A Structured Framework for Formalized and Quantitative Handwriting Examination

The aim of the proposed procedure is to maximize the objectivity and reliability of handwriting assessment by minimizing subjective influence and quantifying the evaluation process. This quantification facilitates both more substantiated probabilistic conclusions and the possibility of statistical research into the significance of individual handwriting characteristics. The procedure incorporates the five main principles defined in [1], which are considered individually in every examination:

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“No two people write exactly alike.

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No one person writes exactly the same way twice, and no two naturally written signatures are exactly the same.

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The significance of any feature, as evidence of identity or non-identity, and the problem of comparison becomes one of considering its rarity, complexity, the relative speed and naturalness with which it is written, and its agreement or disagreement with comparable features.

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No one is able to imitate all of the features of another person’s handwriting and simultaneously write at the same relative speed and skill as the writer that he/she is seeking to imitate.

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In those cases where the writer disguises their normal handwriting or imitates the handwriting of another”.

In handwriting examination, two types of handwriting are typically distinguished: textual handwriting and signatures. Textual handwriting constitutes the main body of written content and is generally more stable and consistent. In contrast, signatures are identifiers often in stylized or abbreviated form (paraph), which exhibit greater variability. While the proposed procedure is suitable for analyzing both types, each presents its specific challenges and considerations. The procedural steps outlined herein are familiar to forensic experts; however, our contribution lies in their comprehensive integration and systematic formalization at every stage. The general framework assumes a typical forensic scenario in which the expert is provided with one or more questioned documents and several known documents—i.e., samples of authenticated handwriting attributed to the presumed author(s). In some cases, known documents may be grouped according to different potential authors. This does not alter the core procedure, which is simply applied to each group independently. The proposed algorithm of handwriting examination follows a two-stage structure: feature evaluation to compare general characteristics of handwriting and congruence analysis, a detailed letter-by-letter comparison to assess graphical and kinematic consistency. Both stages yield quantitative results that are combined into a final similarity score. The full procedure consists of the following steps:

1.

Pre-assessment—preliminary review of all materials to ensure suitability for examination.

2.

Feature evaluation of known documents—a systematic analysis of handwriting features in each known sample.

3.

Determination of variation ranges—establishing the range of variation for each feature across known samples.

4.

Feature evaluation of the questioned document—assessing the same set of features in the questioned handwriting.

5.

Similarity grading for features—comparing the questioned features to known variation ranges and assigning similarity grades.

6.

Evaluation of so-called handwriting elements (defined below).

7.

Calculation of feature-based similarity score—aggregating individual handwriting element comparisons into a cumulative score.

8.

Congruence analysis of letterforms—a detailed examination of each letter and its allographic (variant) forms in both questioned and known samples, including specific letter-pair combinations where necessary.

9.

Evaluation of congruence score—quantitative assessment of consistency between corresponding letters and letter pairs.

10.

Calculation of total similarity score as a function of the feature-based score and congruence score.

11.

Expert conclusion—formulating the final expert opinion based on the total similarity score and contextual case information.

Each of these steps is discussed in detail in the following sections. 2.1. Pre-Assessment Pre-assessment is conducted prior to any detailed, side-by-side comparison of handwriting samples. Its purpose is threefold. The first objective is to assess whether the provided handwritten materials are suitable for comparison. For a meaningful analysis, the documents must be written in the same general style. For instance, it is not appropriate to compare cursive writing with print-style writing, as the differences in form and structure make such comparisons unreliable. The second objective is to define the limitations of the analysis, which depends on the quality, quantity, and type of documents available. Increasingly, forensic handwriting experts must work with copies instead of original documents. This presents inherent limitations—many signs of forgery or document manipulation can only be reliably detected on original materials. However, due to various reasons, clients often simply do not have access to the originals. Additionally, the following aspects must be evaluated:

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Legibility of the documents;

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Verification that known samples are genuinely representative of the purported author;

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Assessment of whether known samples are contemporaneous with the questioned writing;

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Determination of whether sufficient material is available to assess natural handwriting variation, including the presence of multiple letterforms and their usage in various word positions.

