This study presents a novel hybrid metaheuristic algorithm, Sine-Cosine Adaptive Teaching-Learning-Based Optimization (SCATLBO),designed to train Feed-Forward Neural Networks (FNNs) for mono and multi-modal medical image registration. SCATLBO combines the strengths of the Sine-Cosine Algorithm (SCA) for exploration with Teaching-Learning-Based Optimization (TLBO) for exploitation, achieving a balance that enhances the algorithm's capability to avoid local minima and improve convergence rates. Medical image registration, essential for accurate medical analysis, benefits from this hybrid approach as it aligns complex multi-modal images efectively. In this work, SCATLBO was applied to train FNNs on breast MRI images from the Cancer Genome Atlas Breast Invasive Carcinoma (TCGA-BRCA) dataset. The performance of SCATLBO is benchmarked against several well-known metaheuristic algorithms, including TLBO, Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Grey Wolf Optimizer (GWO), and Evolution Strategy (ES), with evaluations based on Mean Squared Error (MSE) for mono-modal and Mutual Information (MI) for multi-modal registration. Experimental results demonstrate that SCATLBO outperforms other techniques in terms of accuracy, convergence speed, and robustness, establishing it as a promising tool for neural network-based image registration tasks. This work contributes to the advancement of metaheuristic training approaches for FNNs, with potential applications in diverse medical imaging fields.
Image registration, which is very useful in medical applications, entails aligning various image files
inside a similar coordinate system to match imaging content. Comparing images captured from diferent
angles, at diferent times, or with diferent sensors or modalities [
Methods of training strategy can be classified into two stochastic and exact methods. Exact methods
are classical mathematical methods based on the gradient. The training algorithm most commonly
used is back-propagation, which relies on gradient descent techniques [
In this study, we explore a novel approach for training Feed-Forward Neural Networks (FNNs) using
a hybridized metaheuristic algorithm, combining Sine-Cosine Algorithm (SCA) [
We begin with the Methodology section(2), where we detail the phases of the SCATLBO algorithm, including the Teaching Phase (Exploitation) (2.1), where the model learns from the best solutions, and the Learning Phase (Exploration) (2.2), enhancing the algorithm’s robustness by promoting diverse learning strategies. We also introduce the Sine-Cosine Modification (SCA) technique (2.3) to improve exploration capabilities and avoid local minima.
The Feed-Forward Neural Network (FNN) framework (2.4) is explained, including the calculation of Mean Squared Error (MSE) (2.4.1) as a primary loss function for monomodal image registration and Mutual Information (MI) (2.5) for multimodal scenarios. This section also discusses the dataset used in this study (2.6) and how we configured parameters for the algorithm (2.7).
In the Result and Discussion section (3), we analyze the algorithm’s performance. We assess the statistical significance of our results using the Wilcoxon Signed-Rank Test (3.1) and make decisions based on multiple criteria through the TOPSIS method (3.2).
Finally, the Conclusion (4) highlights our main findings and suggests future research directions for optimizing FNN structures and tuning parameters in advanced applications.
The proposed methodology leverages the SCATLBO (Sine-Cosine Algorithm combined with TeachingLearning-Based Optimization) for training a FNN to enhance image registration accuracy. The workflow of proposed method is outlined in Figure 1. This process can be summarized as follows: 1. Read Input Image: The workflow starts by reading the input image, such as a DCE-MRI scan, that requires registration. 2. Preprocessing the Image: The input image undergoes preprocessing, which involves normalization, resizing, or other necessary transformations. This step ensures that the image data is consistent and free of noise, preparing it for efective processing by the neural network. 3. Randomly Initialize Weight FNN: The FNN model is initialized with random weights, creating a baseline model that can be iteratively refined. This initialization is essential for ensuring that the model starts from an unbiased point. 4. Apply SCATLBO Optimization: The core of the proposed methodology involves applying SCATLBO optimization to fine-tune the weights of the FNN. The SCATLBO algorithm enhances the optimization process by combining the exploration and exploitation capability. This hybrid approach allows the model to search the weight space more efectively, finding optimal weights that improve the accuracy and robustness of the registration. 5. Validation: After optimization, the model is evaluated through a validation process. The registered image produced by the model is assessed to determine if it meets specific accuracy criteria. 6. Optimized FNN Model: Once the model passes validation, the final output is an optimized FNN model capable of performing high-quality image registration. This optimized model is now ready for deployment in tasks requiring accurate and reliable for image registration.
