LSTM GRFF-Net: hybrid long short-term memory-gated recurrent fractional fusion network for multimodal biometrics recognition

1 Introduction

Information security has received increasing attention in recent years due to advancement in science and technology. Once account numbers and passwords are stolen, impersonation becomes an easy way to replace traditional authentication methods. One of the most exciting security innovations of this century is biometrics. When compared to conventional identification methods, biometrics offers numerous benefits. For example, the technology is impervious to loss, theft, or replication (Wang et al., 2022). Technology that uses a person's physiological and biological features to identify them is known as biometrics. Systems constructed using these features are more reliable and accurate because of their uniqueness (Mustafa et al., 2020). The use of a person's face, fingerprints, finger veins, or other human characteristics to authenticate and recognize them is known as biometric identification (Huang et al., 2023). Modern commercial products offer a varied range of automated biometric recognition concerning anatomical human characteristics. These consist of applications for e-commerce, consumer electronics, banking, immigration, and e-governance (Haider et al., 2023). Many industries, including healthcare organizations, social network purposes, entertainment and gaming methods, cloud computing, homeland security, and big data are currently using biometrics. Furthermore, modalities, such as fingerprint or face biometrics are used by billions of smartphone users to unlock their devices (Haq et al., 2026). A biometric identification system primarily consists of four processes including individual identification, feature value comparison, image acquisition, and image processing feature extraction (Wang et al., 2022). The two types of biometric traits are characterized by extrinsic and intrinsic traits. While intrinsic qualities are unaffected by external factors, extrinsic traits are obvious and vulnerable to external factors (Alay and Al-Baity, 2020).

There are two categories of biometric systems, such as single-modal biometric systems and multimodal biometric systems (Wang et al., 2022). A single biometric feature used to recognize users is referred to as a single-modal biometric system. Meanwhile, the combination of more than two types of single biometric features to create a new feature for identification is known as multimodal biometric technology (Wang et al., 2022). Fusion at the feature and score levels is the foundation of the multimodal recognition system (Haq et al., 2026). A range of biometric sources are combined in the multi-biometric recognition system. Systems for multimodal biometric identification are more secure and more effective at recognizing patterns than unimodal ones (Byeon et al., 2024). When an individual cannot be authenticated because of noisy sensor data, problems with illumination, or susceptibility to impersonation attacks, the multimodal biometric system offers an alternative (Tomar and Singh, 2021). Increased accuracy, enhanced usability, increased resistance to spoofing attacks, and a reduction in false acceptance or rejection rates are some of the advantages of multimodal biometric fusion. Moreover, the process of fusion can provide a more reliable and extensive assessment of an individual's identity, thereby improving the authentication system's overall security (Vekariya et al., 2024). When the fusion representations hidden in the cross-modality and intramodality are fully displayed, many multimodal applications can achieve even higher performance. Multimodal authentication approaches use multiple modalities to extract features, such as fingerprints, retinas, and finger veins (Byeon et al., 2024). A promising method of identity recognition, multimodal biometric systems offer more authentication modes and increased security. Because of its exceptional accessibility in acquisition and ease of use, the multimodal finger biometrics technology received the most attention among them (Huang et al., 2023). Due to their uniqueness and invariance, fingerprints have emerged as a significant biometric feature (Mehdi Cherrat et al., 2020).

Multimodal finger recognition technology is widely used in e-commerce, healthcare, forensics and surveillance, military security systems, and other real-world applications because of the exceptional security and accuracy benefits of multimodal systems (Huang et al., 2023). The high information in the feature vectors makes feature-level fusion the optimal method for designing multimodal systems. Network and system security, knowledge science, and biomedical science are some fields where machine learning (ML) techniques are used (Safavipour et al., 2023). Deep learning (DL) algorithms serve as the foundation for a multimodal biometric identification system and the iris, finger vein, and face are exploited as bio modalities to identify people. Convolutional neural networks (CNNs) are the foundation of the system's architecture and are exploited for mining features and classifying images. Three CNN models were used, one each for the iris, face, and finger vein and the three models were combined to create the multimodal biometric identification system (Alay and Al-Baity, 2020). Learning high-level representations is an essential requirement for DL, which is an advanced branch of ML. In DL, the hierarchy of automatically learning features at various levels of representations can offer a comprehensive understanding of data, including text, image, and audio, without relying entirely on domain expertise and manually crafted features (Al-Waisy et al., 2018). The DL method is the foundation of a secure multimodal biometrics recognition framework. Transfer learning and CNNs have also been used in multimodal biometric recognition systems. These outcomes demonstrate the security, robustness, and dependability of the DL-based multimodal biometric recognition system (Haq et al., 2026). Real-world applications remain difficult with developing multimodal biometric systems that can accurately identify individuals while maintaining an acceptable level of system complexity (Al-Waisy et al., 2017).

Although numerous authentication mechanisms have been proposed, unimodal biometric systems remain vulnerable to noisy sensor acquisition, partial occlusion, environmental variations, spoofing attacks, and missing biometric samples. In practical authentication scenarios, reliance on a single biometric characteristic may result in increased false acceptance rate (FAR) and false rejection rate (FRR), thereby reducing system reliability. To overcome these limitations, multimodal biometric authentication integrates multiple complementary biometric traits, including fingerprint, finger vein, palmprint, finger knuckle, and iris. The fusion of these heterogeneous modalities enhances recognition robustness, improves resistance against spoofing, and provides more reliable authentication than conventional single-modal systems.

The primary objective of this study is to develop a robust multimodal biometric recognition framework, namely LSTM-GRFF-Net, that adaptively integrates heterogeneous biometric traits through hiking optimization algorithm (HOA)-based feature fusion and fractional-order recurrent learning to improve recognition accuracy while reducing FAR and FRR. At first, the finger vein, finger knuckle, palmprint, iris, and fingerprints are preprocessed using the Medav filter. After this, the finger vein image is passed to repeated line tracking, and complete local binary pattern (CLBP) and local Gabor XOR pattern (LGXP) features are mined from palmprint and finger knuckle images. In addition to this, iris template extraction and minutiae extraction are performed using the iris and fingerprint images. Following this, the pre-processed iris and fingerprint are normalized using linear interpolation and passed to feature fusion, while the mined features from finger vein, finger knuckle, and palmprint are subjected to feature fusion. Moreover, all the five biometrics are fused together by HOA. Finally, the recognition of multimodal biometrics is executed by LSTM-GRFF-Net, which is engineered by the integration of fractional calculus (FC), gated recurrent network (GRU), and long short-term memory (LSTM). Unlike existing multimodal biometric recognition approaches that employ conventional feature fusion or standalone recurrent models, the proposed architecture introduces a fractional-order fusion mechanism for integrating LSTM and GRU representations. This mechanism preserves long-range memory information and strengthens the interaction among heterogeneous biometric modalities, thereby improving discriminative capability and recognition performance.

Major contributions:

• Novel LSTM-GRFF-Net Architecture: a novel LSTM-GRFF-Net is proposed for multimodal biometric recognition. Unlike conventional hybrid architectures that directly combine recurrent networks, the proposed framework integrates LSTM and GRU representations through a fractional-calculus-based fusion mechanism.
• Fractional-Order Fusion Strategy: an FC layer is introduced to aggregate the outputs of LSTM and GRU branches. The FC layer preserves long-range feature dependencies and captures complex cross-modal relationships among finger vein, fingerprint, palmprint, iris, and finger-knuckle modalities.
• Complementary Feature Learning: the LSTM branch learns long-term discriminative dependencies from fused biometric representations, while the GRU branch extracts compact feature representations with lower computational complexity. Their complementary information is jointly utilized for robust recognition.
• Enhanced Multimodal Recognition Performance: the proposed architecture effectively exploits heterogeneous biometric information and achieves superior recognition accuracy compared with existing multimodal biometric recognition methods.

The remainder of this paper is organized as follows. Section 2 reviews the related literature and identifies the research challenges. Section 3 presents the proposed LSTM-GRFF-Net framework. Section 4 discusses the experimental results and comparative analysis. Finally, Section 5 concludes the paper and outlines future research directions.

2 Motivation

Every biometric modality has a unique set of advantages and disadvantages. While fingerprints are a common and reliable biometric, they can be impacted by damaged or low-quality fingerprints. Meanwhile, iris recognition is very accurate, but more complex imaging may be needed. However, it is much more difficult for attackers to simultaneously forge multiple biometric traits when combined with iris or finger vein recognition. As a result, this study introduces the effective LSTM-GRFF-Net technique for multimodal biometric recognition.

