 0.1 16 892 20.50GNG – Free number of nodes 101 100,000 32.02

(d) Limited number of nodes 16 100,000 25.01

1236 A.R.F. Araújo, D.C. Costa / Image and Vision Computing 27 (2009) 1229–1239

number of iterations. With an unlimited number of nodes, GNGshowed the highest PSNR results with a much higher number ofstimulus presentations.

For a fair comparison with GNG, a final test was made with theLARFSOM network, which was trained with the following parame-ters: qf = 0.05, e = 0.3, dm = 100, and aT = 4.65. The high activationvalue is to force the network to add many nodes to seek the 101nodes reached by the GNG. No convergence criterion was imposed,just a limit of 100,000 iterations or 101 nodes, the values reachedby the GNG network.

The LARFSOM network reached 101 nodes after 92,631 itera-tions and achieved a PSNR of 33.08 for the yacht image, a resultquite close to that achieved by GNG, shown in Table 8.

Fig. 13. Color palette of LARFSOM (a), SOM (b), FS-SOM (c) and GNG (d) for theimages of sailboat.

Table 10Results of LARFSOM, SOM, FS-SOM and GNG for color segmentation of sailboat forcolor palette analyses, according to Fig. 13.

Network Image Parameters Nodes Iterations PSNR

LARFSOM (a) aT = 4.65 64 9140 30.67SOM (b) g0 = 0.2 64 31,232 30.07FS-SOM (c) g0 = 0.2 64 813 26.84GNG (d) Limited number of nodes 64 100,000 31.44

Table 8Color segmentation of the yacht image by LARFSOM, SOM, FS-SOM and GNG.

Network Image Parameters Nodes Iterations PSNR

LARFSOM (a) aT = 1.65 8 364 24.35SOM (b) g0 = 0.2 8 23,707 23.93

– g0 = 0.1 8 3851 20.07FS-SOM (c) g0 = 0.2 8 306 23.29

– g0 = 0.1 8 270 21.72GNG – Free number of nodes 101 100,000 33.13

(d) Limited number of nodes 8 100,000 24.30

Table 7Color segmentation of the pens image by LARFSOM, SOM, FS-SOM and GNG.

Network Image Parameters Nodes Iterations PSNR

LARFSOM (a) aT = 1.65 9 599 24.74SOM (b) g0 = 0.2 9 22,383 24.88

– g0 = 0.1 9 13,504 20.55FS-SOM – g0 = 0.2 9 914 21.47

(c) g0 = 0.1 9 449 21.68GNG – Free number of nodes 101 100,000 34.71

(d) Limited number of nodes 9 100,000 25.11

Table 6Color segmentation of the sailboat image by LARFSOM, SOM, FS-SOM and GNG.

Network Image Parameters Nodes Iterations PSNR

LARFSOM (a) aT = 1.65 6 437 24.45SOM (b) g0 = 0.2 6 15,766 24.36

– g0 = 0.1 6 4066 21.12FS-SOM (c) g0 = 0.2 6 389 21.69

– g0 = 0.1 6 304 21.47GNG – Free number of nodes 101 100,000 32.55

(d) Limited number of nodes 6 100,000 24.49

A.R.F. Araújo, D.C. Costa / Image and Vision Computing 27 (2009) 1229–1239 1237

We show another comparison between the LARFSOM, SOM, FS-SOM and GNG to the segmentation task. We chose the easiest andhardest images of Fig. 3, house and baboon. The results are detailedin Table 9. The parameters were the same as above for LARFSOM,and the only changes for other models were:� SOM and FS-SOM: g0 = 0.2.� GNG: Nodes limited to the number of LARFSOM nodes.

The LAFSOM again showed the fastest convergence and reachedhigh PSNR values. The SOM network also reached high PSNR val-ues, however at the cost of more iteration. The GNG achieved thebest results, but did not converge.

Table 9Color segmentation of the house and baboon images by LARFSOM, SOM, FS-SOM andGNG.

Network Parameters Image Nodes Iterations PSNR

LARFSOM aT = 1.65 House 6 2041 26.24Baboon 8 550 21.77

SOM g0 = 0.2 House 6 15,090 25.74Baboon 8 23,670 21.97

FS-SOM g0 = 0.2 House 6 1668 21.34Baboon 8 9914 19.54

GNG Limited number of nodes House 6 100,000 26.28Baboon 8 100,000 22.23

4.3. The palette color distribution

LARFSOM, SOM, FS-SOM and GNG used for color segmentationwere analyzed by considering their final palette color distribution.The sailboat image was chosen for this test. The parameters of eachnetwork were:� LARFSOM: qf = 0.05, e = 0.3, dm = 100, and aT = 4.65, to force a

high final number of nodes.� SOM and FS-SOM: Number of nodes equal to the final number

of nodes of LARFSOM, r0 = 0.5, g0 = 0.2.� GNG: Same number of nodes as LARFSOM, eb = 0.05,

en = 0.0006, insertion node interval 1000, error decays a = 0.5and b = 0.0005.

