A Robust Medical Image Fusion Based on Synthetic Focusing Degree Criterion and Special Kernel Set for Clinical Diagnosis

: Medical imaging has been widely used to diagnose diseases over the last two decades. Medical professionals still struggle to diagnose diseases using a single modality since there is a shortage of data in this domain. Therefore, images of specific organs with diseases from a variety of medical imaging systems can be combined using a technique called image fusion. Medical image fusion has prompted immense requisite applications in clinical applications in recent years. However, the fusion of medical images still facing a variety of challenges due to the input image quality. Protonema such as noise and low-contrast input medical images significantly reduces the quality of medical images. Still, recent image fusion methods are not significantly able to address the image quality problems. In order to address these problems, this study introduces a novel image fusion method that provides effective fusion performance even if the input images are noisy or low-contrast by combining the benefits of synthetic focusing degree criterion with a special kernel set. First, a Gaussian Curvature Filter (GCF) is used to sharpen the images in order to perform a Salient Feature Extraction (SFE). Then, we create a synthetic Focusing Degree Condition (FDC) that combines the Spatial Frequency (SF) and the Local Variance (LV) of the images to get the coarse fusion maps. The course fusion maps are then processed using median and morphological filters. The weighted fusion technology is used to generate the fused image. Finally, image enhancement is achieved by adding a special kernel to the fused image to obtain the final fusion result. Experimental results on the publicly available datasets exhibited that the proposed research article obtains the best results in terms of noisy and low-contrast medical images. Overall, it achieves significant performance both qualitatively and quantitively when compared to other competing state-of-the-art methods.


