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1546 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 Figure 2. Basic model for a single PCNN neuron. ((1)). U is obtained by multiplying F with the biased ij ij L ((3)). If U is above the neuromime threshold θ , Y ij ij ij ij will generate a pulse ((4)), and simultaneously θ ij will increase enormously ((5)) to block another pulse in the next iteration. Without an output pulse, θ ij would decay exponentially ((5)), until it drops below the internal activity and at that time a pulse will be outputted again. In this way, these processes run over and over again. In (1)-(5), n denotes the iteration times; α F , α , α and L θ V , V , V θ are attenuation time constants and inherent F L voltage potential of F ij , L and θ , respectively; ij ij W signify synaptic weight strength for F ijkl ij and M and ijkl L ; ij β indicates linking strength determining contribution of the linking input to the internal activity. B. ULPCNN PCNN is qualified to imitate the biological features of HSV and hence apply to image processing [17]-[19]; however, so many parameters in the model should be set during use. So far, the relation between model parameters and network outputs is still ambiguous, and it is really difficult to determine the proper PCNN parameters. Therefore, ULPCNN is presented to simplify the PCNN by means of decreasing parameters and making the linking inputs of ULPCNN neurons uniform [16]. Fig. 3 displays the simplified model for a single ULPCNN neuron. The processes of a single ULPCNN neuron are displayed as F ( n) = S , (6) ij ∑ 1, Y ( n− 1) > 0, ⎧⎪ kl L ( n) = kl ij ⎨ ⎪⎩ 0 , otherwise , ij (7) U ( n) = F ( n) ⋅ (1 +β L ( n)) , (8) ij ij ij Figure 3. Simplified model for a single ULPCNN neuron. Y ( n) ij 1, U ( n) >θ ( n−1), ij ij = ⎧ ⎨ (9) ⎩ 0 , otherwise , θ ( n) = e −α θ θ ( n− 1) + VY ( n) . (10) ij ij θ ij According to (7), if any neuron in the k× l neighborhood fires, L ij will have a unity input, and then the centered neuron will be encouraged to fire. Obviously, impulse expanding behavior is much clearer and more controllable with much fewer parameters than the basic PCNN. IV. THE PROPOSED IMAGE FUSION METHOD Considering that HVS is very sensitive to detailed information, researchers commonly employ fusion rules to choose more significant information in high-frequency subbands. In our study, we provide a new image fusion method based on directional contrast-inspired ULPCNN in the contourlet domain. Directional features are fed into ULPCNN to imitate the biological activity of HSV, and then transmitted in the form of pulses. The linking range for each neuron is adaptive to corresponding directional contrast. The first firing time of each neuron is used to determine the decision in fusion rules. Because of the global coupling characters of the ULPCNNs, global features of images can be made good use of during fusion in our proposed method. Fig. 4 shows the flowsheet of our proposed method. Detailed procedure of the CT-ULPCNN method is given as follows. • Source images A and B are decomposed by the A A contourlet transform to coefficients { a , d } and , B { a , d }, respectively. Denote the coefficients of R B r, p F F the fused image F by { a , d }. Here, R is the R r, p decomposition level, a X (X=A,B,F) denotes the R coefficients in the low-frequency subband of X image X, and d (X=A,B,F) denotes the r, p R r p © 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1547 Figure 4. Flowsheet of our proposed method. coefficients in the pth directional subband at the rth (1 ≤ r ≤ R) scale of image X. • In each directional subband, directional contrast at location (, ) i j can be calculated as Ctr (, i j) = d (, i j) a ( u, v) . (11) X X X r, p r, p r X where a indicates the low-frequency subband at r the rth scale of image X, and the coarse coefficient at location ( uv , ) corresponds to the X X same region as d , (, i j ) does. Then Ctr (, i j ) , r p is imported as the external stimulus S ij into the ULPCNN neuron located at ( i, j ). Its linking range is fixed according to k ij or l ij r p 5, X X Ctr ( i, j) ≥ max( Ctr ) 2 , r, p r, p 3, otherwise. = ⎧ ⎨ ⎩ (12) The ULPCNN operates iteratively as (6)-(10), until all neurons are fired at least once. The first firing time of the neuron at location (, i j) in the pth directional subband at the rth scale of image X X should be recorded as T (, i j ) (X=A,B). , F F • R r, p { a , d } are obtained by the following rules. For the low-frequency, r p ( ) F A B a (, i j) = a (, i j) + a (, i j) 2 , (13) R R R For the high-frequency, d F r, p (, i j) A A B d (, i j), T (, i j) < T (, i j), ⎧ r, p r, p r, p = ⎨ (14) B ⎩ d r, p ( i, j), otherwise. • The fused image F is finally achieved via F F contourlet reconstruction from { a , d }. R r, p V. EXPERIMENTAL RESULTS To certify the effectiveness of our proposed method, we have performed the CT-ULPCNN method on many pairs of images. Considering limitation of space, we take three pairs of images (shown in Fig. 5) as examples to provide the experimental results. Fig. 5(a) is a pair of multifocus images focusing on different objects of the same scene, Fig. 5(b) displays a pair of remote sensing images taken from different wavebands, and Fig. 5(c) is a pair of infrared and visible images. In this section, following two sets of tests are designed to prove the validity of our proposed method. In Test 1, we highlight the advantage of the adaptive ULPCNNs model in our proposed method by comparing its behavior to three existing contourlet-based image fusion algorithms, including CT-Miao [12], CT-Zheng [13], and CT-Yang [14]. Test 2 demonstrates the prominence of the CT-ULPCNN method by its comparison with some typical MSD-based image fusion methods, namely, the gradient pyramid-based method (Gradient) [20], the conventional discrete wavelet transform-based method (DWT) [21], the curvelet transform-based method (Curvelet) [22], and the nonsubsampled contourlet transform-based method (NSCT) [23]. In our experiments, images were all decomposed into four levels in use of the above MSD-based fusion methods. Especially, for the contourlet-based image fusion methods, the decomposed four scales were divided into 4, 4, 8, and 16 directional subbands from coarse to fine scales, respectively. Furthermore, in our proposed method, parameters were set as α = 0.5 , θ V θ = 20 and β = 3 . A. Test 1 Fig. 6-Fig. 8, respectively, provide the fusion results of pepsi, remote and camp using the CT-ULPCNN, CT- Miao, CT-Zheng, and CT-Yang methods. To show more clearly, we select a section of each result to enlarge. As can be seen from Fig. 6, for multifocus images, the CT-Miao, CT-Zheng, and CT-Yang methods all have the problem of ring artifacts in their fusion results, and the partial result of the CT-Zheng has the severest ghost image even with a post-processing of consistency verification (CV) to intentionally reduce the ringing artifacts; whereas our proposed method possesses a result with the fewest ringing artifacts, highest contrast and finest details without the CV. As seen from Fig. 7, the CT-ULPCNN method still has the best performance with the smoothest surface in the flat regions. However, the result of the CT-Yang © 2013 ACADEMY PUBLISHER
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Journal of Computers ISSN 1796-203X
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Corn Moisture Measurement using a C
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Call for Papers and Special Issues
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(Contents Continued from Back Cover
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