2.1 Literature survey

Wang et al. (2022) devised a CNN for identifying multimodal biometrics. This approach avoided overfitting and offered good classification performance and network computation. Unfortunately, this technique was not currently compatible with mobile embedded terminals and was only available on computers with powerful graphics processing units (GPUs). Haider et al. (2023) established AlexNet for multimodal biometric identification. This approach provided optimum testing times and can be applied successfully in real-time applications. This system can be used by a person who has a hand or finger-related disability or injury. However, this method was limited because it relied on biometric modalities that were specific to the human hand and fingers. A Filtered Spatial and Temporal Multimodal Fingerprint and Finger Vein Network (FS-STMFPFV-Net) was introduced by Abdullahi et al. (2023) for a multimodal biometric fingerprint and finger-vein recognition. This method was more computationally friendly and lightweight. Still, this technique was unable to optimize the network while lowering the number of parameters and network size to increase the recognition network's application. Safavipour et al. (2023) devised a deep hybrid multimodal biometric recognition system for multimodal biometric recognition. This method produced the highest recognition precision and was the most stable. However, obtaining a large number of experimental face images was difficult due to the high cost and complex computations associated with this method.

For multimodal finger recognition, Huang et al. (2023) developed an attention-based encoder network. Redundancy among multimodal features was minimized by this method. Nevertheless, this approach was unable to jointly model human speech and gait, two non-picture forms of multimodal data. Byeon et al. (2024) established DenseNet169 for multimodal biometric fusion. This method effectively reduced the negative impact of single-modal outliers on recognition performance and eliminated the problem of low-quality or erroneous data. Nonetheless, there was no significant enhancement in the performance of fusion retrieval. Srivastava et al. (2022) introduced a neuro-fuzzy neural network for human identity validation. This approach was more resilient to noisy data, more flexible, and had lower error rates. The enormous complexity of this approach was its drawback. Vekariya et al. (2024) established Binary Chimp Optimized Adaptive Kernel Support Vector Machine (BCO-AKSVM) for multi-biometric fusion. The development of this method was simple, and it needed less computation time and computational power. Nevertheless, the incorporation of multi-biometric fusion to enhance performance was not demonstrated by this method.

Recent advances in multimodal biometric recognition have increasingly focused on deep learning-based feature fusion to improve authentication robustness and recognition accuracy. Singh et al. developed a Harris hawk optimized CLAHE and novel score-level fusion approach using lightweight CNNs for multimodal biometric recognition. This method improved the recognition performance through effective preprocessing and score-level fusion. However, its applicability was limited by the dependence on lightweight CNN-based feature extraction and fusion strategies (Singh et al., 2024). Alshardan et al. developed a CNN-based multimodal biometric identification framework by integrating fingerprint and finger vein modalities, demonstrating that feature fusion substantially improves recognition performance over unimodal systems (Alshardan et al., 2024). Chen et al. introduced a federated learning-based multimodal biometric recognition framework that enables collaborative model training while preserving user privacy, making it suitable for distributed biometric authentication environments (Chen et al., 2024). Recent studies have also investigated advanced feature fusion strategies for multimodal hand biometrics, showing that adaptive feature selection and deep representation learning significantly enhance recognition reliability and robustness (Artabaz and Sliman, 2025). These developments indicate that effective multimodal biometric systems require both discriminative feature extraction and adaptive fusion mechanisms. Nevertheless, most existing approaches employ fixed or conventional fusion strategies that do not explicitly optimize the contribution of heterogeneous biometric modalities (Almuwayziri et al., 2025). Motivated by this limitation, the proposed LSTM-GRFF-Net employs HOA-based adaptive feature fusion together with a fractional-order recurrent learning framework to improve multimodal biometric recognition performance.

2.2 Major challenges

The different multimodal biometrics recognition techniques face the following challenges:

• ➢ The spatial–temporal inter-frame dependence information was improved by the sequential complementary modules incorporated in the FS-STMFPFV-net (Abdullahi et al., 2023). Nevertheless, this did not consider the improved discriminative power required to produce precise and accurate recognition results.
• ➢ A fast and precise identification of intra-modal features was achieved in Huang et al. (2023) using an attention-based encoder network with fused similarity. However, this method was unable to extract the context from a series of biometric data.
• ➢ The overall recognition accuracy was improved by combining the Finger-Knuckle Print and Iris biometric modalities using a neuro-fuzzy classifier (Srivastava et al., 2022). To improve the biometric system's resilience, accuracy, and security, more biometric features were not included in this approach.
• ➢ High levels of information security in human biometric authentication were attained by the BCO-AKSVM (Vekariya et al., 2024). However, this model failed to ensure that the features are converted to a common range for improving the convergence and performance of the model.
• ➢ In biometric recognition, it was discovered that the conventional biometric DL features worked well. Hybrid multimodal biometric systems, which use fusion for combining multiple biometric sources and traits are currently unable to achieve higher security assurance and improved recognition accuracy. From Table 1, it can be observed that existing hybrid recurrent architectures mainly focus on combining recurrent learning units. However, they do not explicitly model long-range interactions among heterogeneous biometric modalities. The proposed LSTM-GRFF-Net addresses this limitation through a fractional-order fusion mechanism that enhances multimodal feature representation.

Table 1. Comparison of existing hybrid recognition models and proposed LSTM-GRFF-Net.

3 Proposed LSTM GRFF-Net for multimodal biometrics recognition

A biometric is basically a pattern recognition system, which is operated by collecting biometric data from an individual and by mining suitable features from the data. By employing multimodal biometric technology, the safety of identification and accuracy can be improved. Hence, an LSTM-GRFF-Net technique is formulated for recognizing multimodal biometrics. First, the images of finger knuckle, palmprints, finger veins, iris, and fingerprints are pre-processed by employing a Medav filter (Gupta and Roy, 2019) to eradicate the noise. After that, the repeated line tracking model (Veluchamy and Karlmarx, 2017) is exploited for identifying the finger veins, and CLBP (Luo et al., 2018) and LGXP (Saeed, 2021) features are mined from preprocessed finger knuckle and palmprint images, whereas iris template extraction and minutiae extraction (Das, 2020) are carried out on the pre-processed fingerprint and iris images. Here, the iris template extraction is performed by employing Daugman's rubber sheet model (Rana et al., 2019). Then, the mined features from fingerprint and iris are normalized and fed to feature fusion, while identified finger vein, LGXP, and CLBP features are directly passed to feature fusion. Here, the features are fused by HOA (Oladejo et al., 2024), and then the multimodal biometric recognition is executed by LSTM-GRFF-Net, which is formed by fusing FC (Bhaladhare and Jinwala, 2014), LSTM (Sagheer and Kotb, 2019; Surakhi et al., 2021), and GRU (Haidong et al., 2020). Figure 1 illustrates the general outline of LSTM GRFF-Net for multimodal biometrics recognition.

3.1 Image acquisition

Assume the biometric dataset Q contains the finger vein images for multimodal biometrics identification, and it is written as,

Q={Q1,Q2,…,Qa,…,Qu}(1)

Here, Q_*a* denotes the ath finger-vein image sample and u represents the total number of finger-vein images available in the database.

Likewise, the finger knuckle is procured from the dataset Ω, and it is formulated as,

Ω={Ω1,Ω2,…,Ωf,…,Ωp}(2)

where, Ω_*f* denotes the f^*th* finger-knuckle image and p represents the total number of finger-knuckle images in the database.

Consider the dataset F contains the fingerprint images, and it is written as

F={F1,F2,…,Fg,…,Fx}(3)

Here, F_*g* represents the g^*th* fingerprint image and x denotes the total number of fingerprint images in the dataset.

Additionally, the iris image is assumed from the database L, and it is modeled by the below equation.

L={L1,L2,…,Ly,…,Li}(4)

where, L_*y* denotes the y^*th* iris image and i represents the total number of iris images in the database.

Let us consider a database T contains palmprint images, and it is written as

T={T1,T2,…,Tc,…,To}(5)

Here, T_*c* denotes the c^*th* palmprint image and o represents the total number of palmprint images in the database.

3.2 Image pre-processing

To prepare raw images for ML tasks, image pre-processing is vital. For appropriate investigation and interpretation in applications, namely surveillance or medical imaging, the finest pre-processed images are essential. By employing accurate methods, the image's quality is improved, and the noise is eliminated. Moreover, pre-processing is more effective in classification as it eliminates inappropriate data or noise. Here, the image Q_*a* from the finger vein database is taken as input for pre-processing, which is done by exploiting the Medav filter (Gupta and Roy, 2019). This filter is formulated by fusing the median filter and mean filter. Moreover, the median filter effectively minimizes the noise but its complexity is undesirable, whereas the mean filter is employed for detecting the noise in the image, but it cannot eradicate highly tailored noise. Hence, the incorporation of these two models lessens the complexity, which further enhances the performance. Here, the average value ℏ_*avg* of the mask input is connected to the pixel value once its average is calculated. When the value is high, the median value ℏ_*med* is used to replace the pixel otherwise original value is utilized. Here, V₁ implies the pre-processed finger vein image.