Introduction
Clinical diagnosis is significantly impacted by the quality of medical imaging.Consequently, increasing numbers of academics are focused on enhancing the performance of image fusion algorithms.These days, a wide variety of medical images are utilized to diagnose diseases.As a matter of fact, in order to make a diagnosis, clinicians consult a wide range of image kinds for information.The reason for this is that single multimodal images do not provide adequate details appropriate for diagnosis purposes.For instance, radio frequency pulses are used in Magnetic Resonance Imaging (MRI) to create images of the body's organs.It provides details such as fat tissue and muscular anatomy.In contrast, a CT scan is a diagnostic imaging method that generates images of the inside of the body by combining computer technology and X-rays.Any constituent of the body, including the bones, muscles, fat, organs and blood arteries is represented in great detail.A method called medical image synthesis adds extra data from multimodality medical images to produce a single which is a highly informative rich image (Haribabu et al., 2023).Both the diagnosis process by physicians and the recognition of detecting devices will be more suitable with this technology.The transform domain-based image synthesis techniques are widely employed nowadays due to their effectiveness.The process of image fusion involves three main steps; (a) Transforming the image is the first stage.The objective of this stage is to help with the fusion by converting images into coefficients on the transform domain.The formation of synthetic images in a domain that has been changed by particular rules is the second phase.The max fusion principle (Li et al., 2021a), an average fusion principle (Pei et al., 2020), local gradient energy (Fu et al., 2020) and MSMG-WLE (Zhang et al., 2022) are a few examples of fusion principles that are introduced respectively.To generate a composite image, the elements generated through the transform domain are finally transferred to the spatial domain.Lepcha et al. (2020a) present a method to fuse medical images by using a cross-bilateral filter for gray-level similarities and geometric proximity of the neighboring pixels without smoothing borders.The rolling guiding filter is then used to filter the detailed images produced by deducting the cross bilateral filter image output from the original images in order to enable scale-aware operation.Many recent studies have employed image transformation techniques, including wavelet transform-based approaches (Tawfik et al., 2021), Laplacian Decomposition (LD) (Li et al., 2022) and Laplacian Pyramid (LP) transform (Fu et al., 2020).
In addition, Goyal et al. presented a fusion technique that integrates poor-resolution medical photographs with a low computational period in order to enhance target detection accuracy and serve as a basis for clinical diagnosis (Goyal et al., 2021).The Non-Subsampled Curvelet Transform (NSCT) (Li et al., 2021b), contourlet transform (Yang et al., 2010), Non-Subsampled Shearlet Transform (NSST) (Tannaz et al., 2020) and curvelet transform (Nencini et al., 2007) are few techniques that are based on multiscale geometric analysis.A novel technique for fusing multimodal medical images has been proposed recently (Goyal et al., 2022).It uses edge-aware filtering and hybridization of cross-bilateral filters.This approach suggested a novel strategy for determining the weights for the final fusion rule (Lilhore et al., 2022;Ramesh et al., 2022).In recent years, strategies for image synthesis based on sparse representation have also been presented.For instance, a novel approach to image synthesis based on Siamese networks and Sparse Representation (SR) was put forth by Yousif et al. (2022) In order to build an effective method for generating medical images, (Li et al., 2021c) introduced fusion approach by combining SR method with a segment graph filter.The fusion method using pixel significance along with anisotropic diffusion and cross bilateral filtering is proposed by Lepcha et al. (2020b) This method initially methodology uses edge-preserving processing of input photographs with nonlinear techniques with a linear low pass filter to detect essential regions of source images while preserving edges.In order to identify the significant regions that are defined by edges of the right size and high amplitude, the morphological processing of linear filter residuals serves as the basis for the selection of those regions.Furthermore, a fusion method to fuse CT-SPECT images using discrete Hermite transform and SR was proposed by Barba-J et al. (2022).The traditional sparse representation (CSR) (Wang et al., 2021a) and the Joint Sparse Model (JSM) (Zhang et al., 2023a) are two examples of improvement strategies that are based on sparse representation.
In recent years, deep learning-based methods for medical image fusion have been proposed.For example, an image fusion technique that combines Convolutional Neural Network (CNN) and NSCT was presented by Wang et al. (2021b) The combination of SSN and the MSLES was proposed by Ding et al. (2021).The CNN was used and merged with SR by Shibu and Priyadharsini (2021).A cross-encoder (CE)-based technique for image synthesis was presented by Zhu et al. (2022) and Tawfik et al. (2022) introduced the usage of SAE in order to fuse medical photographs in the NSCT domain.An attention network called the Multi-scale Residual Pyramid (MRPAN) was proposed by Fu et al. (2020).Other deep learning-based techniques include multi-CNN, fuzzy neural networks (Fu et al., 2020) and FusionNet (Xu and Ma, 2021).Furthermore, metaheuristic-related optimization methods have shown impressive medical image fusion efficiency in recent times.For instance, Duan et al. (2021) used SML in combination with a Genetic Algorithm (GA) and a log-Gabor filter.A method based on fuzzy logic and Particle Swarm Optimization (PSO) has been presented by Gao et al. (2021) The marine predator's algorithm (Dinh, 2023), equilibrium optimization algorithm (Dinh, 2021b), grasshopper optimization algorithm (Dinh, 2021a), gray wolf optimization (Daniel et al., 2017) and PSO (Tannaz et al., 2020) are a few further optimization methods that are currently in use.One recently proposed optimization algorithm is the CSA (Braik, 2021).Many applications such as the diagnosis of plant leaf diseases (Umamageswari et al., 2023), integrated heat and power economical dispatch (Rizk-Allah et al., 2022), as well as feature selection (Mostafa et al., 2022), have put together successful use of these algorithms.As a result, applying the CSA algorithm to image fusion and enhancement can yield inspiring results.The results indicate that a number of factors influence how well the image synthesis algorithm functions.The first is that there could be low-quality components in the input image, like noise or poor contrast.The majority of recent image fusion techniques are not able to handle input images with noise or poor contrast.Therefore, if there is an input image with poor image quality, the fusion performance of these methods is limited.Many recent researchers have also tried to preprocess the input photographs prior to the fusion of images.For instance, Maqsood and Javed (2020) Pre-processed the input image quality using an improved histogram equalization strategy.
The Fast Local Laplacian Filter (FLLF) was employed by Ullah et al. (2022) to enhance the quality of the source image in the image fusion method.For the fusion of medical images, (Zhang et al., 2023b) provide a novel joint sparse model with coupled dictionary learning.In order to improve multi-source signal preservation and preserve edge/texture information, the framework designed a novel fusion rule.The standard sparse coefficients and novel sparse coefficients with overcomplete coupled dictionaries are used to represent the original medical images.Additionally, the authors developed a pair Feature Difference Guided Network (FDGNet), a novel end-to-end unsupervised learning fusion network for the fusion of medical images (Zhang et al., 2023a).It is shown as feature-weighted guided learning in order for the image fusion task to effectively extract complementary properties from the input images.This means that the feature extraction method is responsible for determining the differences between properties at different stages and the feature restoring method could produce a pair of interactive weights by feature differences as guidance to produce fused results directly.
A novel end-to-end unsupervised network for fusing multi-modal medical images is presented by Liu et al. (2023) It consists of two symmetrical discriminators and a generator.Where the former seeks to create a "real-like" fused image based on precisely designed content and structural loss, whereas the latter is focused on identifying the differences between the fused image and the source ones.They receive alternating training until discriminators are unable to tell the fused image from the original one.Furthermore, preserving feature consistency across several modalities is facilitated by the symmetrical discriminator approach.However, the fused photographs' image quality has not been much better because these methods only slightly increase image quality.Thus, a novel image fusion model is presented in this research that performs well even in cases where an input image has noise or poor contrast.The main contributions of the proposed method are as follows: 1) This study proposes a novel medical image fusion based on synthetic focusing degree criterion with a special kernel set to address the shortages of recent existing methods.To address this shortcoming, the proposed approach fully considers interrelated features between training sets and investigates relevant details between test images 2) An appropriate fusion approach that preserves functional and structural details is developed to highlight and enhance diverse information of source images 3) Experimental results illustrated that the proposed framework performs better in terms of both subjective visual evaluation and objective metrics and it is highly efficient when compared to the state-of-the-art fusion methods using publicly available datasets

