Architecture of oscillatory neural network for image segmentation

Architecture of Oscillatory Neural Network for Image Segmentation

Dênis Fernandes1*, Jeferson Polidoro Stedile2** and Philippe Olivier Alexandre Navaux2

1PUCRS - Pontifícia Universidade Católica do Rio Grande do Sul - Faculdade deEngenharia, Porto Alegre, RS, Brazil

[email protected] - Universidade Federal do Rio Grande do Sul - Instituto de Informática, Porto

Alegre, RS, Brazil [email protected], [email protected]

Abstract

Oscillatory neural networks are a recent approach forapplications in image segmentation. In this context, theLEGION (Locally Excitatory Globally InhibitoryOscillator Network) is the most consistent proposal. Aspositive aspects, the network has got parallel architectureand capacity to separate the segments in time. On theother hand, the structure based on differential equationspresents high computational complexity and limitedcapacity of segmentation, which restricts practicalapplications. In this paper, a proposal of parallelarchitecture for implementation of an oscillatory neuralnetwork suitable for image segmentation is presented. Theproposed network keeps the positive features of theLEGION network, offering lower complexity forimplementation in digital hardware and capacity ofsegmentation not limited, as well as few parameters, withintuitive setting. Preliminary results confirm thesuccessful operation of the proposed network inapplications of image segmentation.

1. Introduction

Several techniques of image segmentation based onartificial neural networks have been developed,particularly using MLP (MultiLayer Perceptron) networksassociated to the Backpropagation algorithm, Hopfieldnetworks or Kohonen maps (SOFM - Self-OrganizingFeature Map), with typical examples found in[5][6][10][13]. Such algorithms have presented goodresults even with the existence of noise or distortions inthe image to be segmented, having several advantages * Professor at Electrical Engineering Department of PUCRS and Ph.D.student at PGCC of UFRGS.∗∗ Student of Electrical Engineering at PUCRS and CNPq scholarshipresearcher at UFRGS.

inherent to neural network topologies. One of thedrawbacks of some of these methods is the necessity oftraining, which can be problematic due to the long timeneeded and the high number of available samplespreviously segmented. Another negative aspect is the highcomputational complexity presented by some of thesearchitectures.

Recently, alternative topologies of artificial neuralnetworks, called oscillatory neural networks, have beenapplied in procedures of image segmentation withfavorable results [2][3][4][11][16]. The study of suchtopologies of neural networks, which have biologicalinspiration on the mechanism of segmentation supposedlyexecuted by the human brain, as well as their applications,are fertile ground for work. The necessity of efficiency inapplications of image processing highly justifies thedevelopment of new hardware architectures for practicalimplementation of such networks, exploring their parallelnature [2][4].

The LEGION network (Locally Excitatory GloballyInhibitory Oscillator Network) [17] is the most consistentproposal of oscillatory neural network with practicalapplications in image segmentation found in thebibliography. Applications of the LEGION networkinclude, for example, a procedure associated to MLPnetworks used for extraction of hydrographic regions inremote sensing images [12]. In [14], a study on the use ofthe LEGION network applied to the segmentation ofmedical images of computerized tomography andmagnetic resonance can be found. In [7], a LEGIONnetwork is used to segment images of electronicmicroscopy in a practical procedure for counting andmeasuring helium bubbles implanted in silicon. In [8], aLEGION network is associated to Kohonen maps toisolate the region of the left ventricle in a procedure toanalyze fetal echocardiographic images. Otherapplications of the LEGION network can also be found inthe bibliography, such as, for example, the separation of aspeaker’s talk from interfering noise [19].

Proceedings of the 14th Symposium on Computer Architecture and High Performance Computing (SBAC-PAD�02) 0-7695-1772-2/02 $17.00 © 2002 IEEE

As a positive characteristic of the LEGION network,its highly parallel architecture is very attractive, whichcan be expressed as high operation speed inimplementations using adequate hardware. Anotherinteresting aspect is related to the capacity of the networkto segregate in time the various segments of the inputimage, which can facilitate the later identification andquantification of these regions. As negative aspects, itshigh computational complexity for implementation indigital hardware, due to its structure based on sets ofdifferential equations, and the limited capacity forsimultaneous discrimination of different segments can bepointed out. The high amount of parameters and theirlittle intuitive setting are also limiting factors.