Similarly, images of finger knuckle Ω_*f*, fingerprint F_*g*, iris L_*y*, and palmprint T_*c* from biometric datasets are fed as input to image pre-processing. Here, the images are pre-processed finger vein V₁ using the Median filter, and the obtained finger-knuckle, fingerprint, iris, and palmprint images are represented as V₂, V₃, V₄, and V₅, respectively.

3.3 Repeated line tracking (finger vein extraction)

Repeated line tracking (Veluchamy and Karlmarx, 2017) is employed for extracting the grid features from the pre-processed vein image V₁. The pixel in the original image is considered the primary point of the line-tracking process. Here, the present tracking point in an image is signified as the existing pixel location, and this point is stimulated from pixel to pixel in the dark line direction. Here, the intensity of the pixel (r, b) is specified asN(r, b), ℓ_I denotes the set of pixels in locus space and the finger vein is symbolized as χ₁. Moreover, the finger vein is mined by the below process.

(i) Discovering the initial point to track the line: a set of finger vein image ℓ_I is utilized for determining the starting point (ra′,ba′) for line tracking, and here two random numbers are designated. Subsequently, the existing tracking point's initial point is stimulated from pixel by pixel in the direction of the image's dark line.

(ii) Movement of tracking point with dark line direction: the locus position table χ_*z* is initially obtained, and then the location of the tracking point for every pixel in an image is utilized for storing the values in this table. Furthermore, the set of adjacent pixels of the existing tracking point is assumed as χ_ε. Hence, the set of nearest pixels in the finger vein image is mentioned as χ_ε(r_*v*, b_*v*). Moreover, the moving attribute determines the nearest pixel's direction along the image's dark line.

(iii) Upgrade locus space table: the pixel's present tracking point is saved in the locus space table when the value is positive or above process is done repeatedly. The finger vein's current tracking point χ_ε(r_*v*, b_*v*) is processed by the aforementioned step. The updation of the locus table is performed a number of times every pixel turns into the current tracking point. Hence, the locus table χ₁(r, b) of the finger vein is attained.

(iv) Obtain the fingerprint: the highest amount of times the pixels formed as the existing tracking point in the repeated line tracking process χ_ε(r_*v*, b_*v*) is obtained from the locus space table. Hence, the prints of finger veins are attained by high values of χf′(r,b). The mined finger vein is mentioned as ξ₁.

3.4 CLBP feature from finger knuckle image

CLBP (Luo et al., 2018) is exploited for evaluating the local differences of center gray level (ζ), sign (γ), and magnitude (μ). Moreover, CLBP includes three features, including Scope, CLBP_μ, and CLBP_γ. Furthermore, the pre-processed finger knuckle V₂ is taken as input. Let H denote the number of neighboring pixels considered around the center pixel, γ_*H* represents the sign information of the H^*th* neighboring pixel, τ_*H* denotes the magnitude information, and R indicates the threshold value used in CLBP encoding.

To encode the sign data of local differences CLBP_γ is exploited, and this feature is similar to local binary pattern (LBP). The expression of CLBP for evaluating sign is written as

CLBPk,w=∑H=0H-1ρ(γH,0)2H(6)

Here, γ_*H* represents the sign, and H exemplifies adjacent pixels.

In order to code the magnitude data of local differences, CLBP_μ is exploited, and it is represented as

CLBPk,w=∑H=0H−1ρ(τH,R)2H,ρ(A,R)={1,A≥R0,A<R(7)

where, τ_*H* characterizes the magnitude.

CLBP_ζ is exploited for encoding the data of the original center gray value, and it is expressed as

CLBPk,w=ρ(wR,Rh),ρ(A,R)={1,A≥R0,A<R(8)

Here, the values of k specifies the number of neighboring pixels, w specifies the neighborhood radius, the average gray-level value of the local neighborhood is mentioned as R_*h*, the threshold value is implied as R, and the extracted CLBP feature vector as ξ₂.

3.5 Minutiae extraction-fingerprint

The pre-processed fingerprint image V₃ is fed as input to minutiae detection (Das, 2020), here the minutia points are recognized in the ridge-improved images. It is exploited in fingerprint matching for identifying the minutiae points in fingerprint images. The fingerprint's minutiae are referred to the points where the ridge lines end or split. Moreover, a Gray-scale Hit-Or-Miss Transformation (GHMT) is used for recognizing the minutiae, Further, GHMT is introduced by the inclusion of gray-scale erosion in the binary HMT model, which makes it accurate for gray-scale images. Here, the GHMT is improved by the concept of template matching, and it is specified below.

Sn⊗(qr′,qy′)=[min2ω1∈qr′(Sn+ω1)]-[max2ω2∈qy′(Sn-ω2)](9)

where, the foreground structuring element is exemplified as qr′, gray-scale fingerprint image is typified as S_*n*, background structuring element is denoted as qy′, second maximum and minimum values of gray-level substitution of dilation operation and binary erosion are symbolized as max² and min², pixels in the background and foreground structuring element are characterized as ω₂ and ω₁.

To detect the minutiae, GHMT employs 16 pre-defined and oriented templates. The templates consisting of ridge lines with valley and background set signifies the foreground area includes bifurcations of the ridges in the fingerprint. These templates do not have the capability to identify the endpoint, but they are effective in identifying the bifurcations. Moreover, the inverted images are considered for identifying the endpoints, and it is designated as

δ∧(U,Y)=Pixν−δ(U,Y)(10)

wherein, δ∧(U,Y) and δ(U, Y) implies the pixel intensity of the inverted and original images at (U, Y), and pixel intensities maximum value in the original image is signified as Pix_ν. Moreover, the GHMT is exploited to detect the minutiae on both the original and inverted images. From all templates, overall 16 filtered outcomes are produced, one for each inverted and original image, which is designated as

ϑorgb′=V3⊗(qr′ϕb′,qy′ϕb′)whereb′∈{1,2,…,16}(11)

ϑinvb′=V3inv⊗(qr′ϕb′,qy′ϕb′)whereb′∈{1,2,…,16}(12)

Here, the orientation of the template is mentioned as ϕ^*b*′, outcomes attained from the filtering of inverted and original images are specified as ϑinvb′ and ϑorgb′, the inverted pre-processed fingerprint image is indicated as V₃inv.

By identifying the maximum values of all pixels amongst the filtering outcomes, the minutiae points are identified, and pixel value which exceeds the threshold is designated as minutiae, and it is modeled as

ξ3=ξ3⋃{(U,Y)}ifmax1≤b′≤16[ϑori/invb′(U,V)]>α(13)

where, the threshold value used for minutiae detection is denoted as α, the extracted minutiae feature set is implied as ξ₃, and ϑori/invb′(U,Y) represents pixel intensity at location (U, Y) of the ^*b*′*th* outcome of the filtered inverted or original image.

3.6 Template extraction—Iris

The pre-processed iris image V₄ is considered as input for extracting the iris template, which is performed by Daugman's rubber sheet method (Rana et al., 2019). The most widespread approach for iris normalization is Daugman's rubber-sheet technique, which changes the circular iris area into a fixed-sized rectangular block. This technique is used for transforming all pixels in a circular iris into a corresponding location on polar axes (C′, φ). Here, the rotated angle at equivalent radius is indicated as φ, and radial distance is typified as C′. Moreover, the angular resolution epitomizes the quantity of data points in the radial direction, while the radial resolution designates the amount of radial lines formed near the iris region.

E[m(C′,φ),j(C′,φ)]→E(C′,φ)(14)

Moreover, the iris region is transformed into a two-dimensional array, where the angular and radial resolution is characterized by horizontal and vertical dimensions. Here, (C′, φ) and (m, j) mentions normalized polar coordinate system and Cartesian polar coordinates, E(m, j) corresponds to the mapped iris area. Furthermore, the extracted iris template is represented as ξ₄.

3.7 LGXP feature from Palmprint image

The LGXP feature is mined by considering from preprocessed palmprint image V₅ as an input. LGXP (Saeed, 2021) determines the Gabor phases, and they are quantized into various code ranges regarding the phase range. Moreover, in order to quantize the accumulated Gabors, behavioral techniques are employed, which are formulated as

LGXPZB=L(λZ,(Pκ,Jκ))⊗L(λZ,(PB,JB)),B=1,2,…,g′(15)

where, the nearest pixel is represented as B,λ designates the Gabor phase orientation, the XOR function is signified as ⊗, Gabor kernels direction is symbolized as Z, the central pixel is characterized as κ, local pattern about the central and nearest pixel local Gabor pattern is represented as LGXPZB(Pκ,Jκ), the quantity of nearest pixels is specified as g′, extracted LGXP feature vector is denoted as ξ₅, L(λ_*Z*(P, J)) typifies the quantization function of the Gabor phase, and L mentions the quantization which estimates the quantized code.