Materials and Methods
This study introduces a novel medical image fusion based on synthetic focusing degree criterion with a special kernel set.This method applied a GCF-based technique where it produces the sharpest regions of the images.In addition, the feature images are obtained from the source images by subtracting the filtered images which provide edge information.Furthermore, the coarse fusion maps are generated using feature images and a synthetic FDC.The Optimized Fusion Maps (OFM) are obtained by the process of coarse fusion maps with morphological filters.The weighted fusion is used to generate the fused images.Lastly, a special kernel set is used to obtain the final fusion result while maintaining the significant details.Fig. 1 displays the framework of the proposed method.

Salient Feature Extraction
The first step of our method is to extract edge features from the source images.The salient feature extraction procedure based on Gaussian Curvature Filter (GCF) is illustrated in this section.

Gaussian Curvature Filter (GCF)
An efficient image feature extraction technique that can synchronously safeguard the edges of images is introduced by Gong and Sbalzarini (2017).It assumed that the surface formed from a perfect, noise-free image is feasible and that the surface's Gaussian curvature is zero at any point.It is not necessary to explicitly calculate the Gaussian curvature by changing each pixel's value to align it with the tangent planes of nearby pixels.Therefore, second-order differentiability of surfaces is no longer necessary.The Gaussian filter for an image pixel located at (i, j) can be described as follows; the method first finds all the local tangent planes which include its neighborhood pixels to enumerate the pixel projections on the local surface: where, dn (n = 1, 2, …, 8) represents the distance between pixel (i, j) and the tangent planes of nearby pixels.Where Ui,j stands for pixel value at location (i, j).To find the closest local surface using the smallest projection distance as follows: (2) In order to make pixel (i, j) fall on this surface, our method modifies its value as follows: where, U'i,j stands for pixel value at (i, j).We utilize the sliding window approach to filter images from the top left to the bottom right to complete the filtering of the whole image.We can keep doing these adjustments until the pixel values stop changing.For ease of use, the GCF operation is referred to in this study as GC (I, m), where, I stands for input image and m stands for iterations number.The Salient Feature Extraction (SFE) from source images could be performed using the GCF.

GCF-Based Feature Extraction
The SFE from the source images could be performed using the GCF.The following is a description of the salient feature extraction process.
To obtain the filtered images,  1 and  2 , the GCF is employed for the source images  1 and  2 .The following is how the filtered images are obtained: where, In and m represent the n th source image and iterations number and GC(.) stands for the GCF operation.
The difference between filtered images and the source images is calculated to determine salient feature matrices.Therefore:

Focus Region Confirmation
Identification of the focus regions is significant in medical image fusion.Therefore, a suitable focus region validation process is required, where a synthetic FDC is proposed in our study.Where SF and LV constitute synthetic FDC.The coarse fusion map which could coarsely identify the focused and unfocused parts could be obtained using synthetic FDC.