The present work aims at presenting a parallelarchitecture for implementation of an oscillatory neuralnetwork in digital hardware, which is suitable forapplications in image segmentation. The proposednetwork offers similar principles of operation to the onesof the LEGION network, possessing parallel architectureand capacity to discriminate in time the segments found.The lower computational complexity, due to thepredominant use of binary logical operations, and the non-limitation of the number of segments to be discriminatedare presented as the main advantages of the proposednetwork in relation to the LEGION network. The use offew parameters, with intuitive setting, is also presented asa positive aspect, as well as the reduced number ofiterations and the easy prevision of the time necessary toget the intended result.

Results found in practical implementations arepresented and prove the successful operation of theproposed architecture according to the expectations.

2. The LEGION Network

In the late 80’s, oscillations of approximately 40 Hzwere discovered in the visual cortex and other areas of thehuman brain. It was verified that such neural oscillationshave a strong correlation with the coherence of the visualstimulus, and synchronism of phase occurs betweenneurons which are physically near and that receive similarstimulus, which can characterize a homogeneous regionof the perceived image. On the other hand, physically nearneurons that receive different stimulus or physicallydistant neurons that receive equal stimulus do not presentsuch synchronism of phase [18]. Using such property oflocal synchronism between oscillators and adding amechanism of global inhibition to get anti-synchronismamong groups of oscillators, the LEGION network wasconceived.

The fig. 1 presents a 2-dimensional architecture ofLEGION network adjusted to applications of imagesegmentation. The network is basically formed by a set ofTerman-Wang oscillators [18]. Only neighboring

oscillators are connected, as presented in fig. 1. A globalinhibitor, on the other hand, is connected to all theoscillators of the network.

Figure 1. Example of LEGION network with 2-dimensional topology.

The behavior of the Terman-Wang oscillator can bedescribed through the differential equations (1) and (2)[18]. From the biological point of view, x(t) can beunderstood as the potential of the nervous cell membrane,or either, the physical variable that represents the outputin the neuron. α , β and ε are parameters of the model andI is an external input. A gaussian signal of small varianceis added to the input of each oscillator to avoid that theinitial conditions of the network imply unwanted states ofstability and also to prevent the possible synchronismbetween distant groups of oscillators with similar inputs[18]. The lateral excitation of an oscillator of theLEGION network, Si(t), is also added to the input, and itis defined as the coupling received from the otheroscillators of the network, being represented by theequation (3). Wik represents the weights related to theconnections between the neighboring oscillators k and i,being correlated with the similarity between the externalinputs of such oscillators. Wz is the weight related to theglobal inhibitor, θ x e θ z are thresholds, Ni(R) means theneighborhood of radius R around the oscillator i, H(x) isthe Heaviside function, κ is a parameter of the sigmoiddefined by (5) and φ adjusts the variation rate of theglobal inhibitor output z(t) (4) [17].

ρ+++−+−= )()(2)()(3)( 3 tSItytxtx

dttdx

i (1)

( )( )( ))(/)(tanh1)(

tytxdt

tdy−+= βαε (2)

∑∈

∞∞ −=)1(

)),(()),(()(iNk

zzxkiki tzSWtxSWtS θθ (3)

))())((()( tztxHdt

tdzzi −−= θφ (4)


)(11),(

θκθ

−−∞+

=xe

xS (5)

A mechanism of weight normalization is presented in[17]. It is shown that the normalization of the weights isnot a necessary condition for the correct functioning ofthe network, however it improves the synchronismbetween neighboring oscillators submitted to similarinputs.

For a determined set of parameters, a LEGIONnetwork can discriminate a limited number of segments,which depends on the ratio between the times ofpermanence of the neurons in the phases active and silent.This limit is called capacity of segmentation of theLEGION network and it is placed in the band of 5 to 10segments [18]. Although such feature presents itself as arestriction to the application of the network in imagesegmentation, it has biological correlation, because it isalso observed in human beings, which present aquantitative limitation for simultaneous discrimination ofseveral objects [17].