3.8 Feature normalization

Feature normalization includes mapping and normalizing coordinates of mined features and scaling feature values to a standard range. Moreover, linear interpolation is utilized, which maps the feature value linearly among the known points. Here, linear interpolation is employed for scaling the features to a specific range, and it is also beneficial in normalizing the features, and thus it can provide better performance. Moreover, the extracted minutiae ξ₃ and iris template ξ₄ is normalized. Here, the normalized minutiae and iris template are indicated as ς₁ and ς₂, which is then subjected to feature fusion.

3.9 Feature fusion

In the feature fusion process, the extracted finger vein ξ₁, CLBP ξ₂, and LGXP ξ₅, and then normalized minutiae ς₁ and iris template ς₂ are fed as input. Here, the fusion process integrates all the features, which is done by utilizing HOA (Oladejo et al., 2024).

Feature-level fusion is adopted in the proposed framework because it preserves the complete discriminative information extracted from each biometric modality before the classification stage. Unlike score-level or decision-level fusion, feature-level fusion enables the learning model to exploit the intrinsic relationships among heterogeneous biometric traits, resulting in richer biometric representations. The extracted finger vein, fingerprint, finger knuckle, palmprint, and iris features possess complementary characteristics. Fingerprints mainly provide ridge-based minutiae information, finger veins encode internal vascular structures that are highly resistant to spoofing attacks, finger knuckle and palmprint features represent texture-based patterns, while iris templates provide highly distinctive anatomical information. Integrating these heterogeneous features allows the proposed system to compensate for the limitations of individual modalities and significantly improves recognition robustness under noisy or partially degraded biometric samples.

Moreover, the integration is done based on the below equation.

Gp′,w′=1ϖ∑c′=1ϖξp′,w′c′*βc′(16)

Here, the image type biometric modality index is specified as c′, ϖ symbolizes the size of the normalized feature, feature dimensions are exemplified as p′ × w′, the weighted coefficient is typified as βc′ which is identified in using the HOA, and the input feature vector corresponding to the c' ^th biometric modality is symbolized as ξp′,w′c′.

Instead of assigning equal importance to every biometric modality, adaptive weighting is performed using HOA. Since different biometric traits contribute unequally depending on image quality and discriminative capability, fixed-weight fusion may introduce redundant or less informative features into the final representation. HOA searches for an optimal set of fusion coefficients that maximizes recognition accuracy while minimizing FAR and FRR. During optimization, each candidate solution represents a weight vector associated with the five biometric modalities, and the search process iteratively updates these weights until the optimal feature combination is obtained. Consequently, the fused feature vector contains more discriminative information and suppresses redundant modality contributions.

Moreover, the overall feature vector M obtained from fused features is formulated by the below expression.

M={M1,M2}(17)

Here, M₁ = {ξ₁, ξ₂, ξ₅}, where extracted CLBP, LGXP, and identified finger vein are fused together, Moreover, M₂ = {ξ₃, ξ₄}, where extracted minutiae, and iris templates are combined.

The optimized fused feature vector serves as the input to the proposed LSTM-GRFF-Net. Since the sequential learning model receives a compact yet highly discriminative multimodal representation instead of independent modality features, both the LSTM and GRU branches can effectively capture long-term inter-modal dependencies. This reduces feature redundancy, accelerates convergence, and improves recognition performance compared with direct feature concatenation or equal-weight fusion strategies.

3.9.1 Feature fusion using HOA

The features are fused by employing a HOA approach. HOA (Oladejo et al., 2024) is considered a global optimization technique, which employs the search space of optimization issues while exploiting the hiker's experience in the traversing of mountains and trails. Moreover, Tobler's Hiking function is utilized for estimating the hiker's new location after a determined period of time, which is done based on the initial location of the hiker. After evaluating each hiker's fitness, the most appropriate hiker is regarded as the lead hiker. Further, HOA is more robust and it has fast convergence with no computational time. In addition to this, the location of the lead hiker is re-evaluated in each iteration to ensure the suitable hiker at all instances becomes the lead hiker. Here, the updated location T′q′,h′+1 of the hiker q′ is represented by the below equation.

T′q′,h′+1=T′q′,h′+Xq′,h′(18)

where, q′ designates hiker, T′q′,h′ mentions the location of the hiker, iteration is denoted as h′, and X implies the current velocity of ^*q*′*th* hiker.

Fitness function: this fitness function is exploited for evaluating the precise solution based on Equation 18. Moreover, accuracy is regarded as the fitness parameter, and it is represented as

F′=V′1+V′2V′1+V′2+V′3+V′4(19)

Here, F′ implies accuracy, V′4 and V′2 typify false negative and true negative, V′3 and V′1 symbolize false positive and true positive, respectively.

3.9.2 HOA parameter settings and optimization strategy

The HOA algorithm was employed to determine the optimal fusion weights for multimodal feature integration. The search space of each fusion weight was restricted to the interval [0,1]. The population size was fixed at 30 hikers, while the maximum number of iterations was set to 100.

The optimization objective was to maximize recognition accuracy while simultaneously minimizing FAR and FRR. During each iteration, candidate fusion weights were updated according to the HOA position update mechanism.

The optimization process was terminated when either the maximum iteration count was reached or when the improvement in fitness value remained below 10–6 for 10 consecutive iterations.

To evaluate the robustness of HOA, sensitivity analysis was performed by varying population size and iteration count. The obtained results indicated stable performance across a wide range of parameter settings.

3.9.3 Justification of HOA-based feature fusion

The proposed framework employs HOA for feature fusion because multimodal biometric traits contribute differently to the recognition process. Conventional fusion methods, such as direct concatenation or equal-weight averaging, assume identical importance for all modalities and therefore cannot effectively suppress redundant or low-quality feature components. Such approaches often increase feature dimensionality and reduce classification efficiency.

The HOA algorithm addresses this limitation by learning adaptive fusion weights according to the discriminative capability of each modality. During optimization, candidate weight vectors are evaluated using the recognition accuracy obtained from the fused feature representation. The optimization process simultaneously maximizes recognition performance while reducing FAR and FRR. Consequently, highly informative modalities receive larger weights, whereas less discriminative modalities contribute proportionally less to the final feature vector.

This adaptive optimization produces a compact and robust multimodal representation, which enables the subsequent LSTM-GRFF-Net to learn richer inter-modal dependencies and improves the overall recognition capability of the proposed biometric system.

3.10 Multimodal biometric recognition

Multimodal biometric systems have been increased widely due to their ability in providing a more precise and secure authentication solution than unimodal systems. Nevertheless, the conventional fusion techniques are insufficient and the irrelevant multimodal features lead to ineffective processes. In order to solve this issue, an LSTM GRFF-Net approach has been presented for multimodal biometrics recognition in this study, where LSTM GRFF-Net is developed by the fusion of LSTM (Sagheer and Kotb, 2019; Surakhi et al., 2021), GRU (Haidong et al., 2020), and FC (Bhaladhare and Jinwala, 2014). Here, M₁ and M₂ from extracted and normalized features are fed as input to LSTM-GRFF-Net. Moreover, LSTM-GRFF-Net consists of three components, which include LSTM, GRU, and LSTM GRFF-Net layer. Initially, the multiplication of the fused vector M₁ with weight s₁ is performed and then the resulting output is normalized. Simultaneously, the feature vector M₁ is fed to LSTM and the resultant outcome is multiplied with normalized output ∑M₁×s₁ to obtain the output K₁. Alternatively, the feature vector M₂ is given to GRU and the output obtained is multiplied by a weight s₂ and then multiplied with K₁to produce the outcome K₂. At last, the outcomes K₁ and K₂ are combined using FC (Bhaladhare and Jinwala, 2014) to produce the final output K₃ in the LSTM-GRFF-Net layer. Figure 2 represents the schematic view of LSTM GRFF-Net for multimodal biometrics recognition.

3.10.1 LSTM model

LSTM (Sagheer and Kotb, 2019; Surakhi et al., 2021) is considered as a well-developed recurrent neural network (RNN), and it is employed for enhancing the overall performance in an efficient way. LSTM is formulated to address the RNN's gradient dissipation problem. Moreover, it is also employed to implement constant error flows through constant error carousels in precise multiplicative units for lowering the gradients in the network. Moreover, the non-linear units are exploited for learning the process of closing and opening the gates for regulating the constant error flow. Subsequently, this approach stimulates the existing RNN methods for estimating long-term information with significant interruptions. Here, the feature vector M₁ is taken as input for LSTM.

Furthermore, the cell state, which resembles a conveyor belt is regarded as the major module of the LSTM structure. Additionally, data from the cell state, which is strongly managed by the structures termed as gates, can be added or removed, which runs straight down the overall chain. At the time d, the hidden state C(d−1) and input M₁ from before time is fed to LSTM. Further, the hidden state (C_*d*) is designated by the below process.