These factors significantly influence the scope, depth, and reliability of the subsequent examination. Finally, understanding the broader context of the case is essential. This includes the circumstances under which the questioned and known documents were created, the parties involved, and any relevant background that may inform the interpretation of handwriting characteristics—such as potential motivations for forgery, attempts at disguise, or psychological conditions that may affect writing style. 2.2. Evaluation of Handwriting Features All known documents, one by one, are evaluated to assess every handwriting feature. The set of these characteristics covers all aspects of handwriting, including spatial structure, shape and dynamics. The selection of features is informed by numerous authoritative sources. To the standard sources traditionally belong, for instance, refs. [19,20,21] in the English-speaking countries or [22,23,24] in the German-speaking regions. The main purpose of this stage is the quantitative assessment of each handwriting feature. The framework supports two primary approaches. The primary and most widely used method is based on ordinal scales. In our practice, we predominantly utilize the eight-point scale proposed in [23,24], which we have found to be the most practical and reliable after testing several alternatives. An example of such a scale for the letter size is given in Table 1. It should be mentioned that the letter size is evaluated using inner middle-zone letters—that is, letters located in the center of words, excluding the first and last letters, to reduce positional bias. Although some experts may disagree with specific scale definitions, clarity and consistency in classification are paramount in forensic handwriting comparison. In this context, unambiguous specification is more critical than universal agreement. The second method involves categorizing handwriting into five size groups—very small, small, medium, large, and very large—and then measuring the proportion of letters falling into each category on a scale from 0 to 1, such that the total sums to 1.0. This approach is more suitable for specialized analyses, such as investigating potential cognitive decline (e.g., in neurodegenerative conditions) [25]. A like definition exists for the majority of handwriting features. They are called evaluative features. However, some more descriptive features have a nominal scale. For example, the definition of the connection form (Table 2). In this case, several values can be chosen since several connection forms can be present in the analyzed handwriting at the same time. A formal and unambiguous definition of all handwriting features is the prerequisite for the objectivity and reliability of their evaluation. Even complicated and indirect ones like speed can then be correctly modeled [25]. A formal and unambiguous definition of all handwriting features is a prerequisite for achieving objectivity and reliability in their evaluation. Clear definitions ensure consistency in feature identification and scoring across different examiners and cases. This works well also for complex or indirect features— such as writing speed—which can be effectively and accurately modeled (see, for example, [26]). All features (especially descriptive ones) are most important for author identification when they differ from the “norm”. However, the natural variability of handwriting can lead to the random occurrence of such a feature in the sample. To evaluate such features, the “three-or-half” rule is used. This means that in order to say that a feature is present in the sample, it should appear at least three times or in half of the cases in which it could potentially be assessed. For example, if we are analyzing the shape of a lower loop and there are only four of them, then two occurrences are sufficient. For textual handwriting, a total of 83 features are defined. For signatures, 45 features are considered, some of which overlap with textual handwriting while others are specific to the structural and geometric characteristics unique to signatures (e.g., overall layout or spatial configuration). The results of these evaluations are compiled into a feature matrix, where each row corresponds to a handwriting feature, and each column represents one of the known documents (see Table 3). 2.3. Assessment of Range of Variation for Handwriting Features Once all known documents have been evaluated, the next step is to define the range of variation for each handwriting feature. This range captures the natural variability in an individual’s writing and serves as a reference for comparing the questioned sample. A special table is used to record this information. In practice, this table is a Microsoft Excel sheet—which offers ease of use and flexibility and simple o integration into a structured database for more advanced applications. The table structure is illustrated in Table 3. In this Table, V1, V2, etc., denote different known documents. Vmin and Vmax are correspondingly minimal and maximal values of the feature among the known samples. It is important to note that a feature value of 0 does not serve as a valid boundary for defining the range. A zero value typically indicates that the feature could not be evaluated—for example, due to insufficient data or the absence of relevant instances in the sample. Such cases are classified as “missing features”. Missing features cannot be used in comparative analysis and are excluded from assessments of similarity or difference. 2.4. Evaluation of Handwriting Features of the Questioned Sample The evaluation of the questioned handwriting does not differ from the evaluation of known documents. The result is a vector of evaluated handwriting features. 2.5. Assessment of Similarity Grad for Handwriting Features The similarity grade for a specific handwriting feature quantifies the extent to which the value observed in the questioned sample (X value) aligns with the values obtained from the known samples (V values). In practical terms, this involves determining whether the X value falls within the variation range defined by the interval [Vmin–Vmax]. In [1], they propose a five-point categorical scale for this evaluation, comprising the following descriptors: clear similar (++), similar (+), inconclusive (~), different (−), clear different (−−), and missing feature/not comparable (N/C). While we follow the conceptual framework of this scale, we implement it in a numerical format to support further quantitative analysis. The similarity grade is expressed as a value ranging from 0 (complete dissimilarity) to 1.0 (complete similarity), using the following discrete levels: 0, 0,25, 0.50, 0,75, 1.0. These values are assigned based on formal comparison rules, which are outlined as follows:

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Similarity grad equals 0 if the X-value is outside the variation range (Vmin–Vmax).

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Similarity grad equals 1 if the X-value is strictly inside the variation range (Vmin–Vmax) or X-value equals Vmin or Vmax when the range is only 2 points, i.e., Vmax − Vmin = 1.

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Similarity grad equals 0.5 or 0.75 if X-value equals Vmin or Vmax and the range is over 2 points, i.e., Vmax − Vmin ≥ 2.

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Similarity grad gets no value (n/c) if X-value = 0 or V-value = 0 (feature cannot be evaluated).

Some evaluation examples are shown in Table 4. This approach is applicable primarily to evaluative features, where values can be placed on a defined ordinal or continuous scale. In contrast, descriptive features are represented not by a single value but by a set of observed characteristics. For these features, the range of variation in the known samples and the value(s) observed in the questioned sample are each expressed as sets. The assessment of similarity in this case is based on the degree of intersection between these two sets:

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If all elements of the questioned sample’s feature set (X) are present in the known set (V), the similarity grade is 1.0.