In [17], a modification in the excitation of the Terman-Wang oscillator is also presented, considering the ideathat a set of oscillators with similar inputs must possess atleast one leader oscillator, which must receive greatlateral excitation from its neighborhood. On the otherhand, isolated oscillators, belonging to noisy fragments,cannot be characterized as leaders. This way, an oscillatorwith great lateral potential can lead the activation of agroup of oscillators corresponding to a homogeneousregion of the input.

Several simulations demonstrate that the LEGIONnetwork is capable to produce satisfactory results inimage segmentation applications [9]. On the other hand,the necessity of a careful setting of the networkparameters for each different image to be segmented wasevidenced. Such procedure is interactive and not muchpractical due to the high number of parameters and theircomplex joint influence on the results obtained. In severalcases, some difficulty in getting synchronism betweenoscillators was observed as well as the necessity of a greatand not easily estimable number of iterations to reach thedesired result.

One concludes through several tests and results foundin the bibliography that the LEGION network is a solutionsuitable for image segmentation applications. As positiveaspects, its property of time separation of the segmentsand the parallel topology, which can bring on fastimplementations using adequate hardware architecture,can be pointed out. As negative aspects, the networkpresents high computational complexity forimplementation in digital hardware, given the greatnumber of differential equations to be solved, and alsolimited capacity of segmentation and high number ofparameters with little intuitive setting procedures.

3. Proposal of the Network Architecture

In face of the practical limitations presented by theLEGION network, a new architecture of oscillatory neuralnetwork was conceived, suitable for image segmentationapplications and also to implementation in digitalhardware with parallel topology.

Like the LEGION network, in case of imagesegmentation applications, the proposed network isimplemented in a 2-dimensional topology with the samedimensions of the image (equal number of pixels andoscillator neurons). Each pixel of the input image willhave therefore a corresponding oscillator in the network.

The 2-dimensional proposed network presents twostructures of connections, making it different, in thisaspect, from the LEGION network. Fig. 2 presents anexample of the structure of the excitatory connections. Aneighborhood relation was adopted where an oscillatorneuron has its excitatory output ve(i,j) connectedsimultaneously to the 8 nearest neurons. This way, theexcitatory output of the oscillator neuron will be alwaysactive when at least one of its nearest neighbors,submitted to a similar input, is in the active phase. For theneurons situated in the borders of the network, theweights related with the nonexistent connections are null,as well as the respective excitatory inputs.

Figure 2. Example of the structure of excitatoryconnections proposed.

Fig. 3 presents an example of the structure of inhibitoryconnections adopted. Each neuron has its inhibitoryoutput vi(i,j) connected only to one neighboring neuron.This structure establishes a priority among the oscillatorneurons of the network in a way that, if there are severalneurons enabled to pass to the active phase, pertaining todifferent segments, only one of them, the one with thehighest priority, will do. In other words, the neuron withthe highest priority inhibits the remainders, keeping themin the silent phase. On the other hand, the excitatory


connections will cause the only neuron qualified by thestructure of inhibitory connections to qualify all the otherneurons belonging to the respective segment. Differentstructures of inhibitory connections could be used such asa helicoidal structure initiating at one extremity or at thecenter of the network, for example. In the topology ofinhibitory connections presented, the neuron with thehighest priority always receives null inhibition in its input.The inhibitory output of the neuron with the lowestpriority in the network will be active only when at leastone neuron of the network has its output in the activephase. In a practical implementation, this signal can beused to detect null images, without any segment, presentin the output of the network.

Figure 3. Example of the structure of inhibitoryconnections proposed.

4. Proposal of the Network Neuron Structure

During the development of the structure of the basicprocessing element (oscillator neuron) of the proposednetwork, simplicity was prioritized, bearing in mind alater implementation in a dedicated digital hardware. So,the use of operations and logical structures with easyimplementation in digital programmable devices such asthe FPGAs (Field Programmable Gate Arrays) wasadopted.