This methodology outlines a systematic approach for developing an optimized FNN model through SCATLBO, which iteratively adjusts the model’s parameters to achieve improved accuracy in image registration. By combining adaptive mechanisms and hybrid optimization strategies, the SCATLBO-FNN model provides an efective solution for tasks requiring precise alignment of medical images, improving both performance and reliability in medical image analysis applications.
1. Read Input Image: The workflow starts by reading the input image, such as a DCE-MRI scan, that requires registration. 2. Preprocessing the Image: The input image undergoes preprocessing, which involves normalization, resizing, or other necessary transformations. This step ensures that the image data is consistent and free of noise, preparing it for efective processing by the neural network. 3. Randomly Initialize Weight FNN: The FNN model is initialized with random weights, creating a baseline model that can be iteratively refined. This initialization is essential for ensuring that the model starts from an unbiased point. 4. Apply SCATLBO Optimization: The core of the proposed methodology involves applying SCATLBO optimization to fine-tune the weights of the FNN. The SCATLBO algorithm enhances the optimization process by combining the exploration capability of the sine-cosine mechanism with the exploitation capability of TLBO. This hybrid approach allows the model to search the weight space more efectively, finding optimal weights that improve the accuracy and robustness of the registration. 5. Validation: After optimization, the model is evaluated through a validation process. The registered image produced by the model is assessed to determine if it meets specific accuracy criteria. 6. Optimized FNN Model: Once the model passes validation, the final output is an optimized FNN model capable of performing high-quality image registration. This optimized model is now ready for deployment in tasks requiring accurate and reliable image registration.
This methodology outlines a systematic approach for developing an optimized FNN model through SCATLBO, which iteratively adjusts the model’s parameters to achieve improved accuracy in image registration. By combining adaptive mechanisms and hybrid optimization strategies, the SCATLBO-FNN model provides an efective solution for tasks requiring precise alignment of medical images, improving both performance and reliability in medical image analysis applications.
In the TLBO algorithm, the Teacher phase adjusts the network parameters (such as weights and biases) based on the best-performing solution in the population. This phase can be seen as an exploitation phase, where the best solution tries to bring other solutions closer to its performance. The parameter update equation for the teacher phase is given by: new = old + × (best − × mean) (1) Where: 1. new and old are the updated and current weights. 2. best is the weight of the best-performing solution (teacher). 3. mean is the mean weight of the population. 4. is a random number between 0 and 1.
5. is a teaching factor, usually chosen as 1 or 2.
In the Learning phase, individuals learn from each other by updating their weights based on the diference between two randomly chosen individuals:
new = old + × ( − ) and be the weights of two randomly selected solutions from the population, and be a random number.
The sine-cosine modification introduces a non-linear exploration mechanism that enhances global search capability. The SCA operator is incorporated as follows: new = {︃old + × sin( ) × | best − old|
old + × cos( ) × | best − old|
Where is an angle that modulates exploration using sine or cosine waves, and is a random number
that controls the intensity of exploration. The SCA phase helps balance exploration and exploitation by
using these sine and cosine functions, making the search space more diverse and preventing the network
from being trapped in local minima. The Feedforward Neural Network (FNN) is trained to minimize a
registration loss, such as Mean Squared Error (MSE)[
A transformation is applied to the output in order to align with .
A feed-forward neural network (FNN) is the most fundamental type of artificial neural network, characterized by a layer-structured architecture where connections between neurons do not form cycles. In FNNs, neurons are organized into three layers: the input layer, the hidden layer, and the output layer. Data flows unidirectionally from one layer to the next, with each neuron in a layer connected to every neuron in the subsequent layer, ensuring there are no backward connections, loops, or cycles.
The output signals generated by artificial neurons are determined by applying an activation function, frequently called a transfer function, to the weighted linear combination () + of inputs. By introducing non-linearity through these activation functions, feedforward neural networks gain the ability to learn intricate, non-trivial patterns in vast amounts of data. Figure 2 depicts a basic schematic of a simple feed-forward network, demonstrating how information flows through it in one direction from input to output. Additionally, Figure 3 displays common activation functions along with their corresponding graphs, which are integral to comprehending how these mathematical operators mold a
Rotation, translation, scaling, and other transformation parameters are represented by the vector = [ 1, 2, . . . , ].
Using the formula = [ 1, 2, . . . , ]
= ℱ (; , ) network’s behavior during the learning process. The interplay between weights, inputs, and activation functions unlocks neural networks potential to model complex patterns beyond the capabilities of shallow architectures like logistic regression.
