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Edited by: Nianyin Zeng, Xiamen University, China

Reviewed by: Ming Zeng, Xiamen University, China; Cheng Wang, Huaqiao University, China; Yingchun Ren, Jiaxing University, China

This article was submitted to Brain Imaging Methods, a section of the journal Frontiers in Neuroscience

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Recent research has reported the application of image fusion technologies in medical images in a wide range of aspects, such as in the diagnosis of brain diseases, the detection of glioma and the diagnosis of Alzheimer’s disease. In our study, a new fusion method based on the combination of the shuffled frog leaping algorithm (SFLA) and the pulse coupled neural network (PCNN) is proposed for the fusion of SPECT and CT images to improve the quality of fused brain images. First, the intensity-hue-saturation (IHS) of a SPECT and CT image are decomposed using a non-subsampled contourlet transform (NSCT) independently, where both low-frequency and high-frequency images, using NSCT, are obtained. We then used the combined SFLA and PCNN to fuse the high-frequency sub-band images and low-frequency images. The SFLA is considered to optimize the PCNN network parameters. Finally, the fused image was produced from the reversed NSCT and reversed IHS transforms. We evaluated our algorithms against standard deviation (SD), mean gradient (Ḡ), spatial frequency (SF) and information entropy (E) using three different sets of brain images. The experimental results demonstrated the superior performance of the proposed fusion method to enhance both precision and spatial resolution significantly.

In 1895 Rontgen obtained the first human medical image by X-ray, after which research of medical images gained momentum, laying the foundation for medical image fusion. With the development of both medical imaging technology and hardware facilities, a series of medical images with different characteristics and information were obtained, contributing to a key source of information for disease diagnosis. At present, clinical medical images mainly include Computed Tomography (CT) images, Magnetic Resonance Imaging (MRI) images, Single-Photon Emission Computed Tomography (SPECT) images, Dynamic Single-Photon Emission Computed Tomography (DSPECT) and ultrasonic images, etc. (

Image fusion is the synthesis of images into a new image using a specific algorithm. The space-time relativity and complementarity of information in fused images can be fully used in the process of image fusion, contributing to a more comprehensive expression of the scene (

The Pulse Coupled Neural Network (PCNN) was discovered by

In our study, a new fusion approach based on the SFLA and PCNN is proposed to address the limitations discussed above. Our proposed method not only innovatively uses SFLA optimization to effectively learn the PCNN parameters, but also produces high quality fused images. A series of contrasting experiments are discussed in view of image quality and objective evaluations.

The remaining part of the paper is organized as follows. Related work is introduced in Section “Related Works.” The fusion method is proposed in Section “Materials and Methods.” The experimental results are presented in Sections “Result” and “Conclusion” concludes the paper with an outlook on future work.

Image fusion involves a wide range of disciplines and can be classified under the category of information fusion, where a series of methods have been presented. A novel fusion method, for multi-scale images has been presented by

Moreover, an algorithm for the fusion of thermal and visual images was introduced by M Kanmani et al. in order to obtain a single comprehensive fused image. A novel method called self tuning particle swarm optimization (STPSO) was presented to calculate the optimal weights. A weighted averaging fusion rule was also used to fuse the low frequency- and high frequency coefficients, obtained through Dual Tree Discrete Wavelet Transform (DT-DWT) (

The algorithm 3.1 represents an image fusion algorithm based on the PCNN and SFLA, where SPECT and CT images are fused. In our proposed algorithm, a SPECT image is first decomposed on three components using IHS transform, which include saturation S, hue H and intensity I. Component I is then decomposed to a low-frequency and high-frequency image through NSCT decomposition. Additionally, a CT image is decomposed into a low-frequency and high-frequency image through NSCT decomposition. Moreover, the two low-frequency images obtained above are fused in a new low-frequency image through the SFLA and PCNN combination fusion rules, while the two high-frequency images obtained above are fused into a new high-frequency image through the SFLA and PCNN combination fusion rules. Next, the new low-frequency and new high-frequency images are fused to generate a new image with intensity I’ using reversed NSCT. Finally, the target image is achieved by using reversed IHS transform to integrate the three components S, H and I’.