Fig. 4 presents the structure of the oscillator neuron ofthe proposed network adjusted to a 2-dimensionaltopology. In order to make better understanding of thefunctioning of the neuron possible, the definitions of theconstants and variables are listed below:• Nn: total number of oscillator neurons in the network;• Ns: adjustable parameter that sets the maximum

number of segments to be separated by the network;• Lm: adjustable parameter that sets a threshold to

similarity determination between the inputs ofneighboring neurons;

• vc(i,j,t): state of the internal counter belonging to theneuron placed at line i and column j in time(iteration) t;

• vo(i,j,t): output signal of the internal comparatorbelonging to the neuron placed at line i and column jin time t;

• ve(i,j,t): excitatory output of the neuron placed at linei and column j in time t;

• vi(i,j,t): inhibitory output of the neuron placed at line iand column j in time t;

• vi(i’,j’,t): inhibitory output of the precedent neuronrelated to the neuron placed at line i and column j intime t;

• vl(i,j,t): leader indication signal related to the neuronplaced at line i and column j in time t;

• Ia(i,j,t): input signal of the neuron placed at line i andcolumn j in time t (in case of an image, it canrepresent a set of features or only one feature such asthe intensity of the related pixel, for example);

• w(i,j,k,l,t): weight related to comparison between theinput of the neuron placed at line i and column j andthe input of the neuron placed at line k and column l,in time t.

A binary counter with a total number of states higheror equal to the number of neurons of the network (Nn) isused to define the internal state of the neuron as a functionof the time, vc(i,j,t). The referred counter always has itsstate returned to zero (synchronous reset) if the neuron isin its active phase (ve(i,j,t)=1), otherwise its state isincremented until reaching the Ns-1 state, remaining sountil receiving one reset, as represented by the equation(6). The use of Nn states in the counter makes thediscrimination of a maximum of Nn segments possible(one state for each segment), an extreme case in whichthere is no similarity between any pair of inputs ofneighboring neurons.

=−−≥−

−

=−

=−−<−

+−

=

0)1,,(1)1,,(

if)1,,(

1)1,,(if00)1,,(

1)1,,(if1)1,,(

),,(

tjivNtjiv

tjiv

tjivtjiv

Ntjivtjiv

tjiv

e

scc

e

e

scc

c

(6)

The output of the internal counter of the neuron is sentto a comparator whose output vo(i,j,t) is equal to one whenits input is equal or higher than the number of segments tobe discriminated by the network minus one, being,otherwise, null (7). Such procedure qualifies the networkto separate the Ns first segments according to the sequenceestablished by the structure of inhibitory connections ofthe network. In the extreme case in which Ns=Nn, thenetwork can separate up to Nn segments.


Figure 4. Neuron internal structure of the proposed network.

nssc

sco NN

NtjivNtjiv

tjiv ≤

−<−≥

= ,1),,(if01),,(if1

),,( (7)

The equation (8) represents the inhibitory output of theoscillator neuron vi(i,j,t), which is obtained through abinary logical operation among the output of its internalcomparator vo(i,j,t), the signal of qualification vl(i,j,t) andthe inhibitory output received from its preceding oscillatorvi(i’,j’,t). Thus, the inhibitory output of the neuron will behigh only when its internal state is equal or higher thanNs-1 and it is qualified as a leader (vl(i,j,t)=1) or that it hasreceived an inhibition from its preceding neuron.

),','()),,(),,((),,( tjivortjivandtjivtjiv iloi = (8)

The qualification signal vl(i,j,t) can be generatedinternally or externally and only the oscillators withvl(i,j,t)=1 will be initially qualified to pass to the activephase (leader oscillators). Oscillators with vl(i,j,t)=0 canonly be activated through a neighbor with similar inputthat is in the active phase. In the external generation of thesignal, the leader oscillators can be established by somecriteria such as the corresponding position in the image,for example. Thus, it could be established thatcorresponding oscillators to the central region of theimage would be the only ones qualified to pass to theactive phase, causing the appearance of only that segmentat the output of the network. In the internal generation ofthe signal, one can use, for example, the criteria that aleader oscillator must possess all the weights related to theunitary excitatory connections, which corresponds to apixel in the center of a homogeneous region. Suchcondition can easily be carried out by using a Booleanoperation and among the excitatory weights of therespective neuron.

