Using an ensemble of neural networks offers a simple yet effective measure to improve performance and robustness beyond that of a single network [11,12,13]. Notably, in high-profile competitions such as ImageNet [14] and Kaggle (www.kaggle.com, accessed on 26 November 2023), ensembles of deep learning architectures have consistently outperformed individual models. Prior studies have demonstrated that ensembling can enhance both accuracy and robustness by exploiting network diversity [15,16,17,18,19,20,21]. Despite these benefits, the use of ensembling for neural networks remains limited due to high training costs. In light of this problem, Snapshot Ensemble [4], Fast Geometric Ensemble [22], and Stochastic Weight Averaging ensemble [6] have been proposed, wherein the authors exploit model diversity and geometric properties of the loss surface to achieve the benefits of ensembling. However, these techniques have mainly been evaluated on relatively large datasets, wherein at least 50,000 images are available in the training set, and there has been limited exploration of their effectiveness on smaller datasets such as LivDet 2015 [7].

Grad-CAM has been successfully applied to explain classifiers in image classification, image segmentation [24], and visual question answering (VQA) [25]. Its success has led to the development of Grad-CAM++ [26], which further enhances the explanation capabilities of Grad-CAM and has been used for object detection and localization [27,28,29]. The authors in [30] employed Grad-CAM as a visualization tool to identify and highlight noise across various channels of a network when processing a fingerprint image. The use of CAM is also presented in the study by [31], where it was used for patch extraction during the inference stage.

The detection of spoof fingerprints remains a prominent research topic, and CNNs have proven to be a successful approach [32]. To stimulate further research efforts in this field, several spoof detection competitions (LivDet 2009–2021) have been organized [7,10,33,34]. Notably, in the LivDet 2015 competition, the authors of [35] employed a transfer learning approach using deep CNNs, specifically AlexNet [36] and VGGNet [37], which were pre-trained on the ImageNet [14] dataset, and fine-tuned some of the layers for spoof detection of fingerprints. Meanwhile, [38] proposed a CNN architecture with similar performance but reduced test time. Improving the robustness of CNN-based spoof detection systems has been explored by [39], who adopted a hybrid approach that combines hyper-parameter tuning of a CNN and Support Vector Machines (SVMs). Siamese network architecture has been employed by the authors of [40] to improve the robustness of a fingerprint spoof detection system. The authors of [41] have proposed an altered ResNet architecture to achieve smaller parameter size and computational efficiency for a practical spoof detection application. Additionally, [42] have improved the accuracy and robustness of their system using the MobileNet-V1 [43] architecture in conjunction with the fusion of minutiae-based center-aligned local patches. However, their approach involves several complex algorithms, such as minutiae detection, local patch extraction, and patch alignment, in the training and testing procedures. Several techniques [44,45,46,47] have been proposed to generate synthetic fingerprints by leveraging style-transfer techniques. The primary objective of these approaches is to increase the number of data samples in order to address challenges associated with limited dataset sizes. A brief summary of the relevant studies is presented in Table 2.