Algorithm 1: An image fusion algorithm based on PCNN and SFLA |
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Input: A SPECT image A and a CT image B |

Output: A fused image F |

Step 1: Obtain three components of image A using IHS transform; saturation S, hue H and intensity I. |

Step 2: Image decomposition |

(1) Decompose the component I of image A to a low-frequency image AL and high-frequency image AH through NSCT decomposition. |

(2) Decompose image B to a low-frequency image BL and high-frequency image BH through NSCT decomposition. |

Step 3: Image fusion |

(1) Fuse the low-frequency images AL and BL to a new low-frequency image CL through the SFLA and PCNN combination fusion rules. |

(2) Fuse the high-frequency images AH and BH to form a new high-frequency image CH through the SFLA and PCNN combination fusion rules. |

Step 4: Inverse transform |

Fuse the low-frequency image CL and high-frequency image CH to a new image with intensity I’ using reversed NSCT. |

Step 5: Reversed IHS transform |

Through the reversed IHS transform, integrate the three components S, H and I’, then obtain the target image F. |

The overall method of the proposed algorithm for the fusion of a SPECT and CT image is outlined in

The proposed method for the process of fusion.

In our proposed method, the SPECT image and CT image are decomposed into a low-frequency and high-frequency image using NSCT.

Non-subsampled contourlet transform (

The structure diagram of the two-level decomposition of NSCT.

An analysis filter {H_{1} (z), H_{2} (z)} and a synthesis filter {G_{1} (z), G_{2} (z)} are used when using NSCT to decompose images and the two filters satisfy H_{1}(z)G_{1}(z) + H_{2}(z)G_{2}(z) = 1. The source image can generate low-frequency and high-frequency sub-band images when it is decomposed by NSP. The next level of NSP decomposition is performed on low-frequency components obtained by the upper-level decomposition. An analysis filter {U_{1} (z), U_{2} (z)} and synthesis filters {V_{1} (z), V_{2} (z)} are contained in the design structure of NSDFB with the requirement of U_{1}(z)V _{1}(z) + U_{2}(z)V _{2}(z) = 1. The high-pass sub-band image decomposed by J-level NSP is decomposed by L-level NSDFB, and the high-frequency sub-band coefficients can be obtained at the number of 2^{n}, where n is an integer higher than 0. A fused image with clearer contours and translation invariants can be obtained through the fusion method based on NSCT (

Fusion rules affect image performance, so the selection of fusion rules largely determines the quality of the final fused image. In this section, the PCNN fusion algorithm based on SFLA is introduced for low-frequency and high-frequency sub-band images decomposed by NSCT.

The PCNN is a neural network model of single-cortex feedback, to simulate the processing mechanism of visual signals in the cerebral cortex of cats. It consists of several neurons connected to each other, where each neuron is composed of three parts: the receiving domain, the coupled linking modulation domain and the pulse generator. In image fusion using the PCNN, the M ^{∗} N neurons of a two-dimensional PCNN network correspond to the M ^{∗} N pixels of the two-dimensional input image, and the gray value of the pixel is taken as the external stimulus of the network neuron. Initially, the internal activation of neurons is equal to the external stimulation. When the external stimulus is greater than the threshold value, a natural ignition will occur. When a neuron ignites, its threshold will increase sharply and then decay exponentially with time. When the threshold attenuates to less than the corresponding internal activation, the neuron will ignite again, and the neuron will generate a pulse sequence signal. The ignited neurons stimulate the ignition of adjacent neurons by interacting with adjacent neurons, thereby generating an automatic wave in the activation region to propagate outward (

The parameters of the PCNN affect the quality of image fusion, and most current research uses the method of regressively exploring the values of parameters, which is subjective to a certain degree. Therefore, how to reasonably set the parameters of the PCNN is the key to improving its performance. In our paper, SFLA is used to optimize the PCNN network parameters.

Shuffled frog leaping algorithm is a particle swarm search method based on groups to obtain optimal results. The flowchart of SFLA is shown in

The flowchart of the shuffled frog leaping algorithm.

F(x) is defined as a fitness function and Ω is a feasible domain. In each iteration, P_{g} is the best frog for a frog population, P_{b} represents the best frog for each group and P_{w} is the worst frog for each group. The algorithm adopts the following update strategy to carry out a local search in each group:

where S_{j} represents the updated value of frog leaping, rand () is defined as the random number between 0 and 1, S_{max} is described as the maximum leaping value, and P_{w,new} is the worst frog of updated group. If P_{w,new} ∈ Ω and F(P_{w,new}) > F(P_{w}), P_{w} can be replaced by P_{w,new}, otherwise, P_{b} will be replaced by P_{g}. At the same time, if P′_{w,new} ∈ Ω and F(P′_{w,new}) > F(P_{w}), P_{w} can be replaced by P′_{w,new}, otherwise P_{w} can be replaced by a new frog and then the process of iteration will continue until the maximum iterations is reached.