The excitatory output of the oscillator neuron ve(i,j,t),represented by equation (9), is unitary when the neuron isqualified, considering its internal state, the condition ofleader and the inhibition received from its preceding

neuron, or if it receives an excitatory signal (ve(k,l,t)=1)from a neighboring neuron whose input is similar to itsown, implying the respective weight w(i,j,k,l,t)=1. Aneuron can receive excitatory signals from severalneurons pertaining to a predefined region ofneighborhood. The clock signal is used to define theinitial states of all the excitatory outputs of the network.Neurons that have their outputs in high logical level aresaid to be in the active phase (ve(i,j,t)=1), and otherwise,they are said to be in the silent phase (ve(i,j,t)=0).

))),1,(),1,(()),1,1(),1,1((

)),,1(),,1(()),1,1(),1,1((

)),1,1(),1,(()),1,1(),1,1((

)),,1(),,1(()),1,1(),1,1((

)),','(),,(((),,(

tjivandtjiwortjivandtjiw

ortjivandtjiwortjivandtjiw



ortjivxortjivandclocktjiv

e

e

e

e

e

e

e

e

iie

−−−+−+

++++++

+−++−+−

−−−−−−

=

(9)

The weights of the network are determined through thecomparison of the input attribute intensities Ia(i,j,t) of theneuron with the respective inputs of the neighboringneurons Ia(k,l,t). In the cases where the differencesbetween such inputs are, in module, below apredetermined threshold Lm, the respective weights will beunitary. If the inputs Ia(i,j,t) are scalar, the determinationof the weights can be carried out by means of operationsof simple implementation, as exemplified in (10).

≤−

>−=

LmtlkItjiI

LmtlkItjiItlkjiw

aa

aa

),,(),,(if1

),,(),,(if0),,,,( (10)

The version of the oscillator neuron presented impliesthat the proposed network groups the input patterns based


on the similarity between the level or the intensity of theinputs of neighboring oscillators. However, differentattributes of the input signal of the network can be used tocarry through the segmentation, such as the average or thevariance in the pixel neighborhood. On the other hand,Ia(i,j,t) can also represent vectors of attributes related tothe pixels of the image. In this case, the weights can bedetermined through the use of a measure of vectorialdistance, such as the Euclidean distance, implying morecomplex structures for its implementation. In colorimages, for example, the Euclidean distance calculated inthe space of the colors could be used to determine theweights, which would result in segmentation by colorsimilarity. Generally, any attribute or set of attributes ofthe input signal can adequately be used to determine theweights of the network.

5. Implementation of the Network and Tests

To verify the functioning of the proposed network, twotypes of implementation were carried through. The firstone is related to the simulation of the behavior of thenetwork through an algorithm implemented in a PCcomputer using Delphi language. The second one is theuse of the Max+plusII program from Altera [1] forsimulation of the network and verification of the viabilityof its implementation in FPGA devices.

Fig. 5 presents an example of image segmentationcarried out through the implementation of an algorithmthat simulates the behavior of the proposed network in aPC computer. The original image, with 100x310 pixels,placed at the top left position, possesses 5 characters inthe same gray level, isolated from each other, on abackground with a different gray level. The proposednetwork found, from the intensity of each pixel of theoriginal image (range from 0 to 255), the existence of 7segments, which are shown in the other images. The firstsegment, presented at the top right position, correspondsto the background, having been the interior part of thecharacter "R" not presented because it is not physicallyconnected. This region appears as an isolated segment,which can be seen in the image at the bottom rightposition. The segments are sequentially presented in theoutput of the network. The characters were correctlysegmented and isolated in time, facilitating the applicationof a procedure of character recognition. In the imagesrelated to the segments, the black tone representsoscillators in the silent phase while the white tonerepresents oscillators in the active phase.

Fig. 6 presents a network with 3x5 neurons (Nn=15)which was simulated with the use of Max+plusII. Thenetwork has one input, a clock signal, common to all theneurons, and, as outputs, the excitatory signals of the 15neurons (S1, S2, ..., S15). The values of Ns, Lm and theinputs of the pixel intensities were considered as

parameters of the network in the stage of compilation. In areal application, however, such inputs must be externallyaccessible. In order to simplify the structure, each neuronis responsible for the determination of only 4 weightsrelated to the excitatory connections. Thus, a neuroncombines the excitations received from 4 of itsneighboring neurons with the respective weightsinternally calculated and sends the excitation alreadycombined with the respective weight to these neighboringneurons. Such artifice also makes it necessary to receivethe intensities of only 4 neighboring neurons forcalculation of the respective weights, diminishing the totalnumber of connections of the network.