Fig. 13 shows the four color palettes produced by the fournetworks considered. Their segmentation results are detailed inTable 10. LARFSOM and GNG produce an n-dimensional topolog-ical neighborhood structure to encode the training patterns.Then, for 2D visualization, the nodes were ordered from thetop-left corner to the bottom-right one according to the nodecreation order. SOM and FS-SOM have 2D pre-defined topologicalstructures and the color palettes show their node neighborhoodrelations.

SOM and FS-SOM maintain a 2D topological order of data distri-bution with respect to their nodes and the topological map is cre-

Table 11Comparisons of SOM, FS-SOM, and GNG with LARFSOM for CPU training times for theLena image.

Network Parameters Nodes Iterations PSNR CPU time(s)

LARFSOM aT = 2.5 12 1308 27.93 0.01aT = 5.0 26 1132 30.90 0.02

SOM g0 = 0.2 12 21,095 25.55 0.31g0 = 0.2 26 23,928 28.99 0.70

FS-SOM g0 = 0.2 12 323 22.53 0.01g0 = 0.2 26 417 22.96 0.02

GNG Limited number ofnodes

12 100,000 28.29 0.71

Limited number ofnodes

26 100,000 31.26 1.28

1238 A.R.F. Araújo, D.C. Costa / Image and Vision Computing 27 (2009) 1229–1239

ated with soft color variance in the palette, thus reducing the num-ber of different final colors. The influence of the winner upon itsneighborhood is reduced in GNG and LARFSOM resulting in a great-er variance in color palettes. This feature can be very useful in im-age color reconstruction, using the colors present in the palette tobuild new ones by color interpolation as mentioned in LARFSOMtraining Step 12, (34).

Fig. 14 shows the original sailboat colors in the 3D RGB colorspace and the color palettes after training. The LARFSOM colorpalette variance fills the 3D original color space of the sailboatimage more widely than GNG, SOM and FS-SOM do, in decreas-ing order as can be seen in Fig. 14. This may occur as thespreading of LARFSOM nodes in the 3D space results in a higherdispersion.

The LARFSOM’s ability to spread its nodes in the 3D color spaceand therefore its significant color variance may be explained by theinfluence of the neighborhood density around the BMUs. The sizeof the neighborhood influences the receptive field value of eachBMU. In a space region where many nodes are close to each other,a high density region, the receptive field value becomes lower for aBMU in that region, as determined by (31). This increases the acti-vation value for such a BMU, see (32). As a consequence, the prob-ability of a new node being inserted in that region is reduced, sincethe activation value needs to be lower than the threshold value sothat a new node can be inserted.

Fig. 14. Color distribution of (a) Sailboat, and color palette distribution of (b)LARFSOM, (c) SOM, (d) FS-SOM and (e) GNG for the sailboat image in RGB 3D colorspace.

4.4. Comparisons between LARFSOM and other models

The most significant feature of LARFSOM is its fast convergenceand suitable PSNR values. The comparisons between LARFSOM,SOM, FS-SOM, and GNG illustrate this capacity. Table 11 shows3

LARFSOM CPU training time compared with SOM, FS-SOM andGNG for the Lena image segmentation. The parameters of each net-work were:� LARFSOM: qf = 0.05, e = 0.3, dm = 100, and aT = 2.5, aT = 5.0, to

force a medium and high final number of nodes.� SOM and FS-SOM: Number of nodes equal to the final number

of nodes of LARFSOM, r0 = 0.5, g0 = 0.2.� GNG: Same number of nodes as LARFSOM, eb = 0.05,

en = 0.0006, insertion node interval 1000, error decays a = 0.5and b = 0.0005.

The LARFSOM network needed only 1308 and 1132 iterationsduring 0.01 and 0.02 s, respectively, to be trained for the Lena im-age, and produced 12 and 26-node networks. SOM needed 21,095(0.31 s) and 23,928 (0.70 s) iterations to converge with 12 and 26nodes, respectively, for the same image and its PSNR was signifi-cantly lower (Table 11). As expected, the modified FS-SOM con-verges quickly. However, the PSNR values were not satisfactory.Finally, it is clear that even achieving the higher PSNR rates for12 and 26 nodes, the GNG network has the highest computationalcost taking 0.71 and 1.28 s, respectively, to stop training, andreaches the maximum number of iterations allowed.