• ➢ The first phase of the LSTM determines which data should be eradicated from the cell state and this decision is established by utilizing the forget gate v′d, and the output is written as

v′d=O(M1L′v′+Cd-1Q′v′+j′v′)(20)

• ➢ The second stage determines which data is stored in the memory cell, and this stage includes two-fold. Initially, the input gate (n′d) determines the value needed to be updated, and then a tanh layer is utilized to create a vector of new candidate values W~d′. Here, the expression of two-fold is given below.

n′d=O(M1L′n′+Cd-1Q′n′+j′n′)(21)

T~d=tanh(M1L′t′+Cd-1Q′t′+j′t′)(22)

Here, the activation function is mentioned as O.

• ➢ The former cell state W′d-1 is then updated to the new cell T_*l*, which is articulated by the below equation.

W′d=W′d-1⊗v′d⊕[O(M1L′n′+Cd-1Q′n′+j′n′)] ⊗[tanh(M1L′t′+Cd-1Q′t′+j′t′) ](23)

• ➢ The final outcome is determined, and the output gate (N′d) determines the portion of the cell state. Following this, the cell state is sent into a tanh layer and multiplied by the output gate.

N′d=O(M1L′N′+Cd-1Q′N′+j′N′)(24)

Cd=[O(M1L′N′+Cd-1Q′N′+j′N′)] ⊗tanh (W′d)(25)

Furthermore, the LSTM has three parameter groups including recurrent weights, like Q′v′,Q′n′,Q′N′,Q′t′, input weights, such as L′v′,L′n′,L′N′,L′t′, bias, like j′v′,j′n′,j′N′,j′t′, and the attained outcome from LSTM is represented as C_*d*.

The produced outcome is then multiplied by the normalized outcome s₁ to attain K₁, which is designated as,

K1=[O(M1L′N′+Cd-1Q′N′+j′N′)]⊗tanh(W′d)*∑M1s1(26)

Here, K₁ postulates the output of the LSTM, and Figure 3 depicts the architecture of RMDL.

3.10.2 GRU model

GRU (Haidong et al., 2020) is regarded as a simplified and improved form of RNN, and the input of GRU taken is the feature vector M₂. This technique is employed to reduce the time taken for training by enhancing the performance of the network. Moreover, GRU is employed in RNN to achieve a fast computation rate and low complexity. Further, the update and reset are the two gates that are present in the GRU. Here, the update gate R′υ is employed to ensure which portion of the candidate's hidden state U′υ should be updated in the current hidden stateP′υ. The rest gate A′υ is used to ensure which portion of the former hidden state P′υ-1 should be ignored. The expression of GRU is formulated as

R′υ=D′(J′e′R′M2υ+G′m′R′P′υ-1+B′R′)(27)

A′υ=D′(J′e′A′M2υ+G′m′A′P′υ-1+B′A′)(28)

U′υ=tanh (J′e′U′M2υ+G′m′U′(A′υ⊙P′υ-1)+B′U′)(29)

P′υ=(1-R′υ)⊙P′υ-1+R′υ⊙U′υ(30)

D′(υ)=1/(1+e-υ)(31)

tanh(υ)=(eυ-e-υ)/(eυ+e-υ)(32)

Here, hidden output is implied as P′υ, dot product operation is represented as ⊙, candidate state is specified as U′υ, Y′υ indicates the υ^*th* sample, activation function if reset and update gates are typified as D′, weight vectors among input layer and candidate gate, reset gate, and update gate are characterized as J′e′U′, J′e′A′, and J′e′R′, the activation function of candidate state is denoted as D′, corresponding biases are epitomized as B′U′,B′R′ and B′A′, weight vectors of cycle connections are mentioned as G′m′U′,G′m′R′, and G′m′A′, the outcome from GRU is symbolized as R′υ.

The obtained output in Equation 27 is multiplied by the weight s₂ and then with K₁ for producing the outcome K₂, and it is modeled as

K2=D′(J′e′R′M2υ+G′m′R′P′υ-1+B′R′)*s2 [O(M1L′N′+Cd-1Q′N′+j′N′)] ⊗tanh(W′d)∑M1s1(33)

where, the outcome attained is characterized as K₂, and the architecture of GRU is shown in Figure 4.

3.10.3 LSTM-GRFF-Net layer

In the LSTM-GRFF-Net layer, the attained outputs K₁ and K₂ are fused together by employing FC (Bhaladhare and Jinwala, 2014). FC (Bhaladhare and Jinwala, 2014) is employed to provide new perceptions, which makes it a prevailing and effective tool in several engineering applications. FC is used for improving the system performance leading to more robust and better scalability. Moreover, the general expression of FC (Bhaladhare and Jinwala, 2014) is expressed as

E(η′+1)=IE(η′)+12IE(η′-1)(34)

Here, E(η′+1)=K3,E(η′)=K1, and E(η′-1)=K2. Moreover, the outcome of the LSTM-GRFF-Net layer at ^η′*th* interval is formulated as

K3=IK1+12IK2(35)

By applying the particular values of K₁ and K₂ in Equation 35, the following equation is obtained

K3=I*([O(M1L′N′+Cd−1Q′N′+j′N′)]⊗tanh(W′d) ∑M1s1)+12I(D′(J′e′R′+G′m′R′P′υ−1+B′R′) s2[O(M1L′N′+Cd−1Q′N′+j′N′)]⊗tanh(W′d) *∑M1s1)(36)

Here, the outcome obtained from the LSTM-GRFF-Net layer is indicated as K₃, which is the final detected output. Table 2 shows the parameters of the LSTM and GRU models.

Table 2. Parameters of LSTM and GRU model architecture.

The proposed LSTM-GRFF-Net was implemented in MATLAB using the Adam optimizer. The LSTM and GRU networks employed 200 and 100 hidden units, respectively, as presented in Table 2. The integrated multimodal dataset was evaluated using a subject-disjoint 90:10 train-test split and five-fold cross-validation protocol. All experiments were conducted under identical settings to ensure fair comparison among competing methods.

3.10.4 Theoretical novelty and design rationale of LSTM-GRFF-Net

Although LSTM and GRU are well-established RNN architectures, the novelty of the proposed LSTM-GRFF-Net lies in the fractional-order integration mechanism introduced between these two complementary learning branches.

Existing hybrid LSTM-GRU models generally perform feature fusion through direct concatenation, weighted averaging, or attention mechanisms. Such approaches mainly capture first-order interactions among features and often fail to preserve long-range dependencies existing across heterogeneous biometric modalities.

In contrast, the proposed LSTM-GRFF-Net introduces an FC-based fusion layer that combines the outputs of LSTM and GRU using fractional-order memory modeling. The LSTM branch captures long-term sequential dependencies from the fused biometric feature space, whereas the GRU branch provides computationally efficient discriminative representations. The FC layer integrates both outputs while preserving historical feature information through fractional memory characteristics.

As a result, the proposed architecture is capable of modeling complex inter-modal and intra-modal biometric relationships among fingerprint, finger vein, palmprint, iris, and finger-knuckle features. This design enables improved feature representation and recognition performance compared with conventional hybrid recurrent architectures.

4 Results and discussion

The effectiveness of the LSTM-GRFF-Net utilized for multimodal biometric recognition is extensively investigated in this section. The FAR, FRR, accuracy, and TAR are among the parameters used to assess the LSTM-GRFF-Net. Moreover, the effectiveness of the technique is examined under various noise setups.

4.1 Experimental setup

The proposed LSTM-GRFF-Net for multimodal biometric recognition was implemented using MATLAB on a personal computer environment as represented in Table 3. To ensure a fair and unbiased evaluation, a subject-disjoint experimental protocol was adopted, where samples belonging to a particular subject were exclusively assigned either to the training set or the testing set, thereby preventing identity overlap between the two subsets.

Table 3. Experimental configuration of LSTM-GRFF-Net.

The integrated multimodal dataset was partitioned using a 90:10 train-test split strategy. Specifically, 90% of the subjects were utilized for training the model, while the remaining 10% were reserved for testing. To improve the statistical reliability of the results and minimize sampling bias, five-fold cross-validation was performed. In each fold, the dataset was randomly partitioned while preserving the subject-disjoint condition.

Furthermore, the experiments were repeated five independent times using different random partitions, and the final performance metrics were computed by averaging the obtained results. A fixed random seed value of 42 was employed during data partitioning and model initialization to ensure experimental reproducibility.

Experimental Reliability: to improve the reliability of the reported results, the proposed LSTM-GRFF-Net was evaluated using a subject-disjoint protocol, five-fold cross-validation, and five independent experimental runs. The reported performance metrics correspond to the average values obtained across all experimental runs, thereby reducing the influence of random data partitioning and model initialization. The use of a fixed random seed further ensures reproducibility and consistent evaluation under identical experimental conditions.