Spatial Frequency
The entire process of image is represented by SF and the activity of image and clarity have a good relationship with the SF.Accordingly, if SF is high, an image will be clearer and its hierarchical structure will be clearer (Li et al., 2001;Rahman et al., 2017).In this study, a Row Frequency (RF) and Column Frequency (CF) are determined for a P  Q local patch in Fn that is centered at location (x, y), where, P represents the row number and Q represents the number of the column: (6) and: where the matrices for the salient features are F1 and F2.

Local Variance
The local map's clarity is measured using the LV.The LV can be used to effectively represent the detailed block.It reflects the contrast between minute details in images.Thus, we use LV as a local measure for finding regional priority regions.We have the following expression for P  Q local patch: where, 1 and 2 represent means of salient feature matrices  1 and  2 , respectively in local neighborhood P  Q.Further, P  Q is fixed to 77 for complete experiments.

Focus Region Confirmation Using Synthetic FDC
We propose a synthetic FDC that combines SF and LV, where SF and LV describe complete qualities and local properties.By using this metric, we can produce coarse fusion maps that could represent both focused as well as unfocused parts.A coarse fusion map is represented by C1 in this study as: It is clear that C1 indicates regions of source image  1 that were focused.In Eq. ( 10), "1" refers to the focussed regions of source image I1 while "0" refers to the unfocused parts.The SF and LV are high in original images The regions will only be categorised as focused regions if it is determined both measurements.Using a synthetic FDC makes a lot of sense because it considers both global and local details of the source images.

Filter Processing
Despite being able to approximate the focused and unfocused region distributions, the coarse fusion map generated from synthetic focus measure contains several thin flanges, slim fractures, slim gulfs and microscopic holes.Thus, more processing is required for coarse fusion maps.In this subsection, morphological filters and median filtering are utilized to fix these flaws.Thin connections and thin protrusions are no longer a concern due to the morphological opening operator.On the contrary, the morphological closing operator can combine narrow breaks and fill thin gaps as discussed in Rahman et al. (2017).The morphological filtering result for the coarse fusion map C1 can be expressed as: where, Cn is the map of the closure operation result and Cm is the map of the opening process result.The terms Θ and ⊕ represents morphological dilation and erosion process, respectively in Eq. ( 11). stances for an element of morphological structure with a radius size ranging from 2-15.

Image Fusion Process
If OFM is taken into consideration, the fused image IF could be computed by:

Image Sharpening Using Special Kernel Set
It is relatively easy to Deblur images using kernels (Al-Ameen et al., 2012).To generate a clearer image, we used the concept of convolving the kernel with the fused image.It only requires one mathematical process and is simple as well as accurate.Using the above Filtered Image (IF), kernel (K) and convolution procedure (⨂), the following procedure is defined for the restoring final fusion image (R):

Datasets and Experimental Details
We considered nine pairs of medical images from the publicly available dataset (in Fig. 2) to validate the performance of the proposed method.A computer with a 2.6 GHz Intel Core i7 processor, 16 GB of RAM and an RTX2060 GPU was used for the experiments.All methods are implemented in MATLAB 2022b.For comparisons, we use seven algorithms, namely Laplacian pyramid and CNN reconstruction with local gradient energy strategy (LPCNNR) (Fu et al., 2020), an unsupervised Enhanced Medical image fusion network (EM Fusion) (Xu and Ma, 2021), MRPAN (Fu et al., 2021), a non-subsampled contourlet transform and CNN (NSCT-CNN) (Wang et al., 2021a), a Cross Encoder Fusion (CEFusion) (Zhu et al., 2022), FDGNet (Zhang et al., 2023b) and Joint Sparse Model with Coupled Dictionary (JSM-CD) (Zhang et al., 2023a) along with five metrics namely, Average Pixel Intensity (API) or mean (F ̅ ), Entropy (H), Average Gradient (AG), overall fusion efficiency (QAB/F) and information loss during fusion process (L AB/F ) (Goyal et al., 2023) to evaluate techniques subjectively and objectively.