Input Layer
Hidden Layer
Output Layer (5) (6) 2.4.1. Mean Squared Error (MSE) The loss function measures the diference in intensity between and the transformed ′ : where ℱ (; , ) represents the FNN model with weights and biases .
MSE =
1 ∑︁ ( () − ′ ())2 =1 min (ℱ (; , )) ,
For monomodal registration, we used Mean Squared Error (MSE), where () and ′ () are the intensities at corresponding points in the fixed and moving images.
The goal of training is to minimize this loss function:
MI measures the shared information between the two images: MI = − ∑︁ ∑︁ ( (), ′ ( )) log =1 =1
( (), ′ ( )) ( ()) · (′ ( )) (7) Where • ( ()) is the marginal probability of the intensity () in the fixed image , • (′ ( )) is the marginal probability of the intensity ′ ( ) in the transformed moving image ′ , • ( (), ′ ( )) is the joint probability of the intensities () and ′ ( ) occurring together. For multi-modal registration, we used Mutual Information (MI).
The Cancer Genome Atlas Breast Invasive Carcinoma (TCGA-BRCA) dataset, which is accessible via
the Cancer Imaging Archive (TCIA), provided 40 pairs of 2D T2-weighted DCE-MRI slices in total
[
In the experiment, we used SCATLBO, TLBO, GWO, PSO, ACO, and ES algorithms to test their performance. In the TLBO algorithm, the population size is set to 25 potential solutions in each iteration. WEPMax (Weighted Exploitation Probability Maximum) controls the maximum exploitation probability, with a value of 1 indicating the highest level of exploitation. WEPMin (Weighted Exploitation Probability Minimum) is set to the minimum level of exploitation.
In PSO, the population size of 25 particles remains constant across iterations, much like TLBO. The velocity of each particle is influenced by its previous velocity through the inertia weight . Additionally, particles are cognitively drawn towards their personal best location via the cognitive coeficient 1.
In GWO, the number of search agents is set to 40, and the maximum number of iterations is 50. In ES, the population size ( ) is set to 40, and the number of neurons ( ) is set to 1.
In ACO, the initial pheromone level ( ) is set to a very small value of 1 × 10− 6. The pheromone update constant () is 20 while the evaporation constant () is 1. Pheromone decays globally at 0.9 and locally at 0.5 per iteration. Solutions are found based on pheromone strength ( ) of 1 and visibility ( ) of 5. Additionally, particles are socially attracted towards the global best location through 2.
The results demonstrate that the SCATLBO algorithm exhibits strong exploration capabilities, which significantly contributes to its efectiveness in training FNNs. SCATLBO’s opposition-based learning mechanism enhances its exploration by generating diverse solutions, allowing the algorithm to identify promising new areas in the search space while avoiding local minima. This balance of exploration and exploitation is essential for successful stochastic optimization, as it enables SCATLBO to navigate the search space efectively and converge on optimal solutions without being trapped in suboptimal regions.
Algorithm 1 SCATLBO (Sine-Cosine Adaptive Teaching-Learning-Based Optimization)
1: Input: Objective function ( ), population size , dimension , max iterations max
2: Initialize: Population = {1, 2, . . . , } randomly.
3: Evaluate fitness () for all individuals in the population.
4: for = 1 to max do
5: Teacher Phase (Exploitation):
6: Identify the teacher best as the solution with the best fitness.
7: Compute the mean of the population mean.
8: for each do
9: Generate a random number ∈ [
new = old + × (best − × mean) Apply SCA modification: new = new + × sin( ) × | best − new| new = new + × cos( ) × | best − new| where ∈ [0, 2 ] is a random angle.
end for Learning Phase (Exploration): for each do
Select two random individuals and ( ̸= ).
Generate a random number ∈ [
Update : Apply SCA modification:
new = old + × ( − ) new = new + × sin( ) × | − | new = new + × cos( ) × | − | 12: 13: 14: 15: 16: 17: 18: 19: or or 20: end for 21: Evaluate fitness () for all updated solutions. 22: Replace with new if (new) < (). 23: Check stopping criteria (e.g., maximum iterations or desired accuracy). 24: end for 25: Output: Best solution best and its fitness (best).
Tables 1 and 2 compare SCATLBO-FNN with other well-known metaheuristic algorithms TeachingLearning-Based Optimization (TLBO), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Grey Wolf Optimizer (GWO), and Evolution Strategy (ES)-using two key performance metrics: Mean Squared Error (MSE) for mono-modal image registration and Mutual Information (MI) for multimodal registration. These metrics are critical for assessing the accuracy and stability of the registration process, with lower MSE indicating better alignment for mono-modal images and higher MI signifying greater statistical dependency in multi-modal cases.