The adopted evaluation protocol was designed to minimize experimental bias by combining repeated executions with cross-validation under identical parameter settings. Consequently, the reported recognition accuracy, FAR, FRR, and TAR represent stable average performance rather than the outcome of a single experimental run.

4.2 Dataset description

Multimodal biometric recognition was achieved in this study using four publicly available biometric datasets, namely SDUMLA-HMT¹, IIT Delhi Finger Knuckle Database², CASIA Palmprint Database³, and Fingerprint Dataset⁴. These datasets were integrated to construct a virtual multimodal biometric framework comprising finger vein, fingerprint, iris, finger-knuckle, and palmprint modalities.

i) SDUMLA-HMT dataset: finger vein, fingerprint, and iris images are acquired from SDUMLA-HMT database (see text footnote 1, 4). This dataset comprises finger vein images of six fingers, iris images from the iris sensor, and fingerprint images collected with five various sensors. Moreover, the dataset was gathered during the summer of 2010 at Shandong University, Jinan, China. There are 106 subjects comprising 45 female and 61 male subjects aged between 17 and 31 years.

ii) IIT Delhi finger knuckle database: finger-knuckle images obtained from IIT Delhi students and staff in New Delhi, India comprise the IIT Delhi finger-knuckle image database (see footnote 2). The images were collected using a digital camera from the individuals on the IIT Delhi campus between August 2006 and June 2007. All of the images in the 158 users' database that is currently accessible are bitmap (^*.bmp) files. Every subject in the database is aged between 16 and 55. Each user has an integer identification/number assigned to them, and these 790 images have been numbered in a sequential manner. These images have a resolution of 80 by 100 pixels and are all available in bitmap format.

iii) CBSR dataset: 5,502 palmprint images from 312 subjects are included in the CASIA Palmprint Image Database (see footnote 3), also known as CASIA-Palmprint. Palmprint images is collected from both the right and left palms for each subject. Every palmprint image is in an 8-bit gray-level JPEG file.

4.2.1 Dataset integration and training/test construction

Since no publicly available dataset simultaneously contains finger vein, fingerprint, finger knuckle, iris, and palmprint modalities for the same subjects, a virtual multimodal dataset was constructed by integrating samples from multiple public biometric databases.

Initially, the SDUMLA-HMT database was utilized as the primary dataset because it provides finger vein, fingerprint, and iris modalities for the same individuals. Subsequently, finger-knuckle images from the IIT Delhi Finger Knuckle Database and palmprint images from the CASIA Palmprint Database were incorporated to create a five-modal biometric framework.

To ensure balanced multimodal representation, an equal number of subjects were selected from all datasets. The common subject count was limited according to the smallest available dataset after preprocessing. Subject identifiers were reassigned to generate unified class labels across all biometric modalities. For each virtual subject, one finger vein sample, one fingerprint sample, one iris sample, one finger-knuckle sample, and one palmprint sample were grouped to form a multimodal biometric profile.

Before feature extraction, all images were resized to a common resolution and preprocessed using the Medav filter. The extracted modality-specific features were then normalized and fused using the proposed HOA-based feature fusion framework.

For performance evaluation, the integrated multimodal dataset was divided into training and testing subsets using a stratified split strategy. Specifically, 90% of the samples were utilized for training and 10% were reserved for testing. To reduce sampling bias and improve robustness, the experiments were repeated using different train-test partitions and the average performance was reported.

For multimodal recognition experiments, the common subject subset selected from all modalities was used to construct unified multimodal biometric profiles as shown in Table 4.

Table 4. Integrated multimodal dataset construction.

Experimental protocol: after dataset integration, subject identities were assigned unique labels and organized into multimodal biometric profiles. The generated profiles were divided according to a subject-disjoint protocol to avoid overlap between training and testing subjects. During each fold of cross-validation, the same partitioning strategy was maintained to ensure consistency and prevent information leakage. The reported FAR, FRR, TAR, and accuracy values correspond to the average performance obtained across all experimental runs.

4.3 Image results

In Figure 5, the image results acquired from the LSTM-GRFF-Net experimentation are displayed. Figures 5a–e signify the input fingerprint, finger vein, palmprint, finger knuckle, and iris images. The preprocessed fingerprint, finger vein, palmprint, finger knuckle, and iris images are represented in Figures 5f–j. Moreover, Figure 5k specifies the minutiae image for the fingerprint image, Figure 5l represents the line tracking image for the finger vein image, Figure 5m denotes the LGXP feature image for the palmprint image, Figure 5n signifies the CLBP feature image for finger knuckle and Figure 5 indicates iris template image.

4.3.1 Statistical significance analysis

To evaluate the reliability of the reported results, statistical significance analysis was performed on the experimental outcomes. Each experiment was executed five independent times using different train-test partitions. The mean and standard deviation were calculated for all evaluation metrics, including accuracy, TAR, FAR, and FRR.

Additionally, 95% confidence intervals (CI) were computed using CI = μ ± 1.96(σ/√n) where μ denotes the mean performance value, σ represents the standard deviation, and n indicates the number of experimental runs.

To assess whether the observed improvements of the proposed LSTM-GRFF-Net over competing approaches were statistically significant, a paired t-test was conducted at a significance level of 0.05. The null hypothesis assumes that no significant performance difference exists between the compared methods. To improve the reliability of the reported results, all experiments were repeated five independent times under a subject-disjoint five-fold cross-validation protocol. The reported performance values correspond to the average obtained over these repeated experiments, thereby reducing the influence of random initialization and data partitioning. This evaluation protocol demonstrates the stability and reproducibility of the proposed framework.

4.4 Comparative techniques

All comparative results reported in this section correspond to the average values obtained from five independent experimental runs under the subject-disjoint five-fold cross-validation protocol. The superior performance of the proposed LSTM-GRFF-Net was further verified through statistical significance analysis. The reported results correspond to the mean values obtained from multiple independent experimental runs, and the associated confidence intervals demonstrate the stability and robustness of the proposed framework. Learning behavior of the LSTM and GRU branches and the fractional-order fusion mechanism. The LSTM effectively captures long-range feature dependencies, while the GRU provides efficient feature abstraction. The FC layer further strengthens multimodal feature interactions by retaining historical feature relationships that are generally lost in conventional fusion strategies. To validate the superiority of the LSTM-GRFF-Net, several methods including FS-STMFPFV-Net (Abdullahi et al., 2023), FAB-Net+AEF-Net (Huang et al., 2023), neuro-fuzzy classifier (Srivastava et al., 2022), BCO-AKSVM (Vekariya et al., 2024), Hunger game search self-attention based Bi-directional long short-term memory model (HGSSA-Bi LSTM) (Priyani et al., 2024), and Contrast Limited Adaptive Histogram Equalization and Harris Hawk Optimization (CLAHE-HHO) (Thirunavukkarasu et al., 2026) are considered. The LSTM-GRFF-Net's performance compared with some techniques for multimodal biometric recognition using finger vein, finger knuckle, iris, palmprint, and fingerprint concerning salt and pepper noise, gaussian noise, and without noise is elaborated as follows.

4.4.1 Based on Gaussian noise

The examination of the LSTM-GRFF-Net contemplating the images with the Gaussian noise is depicted in Figure 6. Figure 6a shows the validation of LSTM-GRFF-Net with regard to FAR. The comparative approaches namely FS-STMFPFV-Net, FAB-Net+AEF-Net, neuro-fuzzy classifier, BCO-AKSVM, HGSSA-Bi LSTM, CLAHE-HHO, and the proposed LSTM-GRFF-Net acquired FAR value of 48.7%, 39.9%, 29.9%, 14.8%, 14%, 11.8%, and 7.7%, respectively, with training sample 90%. Moreover, in Figure 6b, the examination of LSTM-GRFF-Net with regard to FRR is depicted. With a 90% training sample, the existing methodologies attained FRR of 39.9% for FS-STMFPFV-Net, 28.8% for FAB-Net+AEF-Net, 19% for neuro-fuzzy classifier, 8.8% for BCO-AKSVM, 7.9% for HGSSA-Bi LSTM, and 4.8% for CLAHE-HHO, whereas the LSTM-GRFF-Net has measured FRR of 3.9%. The evaluation of LSTM-GRFF-Net on the basis of accuracy is displayed in Figure 6c. The accuracy recorded by FS-STMFPFV-Net, FAB-Net+AEF-Net, neuro-fuzzy classifier, BCO-AKSVM, HGSSA-Bi LSTM, CLAHE-HHO, and LSTM-GRFF-Net is 78.898%, 80.998%, 82.098%, 84.998%, 85.654%, 87.754%, and 88.877%, with 90% training sample. The LSTM-GRFF-Net gained an improved performance of 11.23%, 8.86%, 7.63%, 4.36%, 3.63%, and 1.26% when compared to existing models such as FS-STMFPFV-Net, FAB-Net+AEF-Net, neuro-fuzzy classifier, BCO-AKSVM, HGSSA-Bi LSTM, and CLAHE-HHO. Figure 6d presents the analysis of LSTM-GRFF-Net with respect to TAR. The classical approaches quantified TAR of 75.987% for FS-STMFPFV-Net, 76.988% for FAB-Net+AEF-Net, 79.988% for neuro-fuzzy classifier, 81.988% for BCO-AKSVM, 82.765% for HGSSA-Bi LSTM, and 83.876% for CLAHE-HHO, while the values achieved by LSTM-GRFF-Net is 84.879%, by considering 90% training sample. The LSTM-GRFF-Net acquired an enhanced performance of 10.48%, 9.30%, 5.76%, 3.41%, 2.49%, and 1.18% when compared to prevailing approaches like FS-STMFPFV-Net, FAB-Net+AEF-Net, neuro-fuzzy classifier, BCO-AKSVM, HGSSA-Bi LSTM, and CLAHE-HHO.