The superiority of LARFSOM over the other networks shows it issuitable for real-time systems, where fast accurate results need tobe acquired in short and controlled periods. LARFSOM was the fast-est training network and, except for the GNG, LARFSOM had thehighest PSNR rates.

LARFSOM achieves higher PSNR than SmArt. For the Lena image,SmArt achieved a MSE rate of 562.29 (PSNR of 25.40) leading to 12nodes (learning rate of 0.1) as shown in [21]. The LARFSOM PSNR is27.93 for the same image. SmArt needs at least 2 epochs4 to learnthe color distribution satisfactorily [21], while LARFSOM needs only0.5% of an epoch to converge, as seen in Table 11. An epoch for theLena image would have 262,144 iterations and LARFSOM convergedafter 1308 iterations. Recent models such as FS-SOM [2] and SA-SOM[1] need 80% and 20% of the total image pixels to be presented toachieve good results, respectively, as claimed in [1]. The modifiedFS-SOM, presented in Section 2.3, Tables 5–8, showed that the pro-posed modifications produced a faster training algorithm thatneeded less than 1.5% pixel presentations to converge, leading, how-ever, to worse PSNR values. The fast convergence, without losses ofthe PSNR quality, is a very interesting emerging characteristic of

3 The computer used for tests was a Pentium 4 with 2.66 GHz and 512 MB of RAM.4 One training epoch is the presentation of all pixels on an image to the network.

Iteration is one training cycle, where only one pixel presentation is performed.

Table 12Comparison between LARFSOM and color quantization algorithms found in commer-cial software, tested in the Lena image.

Algorithm Parameters Nodes/colors PSNR

LARFSOM aT = 3.65 16 29.13Optimized median cut Nearest color 16 26.86

Error diffusion 16 24.58Optimized octree Nearest color 16 26.41

Error diffusion 16 25.25Minimum variance quantization Dithering 16 25.77

No dithering 16 28.59

A.R.F. Araújo, D.C. Costa / Image and Vision Computing 27 (2009) 1229–1239 1239

the model proposed that makes it suitable for real time or onlineapplications that require fast processing time.

Although it is not the focus of this paper, a comparison withstandard color quantization algorithms, found in commercialimage processing software, is shown. Algorithms such as OptimizedMedian Cut [11] (nearest color and error diffusion), OptimizedOctree [8,11] (nearest color and error diffusion) and Minimum Var-iance Quantization [16] (with and without dithering) were tested.LARFSOM showed higher PSNR values as shown in Table 12.

5. Conclusion and future work

Using intelligent algorithms for image segmentation are a rich re-search field. Systems proposed often do not have fast, accurate andadaptive training steps. In this paper, a robust and fast model, LARF-SOM, was presented to achieve these goals. Moreover, features of theLARFSOM network such as n-dimensional neighborhood topology,adaptive final number of nodes and rich color variance in resultantcolor palette, make it suitable for image processing systems.

The major contribution of LARFSOM, among other recent andsuccessful image segmentation models such as SmART [21], is itsvery fast convergence, which produces a satisfactory final numberof nodes and color distributions.

For color segmentation, the clustering characteristics with agrowing number of LARFSOM nodes are effective.

Eight images with different segmentation complexities weresuccessfully color segmented. The results showed that LARFSOMis a fast learner; the presentation of a small percentage of the im-age pixels was sufficient to capture the color distributions of theimages. For instance, only 1.5% of the pixels of the image randomlypresented to LARFSOM were needed to generate fine color distribu-tion learning. The adaptive number of nodes of LARFSOM is a majorfeature since the number of objects in the images is unknown be-fore processing.

Comparisons between four SOM-based networks conclude thatLARFSOM was shown to be satisfactorily fast convergent, optimumself-adaptive and achieved good PSNR values. The other models didbetter when a constraint was violated: the good PSNR rates of SOMwith a high number of input presentations; the fast convergence ofSOM towards poor results; and the high PSNR rate for GNG,demanding the pre-establishment of the final number of nodes

and the maximum number of iterations was reached, since it didnot converge.

The color palette of LARFSOM was the richest in color variance,an interesting feature for image reconstruction with color interpo-lation, which may produce high quality images. Hence, imagereconstruction is the future interest of this project. Additionally,the LARFSOM color palette distribution in 3D RGB color space filledthe color space of the original images in accordance with a highernode dispersion and greater color variance than the other modelsdid.

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