Figure 5. Segmentation using an algorithmsimulating the proposed network.

The results of the simulations carried through with theMax+plusII demonstrate that the proposed networkoperates satisfactorily, grouping the similar clusters ofpixels correctly and presenting sequentially each group inits output. To exemplify, fig. 7 represents an image withthe respective values of intensity of each pixel (8bits/pixel), which is used as the input of the network.Considering, for example Lm=20, the represented graylevels must form similar groups of oscillators. Fig. 8presents the waveforms (logical levels 0 and 1) obtainedthrough the simulation, where the grouping of the neuronswith similar inputs and the time separation of each one ofthese groups can be verified. Ns must have a minimumvalue equal to the number of segments contained in theimage. The use of higher values causes the appearance oftime intervals without any segment in the output of thenetwork. The result presented was obtained with Ns=5. Asall the oscillators had started at state 0, the first segment ispresented in the output after the fifth pulse of clock. Fromthere, the four segments are sequentially presented in theoutput, with a clock period without any active outputbetween each sequence. The output seg is the inhibitoryoutput of the neuron with the lowest priority in thenetwork and it can be used as an indicator of the existenceof an active segment in the output of the network. Thissignal and the clock, can also be used to transfer theoutput values of the network to some external device.

In all the simulations it was possible to confirm theeasiness of synchronism between oscillators and thenecessity of a low and easily predictable number ofiterations (pulses of clock) to get the desired result.


Figure 6. Implementation of the proposed network using the Max+plusII.

Figure 7. Input values used in theimplementation with the Max+plusII.

6. Conclusion

The use of oscillator networks to simulate the capacityof image segmentation of the human brain is a recentproposal with satisfactory results. In the context of imagesegmentation, the LEGION network is the mostconsolidated model. Its parallel architecture and thecapacity to separate the segments in time are stronglyattractive. On the other hand, the structure based ondifferential equations implies high complexity forimplementation using digital machines, parallel or not.Another disadvantage of this network concerns thelimitation of the segmentation capacity of the number ofobjects simultaneously discriminated. The high number ofparameters and their little intuitive setting procedures alsorepresent limitations.

Figure 8. Result of the implementation usingMax+plusII.


The architecture of the oscillatory neural networkpresented in this paper has the same advantages of theLEGION network related to the highly parallel topologyand the capacity of segmenting and separating in time thesegments of the input images. On the other hand, theproposed network does not present limitation related tothe number of segments simultaneously discriminatedand, because it uses simple binary logical operations, itoffers lower computational complexity and the possibilityof implementation in programmable logical devices. Theuse of only two parameters, Lm and Ns, of intuitivemeaning and setting, also presents itself as an advantageof the proposed network. Other aspects that are not lesspositive concern the easiness of synchronism betweenoscillators and the necessity of a lower and easilypredictable number of iterations in order to get the desiredresult, as opposed to the LEGION network. The additionof a random signal to the inputs of the network is notnecessary, which also is a factor of complexity reductionof the proposed network.

The possibility of weights determination of theproposed network on the basis of diverse attributes of theinput image can lead to more sophisticated procedures ofsegmentation, such as texture segmentation, for example.It is also pointed out that, being the weights of thenetwork obtained directly from the attributes of the imageto be segmented, the necessity of training of the networkdoes not exist, in contrast to other architectures of neuralnetworks.

The results obtained with the implementation of theproposed network in PC computers, through an algorithmthat simulates its behavior, prove the consistency of theproposal and its several advantages in comparison withthe LEGION network. The implementation of a networkof small dimensions using the Max+plusII program fromAltera also confirms the correct functioning of theproposal and its advantages.

On the basis of the results obtained, it is concluded thatthe new network architecture presented is an attractivealternative for applications involving image segmentation.Its several advantages imply greater viability andflexibility for practical implementation.