4.4.2 Based on salt and pepper noise

The analysis of the LSTM-GRFF-Net considering the images with the pepper and salt noise is shown in Figure 7. Figure 7a illustrates the LSTM-GRFF-Net investigation in relation to FAR. The FAR quantified by FS-STMFPFV-Net is 54.9%, FAB-Net+AEF-Net is 52.9%, neuro-fuzzy classifier is 35.9%, BCO-AKSVM is 27.9%, HGSSA-Bi LSTM is 20.8%, CLAHE-HHO is 13.8%, and LSTM-GRFF-Net is 11.9%, by contemplating 90% training sample. The FRR-based evaluation of the LSTM-GRFF-Net is shown in Figure 7b. The FRR recorded with 90% training sample by FS-STMFPFV-Net, FAB-Net+AEF-Net, neuro-fuzzy classifier, BCO-AKSVM, HGSSA-Bi LSTM, CLAHE-HHO, and LSTM-GRFF-Net is 48.9%, 36.9%, 31%, 24%, 13.9%, 11.9%, and 9%, respectively. In addition, in Figure 7c, the valuation of LSTM-GRFF-Net regarding accuracy is illustrated. The baseline models attained an accuracy of 79.899% for FS-STMFPFV-Net, 82.987% for FAB-Net+AEF-Net, 85.990% for neuro-fuzzy classifier, 86.879% for BCO-AKSVM, 87.868% for HGSSA-Bi LSTM, 89.765% for CLAHE-HHO, for 90% training sample, while LSTM-GRFF-Net recorded an accuracy of 90.876%. The LSTM-GRFF-Net gained an improved performance of 12.08%, 8.68%, 5.38%, 4.40%, 3.31%, and 1.22% when compared to existing models such as FS-STMFPFV-Net, FAB-Net+AEF-Net, neuro-fuzzy classifier, BCO-AKSVM, HGSSA-Bi LSTM, CLAHE-HHO. Likewise, in Figure 7d, the examination of LSTM-GRFF-Net contemplating TAR is displayed. The TAR achieved by classical methodologies, such as FS-STMFPFV-Net is 76.879%, FAB-Net+AEF-Net is 79.888%, neuro-fuzzy classifier is 82.988%, BCO-AKSVM is 85.999%, HGSSA-Bi LSTM is 86.468%, CLAHE-HHO is 86.768%, while the LSTM-GRFF-Net calculated TAR of 87.988%, by contemplating 90% training sample. The LSTM-GRFF-Net acquired an enhanced performance of 12.63%, 9.21%, 5.68%, 2.26%, 1.73%, and 1.39% when compared to prevailing approaches like FS-STMFPFV-Net, FAB-Net+AEF-Net, neuro-fuzzy classifier, BCO-AKSVM, HGSSA-Bi LSTM, CLAHE-HHO.

4.4.3 Based on without noise

The evaluation of LSTM-GRFF-Net for the recognition of multimodal biometrics employing images without noise is shown in Figure 8. The evaluation of LSTM-GRFF-Net concerning FAR is demonstrated in Figure 8a. The comparative models namely FS-STMFPFV-Net, FAB-Net+AEF-Net, neuro-fuzzy classifier, BCO-AKSVM, HGSSA-Bi LSTM, CLAHE-HHO, and the LSTM-GRFF-Net acquired FAR value of 50.9%, 42.9%, 28.9%, 16.9%, 14.9%, 10.8%, and 9.9%, with training sample 90%. In addition, in Figure 8b, the assessment of LSTM-GRFF-Net with respect to FRR is depicted. By considering a 90% training sample, the conventional methods attained FRR of 46% for FS-STMFPFV-Net, 40% for FAB-Net+AEF-Net, 26.9% for neuro-fuzzy classifier, 15% for BCO-AKSVM, 11.9% for HGSSA-Bi LSTM, and 7.9% for CLAHE-HHO, whereas LSTM-GRFF-Net has achieved FRR of 6%. The valuation of LSTM-GRFF-Net on the basis of the accuracy is shown in Figure 8c. The accuracy quantified by FS-STMFPFV-Net, FAB-Net+AEF-Net, neuro-fuzzy classifier, BCO-AKSVM, HGSSA-Bi LSTM, CLAHE-HHO, and LSTM-GRFF-Net is 84.988%, 86.987%, 87.876%, 89.876%, 90.458%, 90.990%, and 92.899%, with 90% training sample. The LSTM-GRFF-Net gained an improved performance of 8.52%, 6.36%, 5.41%, 3.25%, 2.63%, and 2.05% when compared to classical models namely FS-STMFPFV-Net, FAB-Net+AEF-Net, neuro-fuzzy classifier, BCO-AKSVM, HGSSA-Bi LSTM, and CLAHE-HHO. In Figure 8d, the evaluation of LSTM-GRFF-Net in view of TAR is displayed. The prevailing techniques recorded TAR of 77.879% for FS-STMFPFV-Net, 82.999% for FAB-Net+AEF-Net, 83.998% for neuro-fuzzy classifier, 86.877% for BCO-AKSVM, 87.469% for HGSSA-Bi LSTM, and 87.988% for CLAHE-HHO, while TAR values measured by LSTM-GRFF-Net is 89.876%, with 90% training sample. The LSTM-GRFF-Net acquired an enhanced performance of 13.35%, 7.65%, 6.54%, 3.34%, 2.68%, and 2.10% when compared to prevailing approaches like FS-STMFPFV-Net, FAB-Net+AEF-Net, neuro-fuzzy classifier, BCO-AKSVM, HGSSA-Bi LSTM, and CLAHE-HHO.

4.5 Comparative discussion

Table 5 shows the experimental results measured by LSTM-GRFF-Net and currently available multimodal biometric recognition methods. The LSTM-GRFF-Net technique employed for recognizing multimodal biometrics attained effective outcomes with a minimum FAR of 9.9%, and FRR of 6%, a maximum accuracy of 92.899%, and a TAR of 89.876%. The comparative techniques, like FS-STMFPFV-Net, FAB-Net+AEF-Net, neuro-fuzzy classifier, BCO-AKSVM, HGSSA-Bi LSTM, and CLAHE-HHO achieved the FAR value of 50.9%, 42.9%, 28.9%, 16.9%, 14.9%, and 10.8%. The classical schemes gained FRR of 46% for FS-STMFPFV-Net, 40% for FAB-Net+AEF-Net, 26.9% for neuro-fuzzy classifier, 15% for BCO-AKSVM, 11.9% for HGSSA-Bi LSTM, and 7.9% for CLAHE-HHO. The accuracy recorded by FS-STMFPFV-Net, FAB-Net+AEF-Net, neuro-fuzzy classifier, BCO-AKSVM, HGSSA-Bi LSTM, and CLAHE-HHO is 84.988%, 86.987%, 87.876%, 89.876%, 90.458%, and 90.990%. The classical models quantified TAR of 77.879% for FS-STMFPFV-Net, 82.999% for FAB-Net+AEF-Net, 83.998% for neuro-fuzzy classifier, 86.877% for BCO-AKSVM, 87.469% for HGSSA-Bi LSTM, and 87.988% for CLAHE-HHO. The LSTM-GRFF-Net model combines the advantages of both architectures by integrating LSTM and GRU networks enhancing the performance in tasks involving sequential data. The LSTM-GRFF-Net model can capture both short-term and long-term dependencies in sequential data by combining LSTM and GRU. The ability of LSTM to manage long-term dependencies balances the effectiveness of GRU in handling short-term patterns, resulting in a more robust and balanced model.

Table 5. Comparative discussion of LSTM-GRFF-Net with other existing methods.