Fusion Quality Comparison of Medical Images
Fused results on CT1-MRI1 images.Figure 5 displays the qualitative fusion findings of three pairs of CT1 and MRI1 images.The fusion results of the first batch of CT1-MR1 images from comparison techniques and our approach are shown in Figs.3(a-b1-10) displays the fused images of the second batch of CT1-MRI1 images on all approaches.The final set of sources, including CT1-MRI1 images and the fused images of all techniques are presented in Fig. 3(c1-10).Soft tissue structure is not well reproduced by MRPAN or EMFusion.The low brightness of results is caused by CT1 information loss in LPCNNR and CEFusion.Rich texture details are not obtained via FDGNet and CEFusion.Functional information on NSCT-CNN is absent.The fusion results of FDGNet and JSM-CD show distorted MRI image information.It is simple to observe visually that our algorithm preserves both structural and functional information (soft tissue, skull).This is evident when comparing the results of all approaches.The clearest details can be found in the fused images.This suggests that our technique produces fusion results with the highest level of image detail preservation.Fused results on other pairs of medical images.The fused images from the additional three medical image pairs are performed experimentally.Our approach was able to transfer more features from input images to the final fusion images by combining the analysis of Figs.3-4.By carefully observing the image pair results, this subjective result validates that the proposed fusion rule can preserve the maximum extent of source image information.

Objectives Evaluation for Medical Images
The mean value of the quantitative evaluation for all algorithms on medical images (Fig. 2) is tabulated in Table 1.Table 1 clearly shows that AG, entropy (H), API, Q AB/F and L AB/F are the highest in the case of the proposed method as compared to other competing methods.The higher AG values show that the results of the proposed method effectively preserve the functional and structural information present in the original images.The best Q AB/F results demonstrate the contrast-optimal nature of our approach.It illustrates how fused results are less prone to noise and have more texture and detail.The less L AB/F suggests the proposed method performance avoids distortion and is comparable to the standard images.Based on an analysis and observation of Table 1, it can be concluded that our method is capable of preserving both functional and structural details due to the ideal values for measurements.As a result, the subjective analysis and objective evaluation coincide with providing more proof that our approach produces the best results.

Further Objective Graphical Representations
The objective analysis of different image fusion techniques is presented in Table 1.The objective assessment metric values for 9 image sets are presented in Fig. 5. to further illustrate the efficiency of our strategy.When examining Fig. 5, it is clear that our approach performs best on all objective metrics such as AG, H, API  / and  / for every pair of images.These conclusions indicate that our method preserves better functional and structural details from the original images in the fused results.The proposed method of fused image contrast is cleaner and more consistent with visual perception when compared to the comparative methods.2, our solution outperforms other methods and is placed in first place requiring a less timeconsuming kernel set to enhance input images.By using a synthetic focusing degree criterion, the proposed solution greatly lowers the time cost as compared to other methods.Our approach outperforms other algorithms in the case of both qualitative and quantitative analysis but marginally improves in some cases.

Conclusion
In this study, a synthetic focusing degree criterion with a special kernel set is used for medical image fusion to achieve the best fusion performance.Firstly, the GCF is used to get the sharpest parts of the medical images by carrying out salient feature extraction.Then, we generate a synthetic FDC that combines the SF and LV of the image to obtain the coarse fusion maps.To generate optimized fusion maps, the course fusion maps are further processed using median and morphological filters.A weight fusion process is utilized to obtain fused images.The enhancement is then accomplished by adding a specific kernel set to the fused images.The proposed algorithm validates capability using nine pairs of CT-MRI medical images.
The proposed approach decreases computational complexity and execution time while improving diagnostic computing accuracy.Our method exhibits a major boost in competence when compared to other competing algorithms.It can be observed that the qualitative interpretation of all the fused images recovered through the proposed algorithm has superior visual quality.However, this method is not able to work for different types of medical images which is its limitations.Our method can be upgraded by using different types of filters which have been left for future research works.Furthermore, image fusion and the importance of this technique have huge prospects for improvement by proposing several image fusion algorithms in order to reduce noise and artifacts.

Table 1 :
Mean quantitative metrics of medical images (Fig.2) using different techniques (Red+ (1), violet + (2) and green + (3) are the first, second and third scores, respectively) Table 2 presents the mean time spent on nine pairs of 256×256 CT/MRI images utilizing Table 2: Average time consumption of all techniques for fusion of medical images (unit: s) proposed method in addition to seven state-of-the-art methods.Based on an intuitive observation of Table