7. Bibliographical References

[1] ALTERA, MAX+PLUS II Software Overview,http://www.altera.com/products/software/maxplus2/mp2-index.html (06/20/2002).[2] ANDO, H., MIYAKE, M., MORIE, T., NAGATA, M.,IWATA, A. “A Nonlinear Oscillator Network Circuit for ImageSegmentation with Double-threshold Phase Detection”, ICANN99, IEE, Edinburgh, UK, 1999, p. 655-660.[3] BUHMANN, J., von der MALSBURG, C. “SensorySegmentation by Neural Oscillators”, IJCNN 91, IEEE, Seattle,EUA, 1991, pp. II603-II607.

[4] COSP, J., MADRENAS, J. “A Neural Network for SceneSegmentation Based on Compact Astable Oscillators”, ICANN99, IEE, Edinburgh, UK, 1999, p. 690-695.[5] DAHMER, A. Segmentação de ImagensEcocardiográficas Utilizando Redes Neurais e Medidas deTextura, Master Thesys, UFRGS-PPGC, Porto Alegre, 1998.[6] DAHMER, A., PICCOLI, L., SCHARCANSKI, J.,NAVAUX, P. O. A. “Fetal Echocardiographic ImageSegmentation Using Neural Networks”, IPA'99 ImageProcessing and Applications Conference, IEE, Manchester, UK,1999.[7] FERNANDES, D., NAVAUX, P. O. A., FICHTNER, P.F. P. “Segmentation of TEM Images Using Oscillatory NeuralNetworks”, SIBGRAPI 2001, IEEE, Florianópolis, 2001, p.289-296.[8] FERNANDES, D., SIQUEIRA, M. L., NAVAUX, P. O.A. “Segmentation of Fetal Echocardiographic Images UsingSelf-Organizing Maps and Oscillatory Neural Networks”, SIARP2001, IARP, Florianópolis, 2001, p.55-60.[9] FERNANDES, D. Segmentação de Imagens Baseada emRedes Neurais Oscilatórias, TI976, UFRGS-PPGC, PortoAlegre, 2001.[10] GHOSH, A., PAL, N. R., PAL, S. K. “Object backgroundclassification using Hopfield type neural network”. Int. J.Pattern Recognition Artificial Intelligence, 1992, v.6, n.5, p.989-1008.[11] KUROKAWA, H., MORI, S. “A Local Connected NeuralOscillator Network for Sequential Character Segmentation”,ICNN 97, IEEE, Texas, EUA, 1997, p.838-843.[12] LIU, X., CHEN, K., WANG, D. L. “Extraction ofhydrographic regions from remote sensing images using anoscillator network with weight adaptation”. Transactions onGeoScience and Remote Sensing. IEEE, 2001, 39(1), 207-211.[13] PICCOLI, L. Segmentação e Classificação de ImagensEcocardiográficas Utilizando Redes Neurais. Master Thesys.UFRGS-PPGC, Porto Alegre, 1999.[14] SHAREEF, N., WANG, D. L., YAGEL, R. “Segmentationof Medical Images Using LEGION”, Transactions on MedicalImaging, IEEE, 1999, v.18, n.1.[15] SIQUEIRA, M. L. Obtenção de Medidas Cardíacas FetaisAtravés de Imagens Ecocardiográficas Segmentadas, MasterThesys, UFRGS-PPGC, Porto Alegre, 2002.[16] TERMAN, D., WANG, D. L. “Global competition andlocal cooperation in a network of neural oscillators”, Physica D,1995, v.81(1-2), pp.148-176.[17] WANG, D., TERMAN, D. “Image Segmentation Based onOscillatory Correlation”. Neural Computation, MIT, 1997, v.9,p.805-836.[18] WANG, D. “Relaxation Oscillators and Networks”. WileyEncyclopedia of Electrical and Electronics Engineering, Wiley& Sons, 1999, v.18, p.396-405.[19] WANG, D., BROWN, G. J. “Separation of Speech fromInterfering Sounds Based on Oscillatory Correlation”.Transactions on Neural Networks, IEEE, 1999, v.10, n.3, p.684-697.


Architecture of oscillatory neural network for image segmentation

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