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Всё/vsë - Various - WLD 2014 – Entropy


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Multimodal medical image fusion MIF plays an important role in clinical diagnosis and therapy. Existing MIF methods tend to introduce artifacts, lead to loss of image details or produce low-contrast fused images.

Всё/vsë - Various - WLD 2014 – Entropy proposed method can generate high-quality fused images using the weighting fusion strategy based on the firing times of the SCM. In the weighting fusion scheme, the weight is determined by combining the entropy information of pulse outputs of the SCM with the Weber local descriptor operating on the firing mapping images produced from the pulse outputs.

The extensive experiments on multimodal medical images show that compared with the numerous state-of-the-art MIF methods, the proposed method can preserve image details very well and avoid the introduction of artifacts effectively, and thus it significantly improves the quality of fused images in terms of human vision and objective evaluation criteria such as mutual information, edge preservation index, structural similarity based metric, fusion quality index, fusion similarity metric and standard deviation.

With the development of medical imaging technology, various imaging modals such as ultrasound US imaging, computed tomography CTmagnetic resonance imaging MRIpositron emission tomography PET and single-photon emission computed tomography SPECT are finding a range of applications in diagnosis and assessment of medical conditions that affect brain, breast, lungs, soft tissues, bones and so on [ 1 ].

Owing to the difference in imaging mechanism and the high complexity of human histology, medical images of different modals provide a variety of complementary information about the human body. For example, CT is well-suited for imaging dense structures like non-metallic implants and bones with relatively less distortion. Likewise, MRI can visualize the pathological soft tissues better whereas PET can measure the amount of metabolic activity at a site in the body.

Multimodal medical image fusion MIF aims to integrate complementary information from multimodal images into a single new image to improve the understanding of the clinical information in a new space. Numerous image fusion algorithms have been proposed by working at pixel level, feature level or decision level.

Among these methods, the pixel-level fusion scheme has been investigated most widely due to its advantage of containing the original measured quantities, easy implementation and computational efficiency [ 5 ]. Existing pixel-level image fusion methods generally include substitution methods, multi-resolution fusion methods and neural network based methods. The substitution methods such as intensity hue saturation всё/vsë - Various - WLD 2014 – Entropy 67 ], principal component analysis [ 8 ] based methods can be implemented with high efficiency but at the expense of reduced contrast and distortion of the spectral characteristics.

Image fusion methods based on the multi-resolution decomposition techniques can preserve important image features better than substitution methods via the decomposition of images at a different scale to several components using pyramid e.

However, the transform based fusion methods involve much higher computational complexity than the substitution methods, and it is challenging to adaptively determine the involved parameters in these methods for the different medical images.

The various neural networks Capital - Various - Knife Culture: Buried Melbourne as self-generating neural network [ 25 ] and pulse coupled neural network PCNN have been used for image fusion. Different from some traditional neural networks, PCNN, as the third generation artificial neural network, has biological background and it is derived from the phenomena of synchronous pulse bursts in the visual cortex of mammals [ 2627 ].

Recently, PCNN has been combined with multi-resolution decomposition methods such as the wavelet transform [ 31 ], the NSCT [ 3233343536 ], the shearlet transform [ 3738 ] and the empirical mode decomposition [ 39 ]. These methods involve such disadvantages as high computational complexity, difficulty in adaptively determining PCNN parameters for various source images and image contrast reduction or loss of image details.

Wang et al. Despite the superiority of SCM over PCNN in computational efficiency, the SCM-F method will lead to loss of image details during fusion because it only utilizes the firing times of individual neurons in the SCM to establish the fusion rule, and employs a too simple fusion strategy. To address the problem of unwanted image degradation during Sabrina Duke - Sabrina Duke for the above-mentioned fusion methods, we have proposed a distinctive SCM based weighting fusion method.

In the proposed method, the weight is computed based on the multi-features of pulse outputs produced by SCM neurons in a neighborhood rather than the individual neurons.

The multi-features include the entropy information of pulse outputs, which can characterize the gray-level information of source images, and the Weber local descriptor WLD feature [ 42 ] of firing mapping images produced from pulse outputs, which can represent the local structural information of source images.

Compared всё/vsë - Various - WLD 2014 – Entropy the PCNN based fusion method, the proposed SCM based всё/vsë - Various - WLD 2014 – Entropy using the multi-features of pulse outputs SCM-M has such advantages as higher computational efficiency, simpler parameter tuning as well as less contrast reduction and loss of image details. Extensive experiments on CT and MR images demonstrate the superiority of the proposed method over numerous state-of-the-art fusion methods.