Three parameters α_{𝜃},β and V _{𝜃} in PCNN are essential for the results of image fusion. Therefore, as it is shown in _{𝜃},β,V _{𝜃}) and the optimal configuration scheme of the PCNN parameters can finally be obtained by searching for the best frog X_{b}(α_{𝜃},β,V _{𝜃}).

The process of PCNN parameter optimization based on SFLA.

In our proposed method, possible configuration schemes of parameters are defined, which constitute a solution space for the parameter optimization. After generating an initial frog solution space, F frogs in the population are divided into m groups, and each group is dependent on one another. Starting from the initial solution, the frogs in each group first carry out an intraclass optimization by a local search, thereby continuously updating their own fitness values. In N iterations of local optimization, the quality of the whole frog population is optimized with the improvement of the quality of frogs in all groups. The frogs of the population are then fused and regrouped according to the established rule, and local optimization within the group is carried out until reaching the final iteration conditions. Finally, the global optimal solution of the frog population is defined as the optimal PCNN parameter configuration. The final fusion image is thus obtained using the optimal parameter configuration above.

In order to verify the accuracy and preservation of the edge details in our proposed method, three sets of CT and SPECT images were fused based on our method. The results of each set were compared with four fusion methods; IHS, NSCT+FL, DWT, NSCT+PCNN. In the method of NSCT+FL, images are first decomposed by NSCT to obtain high-frequency and low-frequency coefficients, and then fusion images are obtained by taking large value high-frequency coefficients and taking average value low-frequency coefficients. In NSCT+PCNN, images are decomposed by NSCT and fused by the PCNN.

Experiments were implemented on the image database from the Whole Brain Web Site of Harvard Medical School (

A series of fusion results of SPECT and CT images, based on different methods including IHS, NSCT+FL, DWT, NSCT+PCNN, and our proposed method is shown in

A series of contrasting experiments for normal brain images on fusion images based on different fusion methods (set 1).

A series of contrasting experiments for glioma brain images on fusion images based on different fusion methods (set 2).

A series of contrasting experiments for brain images of patients diagnosed with Alzheimer’s disease on fusion images based on different fusion methods (set 3).

A set of metrics is used to compare the performance of the fusion methods including IHS, DWT, NSCT, PCNN, a combination of NSCT and the PCNN, and our proposed method. The evaluation metrics including standard deviation (SD), mean gradient (Ḡ), spatial frequency (SF) and information entropy (E) are entailed as follows (

Standard deviation

Standard deviation is used to evaluate the contrast of the fused image, which is defined as

where Z(i,j) represents the pixel value of the fused image and

The SD reflects the discrete image gray scale relative to the mean value of gray scale. And a higher value of SD demonstrates the performance of a fused image.

Mean gradient (Ḡ)

Ḡ corresponds to the ability of a fused image to represent the contrast of tiny details sensitively. It can be mathematically described as

The fused image is clearer when the value of mean gradient is higher.

Spatial frequency (SF)

Spatial frequency is the measure of the overall activity in a fused image. For an image with a gray value Z(x_{i},y_{j}) at position (x_{i},y_{j}), the spatial frequency is defined as

Where row frequency

Column frequency

The higher the value of frequency, the better the fused image quality.

Information entropy (E)

Information entropy is provided by the below equation

where L is image gray scale and Pi is the proportion of the pixel of the gray value i in whole pixels. A higher value of entropy indicates more information contained in the fused image.

Experiment results on fused images of SPECT images and CT images are shown in

Performance evaluations on normal brain fused images based on different methods.

Metric | IHS | NSCT+FL | DWT | NSCT+PCNN | Proposed | |
---|---|---|---|---|---|---|

Set 1 | Standard deviation | 51.6141 | 55.2178 | 42.5312 | 57.1188 | 57.2258 |

Mean gradient | 8.8561 | 8.714 | 6.2027 | 8.8568 | 8.8071 | |

Spatial frequency | 33.5851 | 33.2324 | 22.0093 | 33.7566 | 33.6546 | |

Information entropy | 2.6859 | 2.7565 | 3.0483 | 2.7729 | 3.0621 | |

Set 2 | Standard deviation | 43.278 | 49.5989 | 43.0915 | 52.9246 | 53.1691 |

Mean gradient | 6.686 | 6.6633 | 4.5622 | 6.5672 | 6.7489 | |

Spatial frequency | 20.3855 | 19.9558 | 12.7416 | 19.8214 | 20.0956 | |

Information entropy | 3.6325 | 3.9243 | 4.2501 | 3.8386 | 3.9424 | |

Set 3 | Standard deviation | 50.0926 | 55.7124 | 47.4476 | 57.1246 | 57.1268 |

Mean gradient | 6.2153 | 6.1775 | 4.1822 | 6.086 | 6.1796 | |

Spatial frequency | 19.244 | 18.9682 | 12.0096 | 18.7269 | 18.7335 | |

Information entropy | 3.6226 | 3.7122 | 4.0074 | 3.7139 | 3.7399 |

Performance evaluations on glioma brain fused images based on different methods.

