You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Methods for learning feature representations for offline handwritten signature verification have been successfully proposed in recent literature, using deep convolutional neural networks to learn representations from signature pixels. Such methods reported large performance improvements compared to handcrafted feature extractors. However, they also introduced an important constraint: the inputs to the neural networks must have a fixed size, while signatures vary significantly in size between different users. In this paper, we propose addressing this issue by learning a fixed-sized representation from variable-sized signatures by modifying the network architecture, using spatial pyramid pooling. We also investigate the impact of the resolution of the images used for training and the impact of adapting (fine-tuning) the representations to new operating conditions (different acquisition protocols, such as writing instruments and scan resolution). On the GPDS dataset, we achieve results comparable with the state of the art, while removing the constraint of having a maximum size for the signatures to be processed. We also show that using higher resolutions (300 or 600 dpi) can improve performance when skilled forgeries from a subset of users are available for feature learning, but lower resolutions (around 100dpi) can be used if only genuine signatures are used. Lastly, we show that fine-tuning can improve performance when the operating conditions change.

Cited Abstract(s):
[1]: Some of the fundamental problems faced in the design of signature verification (SV) systems include the potentially large number of input features and users, the limited number of reference signatures for training, the high intra-personal variability among signatures, and the lack of forgeries as counterexamples. In this paper, a new approach for feature selection is proposed for writer-independent (WI) off-line SV. First, one or more preexisting techniques are employed to extract features at different scales. Multiple feature extraction increases the diversity of information produced from signature images, allowing to produce signature representations that mitigate intra-personal variability. Dichotomy transformation is then applied in the resulting feature space to allow for WI classification. This alleviates the challenges of designing off-line SV systems with a limited number of reference signatures from a large number of users. Finally, boosting feature selection is used to design low-cost classifiers that automatically select relevant features while training. Using this global WI feature selection approach allows to explore and select from large feature sets based on knowledge of a population of users. Experiments performed with real-world SV data comprised of random, simple, and skilled forgeries indicate that the proposed approach provides a high level of performance when extended shadow code and directional probability density function features are extracted at multiple scales. Comparing simulation results to those of off-line SV systems found in literature confirms the viability of the new approach, even when few reference signatures are available. Moreover, it provides an efficient framework for designing a wide range of biometric systems from limited samples with few or no counterexamples, but where new training samples emerge during operations.

[2]: Standard signature verification (SV) systems are writer-dependent (WD), where a specific classifier is designed for each individual. It is inconvenient to ask a user to provide enough number of signature samples to design his WD classifier. In practice, very few samples are collected and inaccurate classifiers maybe produced. To overcome this, writer-independent (WI) systems are introduced. A global classifier is designed using a development database, prior to enrolling users to the system. For these systems, signature templates are needed for verification, and the template databases can be compromised. Moreover, state-of-the-art WI and WD systems provide enhanced accuracy through information fusion at either feature, score or decision levels, but they increase computational complexity. In this study, a hybrid WI-WD system is proposed, as a compromise of the two approaches. When a user is enrolled to the system, a WI classifier is used to verify his queries. During operation, user samples are collected and adapt the WI classifier to his signatures. Once adapted, the resulting WD classifier replaces the WI classifier for this user. Simulations on the Brazilian and the GPDS signature databases indicate that the proposed hybrid system provides comparative accuracy as complex WI and WD systems, while decreases the classification complexity.

[3]: The limited number of writers and genuine signatures constitutes the main problem for designing a robust Handwritten Signature Verification System (HSVS). We propose, in this paper, the use of One-Class Support Vector Machine (OC-SVM) based on writer-independent parameters, which takes into consideration only genuine signatures and when forgery signatures are lack as counterexamples for designing the HSVS. The OC-SVM is effective when large samples are available for providing an accurate classification. However, available handwritten signature samples are often reduced and therefore the OC-SVM generates an inaccurate training and the classification is not well performed. In order to reduce the misclassification, we propose a modification of decision function used in the OC-SVM by adjusting carefully the optimal threshold through combining different distances used into the OC-SVM kernel. Experimental results conducted on CEDAR and GPDS handwritten signature datasets show the effective use of the proposed system comparatively to the state of the art. We propose handwritten signature verification for writer independent parameters.We propose to design HSVS system using only genuine signatures using OC-SVM.Applying a soft threshold in order to reduce the misclassification of the OC-SVM.Combination scheme is proposed through versus distances used into the OC-SVM kernel.Competitive results are obtained comparatively to the state of the art.

[4]: In this work we address two important issues of off-line signature verification. The first one regards feature extraction. We introduce a new graphometric feature set that considers the curvature of the most important segments, perceptually speaking, of the signature. The idea is to simulate the shape of the signature by using Bezier curves and then extract features from these curves. The second important aspect is the use of an ensemble of classifiers based on graphometric features to improve the reliability of the classification, hence reducing the false acceptance. The ensemble was built using a standard genetic algorithm and different fitness functions were assessed to drive the search. Two different scenarios were considered in our experiments. In the former, we assume that only genuine signatures and random forgeries are available to guide the search. In the latter, on the other hand, we assume that simple and simulated forgeries also are available during the optimization of the ensemble. The pool of base classifiers is trained using only genuine signatures and random forgeries. Thorough experiments were conduct on a database composed of 100 writers and the results compare favorably.
The problem of Offline Signature Verification is either formulated as Writer-Dependent, with one classification task defined for each user enrolled to the system, or as a Writer-Independent problem, where we consider a single problem, of comparing a questioned signature to a reference signature. In the literature, Writer-Dependent classification is most commonly used: for each user, a set of reference (genuine) signatures are used as positive samples, and a set of genuine signatures from other users (in this context called Random forgeries") are used as negative samples, and a binary classifier is trained. Alternatively, some authors propose using one-class classifiers for the Writer-Dependent formulation, using only genuine signatures from the user as positive samples (e.g. [3] ). Writer-Independent classification, on the other hand, is often used by training a binary classifier on a dissimilarity space, where the inputs are the absolute difference of two feature vectors: @math , where @math and @math are feature vectors extracted from two signatures, and we consider a binary label: @math if both signatures are from the same user, and @math otherwise [4] [1] [2] .