From the tables, it is evident that SCATLBO-FNN achieves the lowest average error (AVG) and highest accuracy in both mono-modal (Table 1) and multi-modal (Table 2) registrations, indicating superior alignment performance and consistent accuracy. Additionally, SCATLBO demonstrates a competitive execution time compared to other algorithms, balancing performance eficiency with computational cost. The low standard deviation (STD) values for SCATLBO also reflect its stability, showing less variation across diferent trials, which is crucial in achieving reliable results in medical image registration.
Figure 5 illustrates the convergence behavior of SCATLBO-FNN in both mono-modal and multi-modal scenarios. The convergence graph shows that SCATLBO quickly minimizes the error, highlighting its strong initial exploration phase. As the iterations proceed, the algorithm stabilizes, indicating efective exploitation of promising solutions. This stability in convergence confirms that SCATLBO is less likely to be trapped in local optima, allowing it to achieve optimal or near-optimal solutions across diferent registration tasks.
Overall, these comparative metrics underscore the robustness of SCATLBO-FNN. The hybrid approach, which combines SCA’s exploration with TLBO’s exploitation, makes SCATLBO a powerful and eficient tool for training FNNs in complex medical imaging tasks. This combination enables SCATLBO to outperform other metaheuristic algorithms in terms of accuracy, stability, and convergence speed, establishing it as a highly efective optimization technique for neural network-based image registration.
The Wilcoxon Signed-Rank Test [
Our results, shown in both mono-modality (Table 3) and multi-modality (Table 4) evaluations, yielded a p-value of 0.002, which is well below the 0.05 threshold. This confirms that SCATLBO-FNN outperforms other methods with statistical significance, validating its efectiveness in FNN optimization for image registration tasks.
Furthermore, Table 5 provides a comparative performance ranking of the algorithms based on their overall eficiency and accuracy in training Feed-Forward Neural Networks (FNNs). SCATLBO-FNN achieved the highest rank, indicating its superior performance across both mono-modal and multi-modal registration tasks. This advantage is attributed to SCATLBO’s balanced exploitation and exploration phases, achieved by combining the strengths of SCA for exploration and TLBO for exploitation.
In contrast, other algorithms such as TLBO, PSO, ACO, GWO, and ES ranked lower due to slower convergence or a tendency to become trapped in local minima. The rankings underscore the benefits of SCATLBO’s hybrid approach, where the integration of SCA and TLBO enables faster and more accurate convergence compared to standalone metaheuristics. This comparative ranking, together with the Wilcoxon test results, supports SCATLBO as a robust and efective choice for FNN optimization in medical image registration, ofering greater accuracy and consistency than other established methods.
The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a widely used
multicriteria decision-making (MCDM) method that facilitates the ranking and selection of optimal solutions
based on multiple evaluation standards [
In this study, TOPSIS was employed to evaluate and rank SCATLBO against other metaheuristic algorithms based on key performance metrics such as accuracy, convergence speed, and error minimization. By taking both ideal and worst-case scenarios into account, TOPSIS provides an objective framework to compare SCATLBO?s efectiveness in optimizing Feed-Forward Neural Networks (FNNs) for medical image registration tasks. This robust decision-making approach ensures that SCATLBOs performance is assessed comprehensively, validating it as a highly efective algorithm for complex, multi-modal registration problems.
In this work, we introduced SCATLBO, a hybrid metaheuristic combining the Sine-Cosine Algorithm (SCA) and Teaching-Learning-Based Optimization (TLBO), to train Feed-Forward Neural Networks (FNNs) for medical image registration. SCATLBO was evaluated on the TCGA-BRCA dataset and compared with five established algorithms, demonstrating superior accuracy, faster convergence, and robustness against local minima. Its balanced exploration-exploitation strategy and opposition-based learning contribute to its high performance in both mono-modal and multi-modal registration tasks.
Future Work: SCATLBO could be extended to other neural architectures, such as CNNs, to handle more complex imaging tasks. Additionally, future studies could explore adaptive mechanisms for parameter tuning, as well as applications across diverse medical datasets to assess generalizability and robustness in various medical imaging contexts.
Thanks to the developers of ACM consolidated LaTeX styles https://github.com/borisveytsman/acmart and to the developers of Elsevier updated LATEX templates https://www.ctan.org/tex-archive/macros/ latex/contrib/els-cas-templates.
The author(s) have not employed any Generative AI tools.