Metric | IHS | NSCT+FL | DWT | NSCT+PCNN | Proposed | |
---|---|---|---|---|---|---|

Set 1 | Standard deviation | 41.7514 | 55.2055 | 39.8132 | 58.0374 | 58.3122 |

Mean gradient | 5.2953 | 5.5442 | 3.8166 | 5.459 | 5.5678 | |

Spatial frequency | 16.2064 | 16.5277 | 10.1649 | 16.466 | 16.4776 | |

Information entropy | 3.9255 | 4.1433 | 4.6303 | 4.08 | 4.1788 | |

Set 2 | Standard deviation | 44.154 | 55.5879 | 42.436 | 57.7284 | 57.775 |

Mean gradient | 6.2881 | 6.6316 | 4.595 | 6.535 | 6.7276 | |

Spatial frequency | 17.6675 | 17.9369 | 11.359 | 17.9359 | 17.9095 | |

Information entropy | 4.3966 | 4.7513 | 5.1901 | 4.6312 | 4.837 | |

Set 3 | Standard deviation | 48.6572 | 54.0708 | 41.78 | 56.2065 | 56.3546 |

Mean gradient | 6.8855 | 6.8515 | 4.8166 | 6.774 | 6.7977 | |

Spatial frequency | 27.8964 | 27.8583 | 17.8725 | 27.7365 | 27.7654 | |

Information entropy | 2.4852 | 2.5749 | 2.8442 | 2.5239 | 2.658 |

Performance evaluations on fused brain images of patients diagnosed with Alzheimer’s disease, based on different methods.

Metric | IHS | NSCT+FL | DWT | NSCT+PCNN | Proposed | |
---|---|---|---|---|---|---|

Set 1 | Standard deviation | 66.1357 | 65.3766 | 51.0336 | 69.5392 | 66.5782 |

Mean gradient | 9.9938 | 10.0303 | 6.509 | 10.0089 | 10.2068 | |

Spatial frequency | 26.7087 | 26.7329 | 16.1614 | 26.6568 | 27.1771 | |

Information entropy | 4.7735 | 4.834 | 5.4105 | 4.8036 | 4.8966 | |

Set 2 | Standard deviation | 59.1931 | 59.2093 | 52.0837 | 61.4981 | 60.6457 |

Mean gradient | 6.7482 | 7.0266 | 4.5756 | 7 | 7.0461 | |

Spatial frequency | 19.0263 | 19.3264 | 11.8249 | 19.3257 | 19.512 | |

Information entropy | 3.9901 | 4.1834 | 4.5922 | 4.0985 | 4.2156 | |

Set 3 | Standard deviation | 56.0974 | 58.787 | 47.6032 | 56.0943 | 57.7578 |

Mean gradient | 7.9023 | 8.111 | 5.4579 | 7.9592 | 7.966 | |

Spatial frequency | 22.2846 | 22.4084 | 13.907 | 21.9421 | 22.0022 | |

Information entropy | 3.895 | 4.1058 | 5.1943 | 4.2228 | 4.2897 |

In this paper, a new fusion method for SPECT brain and CT brain images was put forward. First, NSCT was used to decompose the IHS transform of a SPECT and CT image. The fusion rules, based on the regional average energy, was then used for low-frequency coefficients and the combination of SFLA and the PCNN was used for high-frequency sub-bands. Finally, the fused image was produced by reversed NSCT and reversed IHS transform. Both subjective evaluations and objective evaluations were used to analyze the quality of the fused images. The results demonstrated that the method we put forward can retain the information of source images better and reveal more details in integration. It can be seen that the proposed method is valid and effective in achieving satisfactory fusion results, leading to a wide range of applications in practice.

The paper focuses on multi-mode medical image fusion. However, there is a negative correlation between the real-time processing speed and the effectiveness of medical image fusion. Under the premise of ensuring the quality of fusion results, how to improve the efficiency of the method should be considered in the future.

Publicly available datasets were analyzed in this study. This data can be found here:

CH conceived the study. GT and CH designed the model. YC and YP analyzed the data. YL and WC wrote the draft. EN and YH interpreted the results. All authors gave critical revision and consent for this submission.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.