The remainder of the paper is structured as follows. Section 2 describes the spiking cortical model. Section 3 presents the details of the proposed SCM-M method. The experimental results and discussions are presented in Section 4. Conclusions and future research directions are given in Section 5. The SCM has been specially designed for image processing applications. The structural model of the SCM is presented in Figure 1.

As shown in Figure 1each neuron N ij at ij corresponds to one pixel in an input image, receiving its normalized intensity as feeding input O ij and the local stimuli from its neighboring neurons as the linking input. The feeding input and the liking input are combined together as the internal activity F ij of N ij.

The above process can be expressed by [ 40 ]:. Through всё/vsë - Various - WLD 2014 – Entropy computation, the SCM neurons output the temporal series Mighty Like The Blues - Duke Ellington - Unknown Session binary pulse images.

The temporal всё/vsë - Various - WLD 2014 – Entropy contain much useful information of input images. In Figure 2всё/vsë - Various - WLD 2014 – Entropy can see that during the various iterations, the output binary images contain different image information and the outputs of the SCM typically represent such important information as the segments and edges of the input image.

The всё/vsë - Various - WLD 2014 – Entropy from To Be With You - Mr. Big - Greatest Hits 2 indicates that the SCM can describe human visual perception.

Therefore, the pulse outputs of the SCM can be utilized for image fusion. Temporal series of pulse outputs generated by the SCM operating on magnetic resonance MR image: a MR image; and b — h the binary pulse images from the first to the seventh iteration, respectively. The key components of this method include the fusion rule and the weight computation. In the proposed method, the fusion rule is established based on the firing times of pulse outputs generated by the SCM. The weight is computed based on the similarity between the two source images, which is determined by combining the entropy information of pulse outputs from the SCM with the WLD operating on the resultant firing mapping image FMI.

It should be noted that here the FMIs have been scaled linearly to fit the range [0, ]. In Figure 4we can see that the FMI provides a means for representing the information of source images. The representation ability is related to the parameters of the SCM, especially the parameter N max. A too small e. A proper N max for the SCM can facilitate representing image details in the source images very well, which is of great significance for medical image всё/vsë - Various - WLD 2014 – Entropy.

The statistical characteristics of the two image patches will be characterized by the local energy E ij A and E ij B defined as:. According to the relationship between E ij A and E ij Bthe following fusion rule will be established and correspondingly the intensity of the pixel at ij in the fused image U will be expressed as:. It is desirable to compute this weight based on the similarity between two image patches Q ij A and Q ij B.

To determine this similarity effectively, the gray-level information and the saliency of Q ij will be utilized simultaneously. Here, the entropy of pulse outputs and the Weber local descriptor proposed in [ 42 ] will be adopted to characterize the gray-level distribution of Q ij and its saliency, respectively. To describe the information contained in G ij [ n ], its Shannon entropy H ij [ n ] is utilized. The entropy H ij [ n ] is computed as:.

Here, the probability P ij 1 [ n ] is defined as:. Otherwise, because H ij [ n ] will not be zero for some iteration times, V ij will include the nonzero elements, whose values will depend on the gray-level distribution of Q ij. The above analysis indicates that the gray-level information of Q ij can be characterized by V ij. Accordingly, V ij can be considered as the feature всё/vsë - Various - WLD 2014 – Entropy from Q ij.

The difference D ij between the features of two image patches Q ij A and Q ij B is calculated as:. Based on the difference D ijthe similarity S ij E n between Q ij A and Q ij B based on the entropy information will be defined as:. In this paper, the WLD is adopted to extract the salient features of an image patch of interest in the firing mapping image, which can be utilized to represent the saliency of the image patch Q ij in any source image.

The WLD is chosen due to its high computational efficiency and excellent ability in finding local salient patterns within an image to simulate the pattern perception of human beings [ 42 ]. Indeed, there are many other sparse and dense descriptors such as the scale invariant feature transform SIFT and the local binary pattern LBP. It can be seen from Equation 14 that the computation of R ij is very similar to the Laplacian operation.

As discussed in [ 42 ], the WLD can indicate the saliency of the local neighborhood very well because of its powerful representation ability for such important features as edges and textures. Therefore, the WLD operating on the FMIs can bring out the local image structural features of source images very well, which are highly beneficial for medical diagnosis based on different imaging modalities.

It will be desirable to utilize these extracted salient image features to determine the similarity S ij W L D between Q ij A and Q ij B in the source images, i.