4.6 Ablation study

An ablation study is a method in which specific features of the model are removed to assess its performance. Figure 9 shows the ablation test of the devised LSTM-GRFF-Net model. Figure 9a shows the FAR evaluation of the devised model. When the training sample is considered as 90, the LSTM-GRFF-Net without preprocessing, LSTM-GRFF-Net without feature normalization, LSTM-GRFF-Net without feature fusion, LSTM, GRU, and LSTM-GRFF-Net obtained values of 0.509, 0.366, 0.217, 0.210, 0.178, and 0.099. The FRR evaluation of the model is interpreted in Figure 9b. The values of 0.388, 0.310, 0.277, 0.218, 0.158, and 0.060 are obtained by the LSTM-GRFF-Net without preprocessing, LSTM-GRFF-Net without feature normalization, LSTM-GRFF-Net without feature fusion, LSTM, GRU, and LSTM-GRFF-Net for the training data 90%. Figure 9c articulates the accuracy evaluation of the devised model. The accuracy noted by the LSTM-GRFF-Net without preprocessing, LSTM-GRFF-Net without feature normalization, LSTM-GRFF-Net without feature fusion, LSTM, GRU, and LSTM-GRFF-Net are 83.765, 84.987, 86.877, 88.766, 90.655, and 92.899 for the training sample 90%. The TAR estimation of the proposed scheme is presented in Figure 9d. The TAR value of 89.876 is obtained by the LSTM-GRFF-Net model whereas the LSTM-GRFF-Net without preprocessing, LSTM-GRFF-Net without feature normalization, LSTM-GRFF-Net without feature fusion, LSTM, and GRU obtained values of 80.876, 81.987, 83.879, 85.877, and 86.876, respectively.

4.7 Assessment using uneven lighting condition

The evaluation of LSTM-GRFF-Net for the recognition of multimodal biometrics based on uneven lighting conditions is shown in Figure 10. The evaluation of LSTM-GRFF-Net concerning FAR is demonstrated in Figure 10a. The comparative models namely FS-STMFPFV-Net, FAB-Net+AEF-Net, neuro-fuzzy classifier, BCO-AKSVM, HGSSA-Bi LSTM, CLAHE-HHO, and the LSTM-GRFF-Net acquired FAR value of 0.458, 0.399, 0.366, 0.277, 0.248, 0.166, and 0.127 with training sample 90%. In addition, in Figure 10b, the assessment of LSTM-GRFF-Net with respect to FRR is depicted. By considering a 90% training sample, the conventional methods attained FRR of 0.410 for FS-STMFPFV-Net, 0.358 for FAB-Net+AEF-Net, 0.309 for neuro-fuzzy classifier, 0.277% for BCO-AKSVM, 0.210% for HGSSA-Bi LSTM, and 0.198 for CLAHE-HHO, whereas LSTM-GRFF-Net has achieved FRR of 0.159. The valuation of LSTM-GRFF-Net on the basis of the accuracy is shown in Figure 8c. The accuracy quantified by FS-STMFPFV-Net, FAB-Net+AEF-Net, neuro-fuzzy classifier, BCO-AKSVM, HGSSA-Bi LSTM, CLAHE-HHO, and LSTM-GRFF-Net is 83.876%, 84.887%, 85.876%, 86.876%, 87.767%, 88.877%, and 89.876% with 90% training sample. In Figure 8d, the evaluation of LSTM-GRFF-Net in view of TAR is displayed. The prevailing techniques recorded TAR of 78.898% for FS-STMFPFV-Net, 79.866% for FAB-Net+AEF-Net, 80.788% for neuro-fuzzy classifier, 81.977% for BCO-AKSVM, 83.977% for HGSSA-Bi LSTM, and 84.987% for CLAHE-HHO, while TAR values measured by LSTM-GRFF-Net is 86.877%, with 90% training sample. The statistical analysis of Table 6 demonstrates that the proposed LSTM-GRFF-Net consistently outperforms competing multimodal biometric recognition approaches across all evaluation metrics. The narrow confidence intervals indicate stable model behavior, while the obtained p-values confirm that the observed improvements are statistically significant at the 95% confidence level. Therefore, the performance gains achieved by the proposed framework are not attributable to random variation but arise from the effectiveness of the fractional-order fusion strategy and complementary recurrent learning architecture.

Table 6. Statistical evaluation analysis.

4.8 Computational complexity and scalability analysis

The computational complexity of the proposed LSTM-GRFF-Net mainly depends on three stages: feature extraction, HOA-based feature fusion, and multimodal biometric recognition. Let N denote the number of biometric samples, D represents the fused feature dimension, H indicates the number of hidden units, T denotes the sequence length, P represents the HOA population size, and I denotes the maximum number of optimization iterations.

The feature extraction stage is executed independently for each biometric modality and therefore scales linearly with the number of input samples. During feature fusion, the HOA algorithm optimizes fusion weights with a computational complexity of O(P×I×D), where P and I correspond to the population size and maximum iterations, respectively. In the recognition stage, both LSTM and GRU process sequential feature representations with a computational complexity of O(T×H²). Although the inclusion of dual recurrent branches slightly increases computational cost compared with a single recurrent model, it enables more effective learning of both long-term and short-term dependencies from multimodal biometric features.

From a memory perspective, the proposed framework stores only the fused feature vectors and trainable parameters associated with the LSTM, GRU, and FC fusion layer, resulting in moderate memory requirements when compared with conventional deep multimodal architectures. Furthermore, the architecture exhibits good scalability because feature extraction and multimodal fusion are performed independently before the recognition stage. Consequently, additional biometric modalities can be incorporated into the framework with minimal architectural modifications, making the proposed approach suitable for large-scale multimodal biometric applications. The actual training time and memory consumption depend on the hardware configuration, dataset size, and implementation environment, and therefore may vary across deployment platforms.

4.9 Statistical evaluation

To further evaluate the robustness of the proposed LSTM-GRFF-Net, statistical analysis was performed using the results obtained from five independent experimental runs. For each performance metric, the mean and standard deviation were calculated to evaluate the stability of the proposed model. Furthermore, a paired t-test was conducted between the proposed method and the best-performing baseline at a 95% confidence level (p < 0.05). The obtained results demonstrate that the proposed method consistently outperforms the competing approaches, confirming that the performance improvement is statistically significant rather than resulting from random experimental variations.

5 Conclusion

Although the proposed LSTM-GRFF-Net demonstrated superior performance in terms of accuracy, FAR, FRR, and TAR, additional biometric evaluation metrics such as receiver operating characteristic (ROC) curves, equal error rate (EER), precision, recall, and F1-score can provide a more comprehensive assessment of recognition performance. Therefore, the incorporation of these evaluation measures and their detailed analysis will be considered in future work to further validate the robustness and generalization capability of the proposed multimodal biometric recognition framework. Various traditional multimodal biometric methods have been found to be ineffective in recognizing biometrics. Therefore, a new model named LSTM-GRFF-Net has been developed for multimodal biometric recognition. Initially, the finger vein, finger knuckle, palmprint, iris, and fingerprint images are preprocessed using the Medav filter. Next, the finger vein is identified using repeated line tracking, and CLBP, and LGXP features are extracted from the finger knuckle and palmprint images. In addition to this, iris template extraction and minutiae extraction are performed on the iris and fingerprint images. Following this, the iris template and minutiae are normalized using linear interpolation and passed to feature fusion, while the mined features from finger vein, finger knuckle, and palmprint are subjected to feature fusion. Moreover, all the five biometrics are fused together by HOA. Finally, the recognition of multimodal biometrics is carried out by utilizing LSTM-GRFF-Net. The LSTM-GRFF-Net measured a maximum accuracy, and TAR of 92.899% and 89.876%, where FAR and FRR attained a minimum value of 9.877% and 5.988%. Future work aims to develop more effective algorithms and feature selection methods to process the biometric data for enhancing speed.

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Nomenclature

Table A1.

Footnotes

Edited by: Maheswar Rajagopal, KPR Institute of Engineering and Technology, India

Reviewed by: Swapnil Parikh, Parul University, India

Yazeed AlZahrani, Prince Sattam Bin Abdulaziz University, Saudi Arabia

Footnotes

SDUMLA-HMT dataset was taken from “http://www.sai.sdu.edu.cn/info/1075/1115.htm” and accessed on August, 2024.

IIT Delhi Finger Knuckle Database (Version 1.0), was taken from “https://www4.comp.polyu.edu.hk/~csajaykr/IITD/iitd_knuckle.htm, http://vcipl-okstate.org/pbvs/bench/”, accessed on August, 2024.

CBSR dataset was taken from “https://www.kaggle.com/datasets/kundurunonieshreddy/finger-print-dataset?select=Dataset” and accessed on August, 2024.

Finger print dataset was taken from https://time.sdu.edu.cn/kycg/gksjk.htm and accessed on August, 2024.