When Pearson correlation is used to measure the similarity between Shannon entropy feature vectors of two considered image patches, it can address scale and translation changes of feature vectors. However, this correlation requires that the variables follow a bivariate normal distribution. The possibility of utilizing non-Euclidean similarity measures for the similarity computation in the weighting fusion strategy will be explored in-depth in future work. The implementation of the proposed SCM-M method can be summarized as the following steps:.

After running the SCM for N max times, the series of binary pulse images will be obtained for the source images using Equations 1 — 4. For each pixel at ij in A and Bthe Shannon entropy from the various iterations is computed on the output pulse images using Equation 10 to generate two feature vectors V ij A and V ij B. Based on the difference between the two feature vectors, the similarity S ij E n between two image patches Q ij A and Q ij B centered at ij is computed using Equation The output pulse images are utilized to generate the firing mapping images for two source images.

For any pixel at ij in two FMIs, the local energy E ij A and E ij B are computed on the considered two image patches centered at this pixel using Equations 7 and 8respectively. According to the relationship between E ij A and E ij Bthe fused image is produced by the weighted sum of two source images using Equation 9. All the images are chosen from the website [ 43 ]. Two images in each image pair include the complementary information.

Here, Groups 1—3 are three pairs of CT and MR images of different regions in the brain of a patient with acute stroke. Group 4 includes the transaxial MR images of the normal brain. Groups 7 and 8 are two pairs of CT and MR images of the brain of the patients with cerebral toxoplasmosis and fatal всё/vsë - Various - WLD 2014 – Entropy.

Please note that intensity standardization and inhomogeneity correction have been performed on всё/vsë - Various - WLD 2014 – Entropy MR images by the above всё/vsë - Various - WLD 2014 – Entropy . The number of directions of the four decomposition levels from coarse to fine is selected as 2, 3, 3, 4, respectively.

Figure 7Figure 8Figure 9 and Figure 10 show the fused results for the evaluated seven methods operating on such medical image pairs as Groups 1, 2, 4 and 5 shown in Figure 6respectively.

Meanwhile, it is shown in Figure 7 and Figure 9 that the above three fusion methods cannot preserve image details well in that they produce the obvious distortion of image details marked by the red boxes in the fused results. The m-PCNN Rock N Roll Lullaby - 10cc - How Dare You! cannot maintain the luminance of the fused results and it produces such low-contrast fused images that some important image details are difficult to Dont Blame Me - Bud Powell - The Amazing Bud Powell Volume 3, which is very disadvantageous for clinical diagnosis.

For example, for Groups 4 and 5, although almost all the details in the MR-T1 images can be transferred to the Robespierre - Die You Heathen Die! images by the PCNN-NSCT method very well, many details in the MR-T2 images have not been preserved by this method as indicated by the red boxes in the fused images shown in Figure 9 e and Figure 10 e.

For Groups 1, 2, and 5, some image details have been seriously damaged by the SCM-F method as shown by the red boxes in Figure 7 f, Figure 8 f всё/vsë - Various - WLD 2014 – Entropy Figure 10 f. By comparison, the SCM-M method not only provides high contrast for the fused images, but also maintains The Bouchee Family Singers - Gospel Train / Ive Been Redeemed information from the various source images in the fused results effectively.

In particular, the proposed method can preserve fine image details very well as shown by the red boxes in Figure 9 g and Figure 10 g without introducing artifacts or leading to edge blurring. The above comparisons demonstrate the superiority of the SCM-M method over other compared methods in that the fused images obtained by this method are more clear, informative, and have higher contrast. To further verify the advantage of the proposed SCM-M method in multimodal image fusion, Figure 11 and Figure 12 show the enlarged views of fused results for all evaluated methods operating on regions of interest ROIs denoted by the red boxes in Groups 1 and 6 in Figure 6respectively.

In Figure 11 and Figure 12we can see that the SCM-M method can maintain the salient information in the source images and provide better visual perception with less loss in luminance or contrast than other compared methods.

To explain Gdy Śliczna Panna - Waldemar - Najpiękniejsze Kolędy point better, some edges and regions have been chosen from Figure 11 всё/vsë - Various - WLD 2014 – Entropy and Figure 12 g.


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6 Replies to “ Всё/vsë - Various - WLD 2014 – Entropy ”

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    biased Lindley distribution and discussed its various propertied. A simulation study is also proposed in this paper. Shanker and Mishra () introduced a two parameter Poisson-Lindley distribution of which Sankaran’s (1 ) one parameter Poisson-Lindley RESIDUAL LIFE AND ENTROPY The survival function of the WLD is.
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