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If none of the elements intersect—i.e., the sets are completely disjoint—the similarity grade is 0.0.

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In partial overlaps, intermediate values (e.g., 0.25, 0.50, 0.75) may be used to represent the relative proportion of matching elements, depending on the number and relevance of shared features.

This approach ensures that both quantitative and qualitative handwriting characteristics are systematically assessed, providing a unified framework for feature-level similarity evaluation. 2.6. Assessment of Similarity Grad for Handwriting Elements As previously mentioned, the handwriting analysis encompasses 83 distinct features, each contributing differently to the identification process. While efforts are ongoing to define the identification significance of individual features formally, it remains a complex and context-dependent task. Therefore, a more effective and practically relevant strategy is to assess the similarity of handwriting elements. A handwriting element refers to a specific structural or stylistic aspect of handwriting—such as margins, baseline alignment, slant, or letter proportions—that represents a higher-order construct composed of multiple individual features. Each handwriting element is considered to have equal evidentiary weight in the context of writer identification. The principal handwriting elements are listed in Table 5. The similarity score for a handwriting element is derived from the similarity grades of its associated features, following these rules:

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If all features of a given element have a similarity grade of 1.0, the element score is also 1.0.

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If any feature within the element has a similarity grade of 0.0, the element score is likewise 0.0, regardless of other feature scores. For example, if the shape of the left margin in the questioned document differs from that in all known samples, the entire “margins” element is considered dissimilar, and its score is set to 0.0.

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In all other cases (i.e., partial similarity), the score for the handwriting element is determined based on the specific constellation of feature-level scores. This may involve weighted or contextual interpretation depending on the nature of the differences observed.

The outcome of this step is a vector of similarity scores, one for each handwriting element. This vector provides a structured, intermediate representation of the similarity between the questioned and known handwriting samples and forms the basis for the final similarity assessment. 2.7. Evaluation of Feature-Based Similarity Score The total feature-based similarity score is calculated as the average of the similarity grades assigned to all evaluated handwriting elements. This aggregated value provides an overall measure of how closely the questioned sample aligns with the known samples in terms of observable handwriting characteristics. However, since the completeness of the evaluation directly affects its reliability, the raw average is adjusted using a reliability coefficient. This coefficient reflects the proportion of handwriting features that were successfully evaluated and accounts for cases where missing or inconclusive data might reduce the robustness of the analysis. To model this adjustment, a sigmoid (S-shaped) function is applied:

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The reliability coefficient equals 1.0 when more than 80% of all defined features were evaluated.

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It equals 0 when fewer than 20% of the features were assessed.

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For intermediate values, the coefficient increases non-linearly with the proportion of evaluated features, reflecting a gradual improvement in confidence as more data becomes available.

This method ensures that the final feature-based similarity score not only reflects the degree of similarity observed but also accounts for the strength and completeness of the underlying data. In most practical cases, where a sufficient number of features can be assessed, the reliability coefficient tends to be close to 1.0, thus minimally affecting the uncorrected similarity score. 2.8. Congruence Analysis The congruence analysis is a systematic, step-by-step comparison of all allographic variations of each letter present in the questioned document with their corresponding forms in the known documents. This analysis constitutes a core component of any handwriting examination, allowing for detailed scrutiny of letterforms at both graphical and dynamic levels. Where necessary, the scope of the analysis extends beyond isolated letters to include letter pairs or combinations. This is particularly relevant when certain handwriting features, such as connecting strokes or contextual variations, depend on adjacent letter interactions. To ensure a consistent and objective approach, each comparative unit (i.e., letter or letter pair) is analyzed according to a standardized set of characteristics, as outlined in Table 6. The output of this process is a vector of congruence scores, one for each comparative unit. Each congruence score is a quantitative value ranging from 0 to 1, reflecting the degree of graphical and kinetic correspondence between the questioned and known samples based on the defined characteristics. This vector provides a granular representation of the letter-by-letter compatibility, forming the basis for the final integration of the congruence analysis into the overall similarity assessment. Signatures are analyzed as common comparative units. If a signature is transcribed alphabetically, each individual letter is also subject to congruence analysis. 2.9. Evaluation of Congruence Score The total congruence score is calculated as the mean value of the individual congruence scores assigned to each comparative unit. Each comparative unit has already been evaluated on a scale from 0 to 1, reflecting the degree of graphical and kinematic compatibility between the questioned and known samples. The total congruence score thus represents the overall consistency of letterform execution across all units examined. This score provides a quantitative measure of structural similarity at the micro-level of handwriting, complementing the feature-based similarity score obtained in previous steps. Together, they contribute to a more robust and balanced final evaluation of authorship likelihood. 2.10. Calculation of Total Similarity Score The total similarity score is derived as a weighted combination of the two core components of handwriting comparison: the feature-based similarity score and the congruence score. It provides an integrated, quantitative assessment of the degree of similarity between the questioned and known handwriting samples. The weights are assigned based on the nature of the handwriting under examination. For textual handwriting, the feature-based score is given greater emphasis, reflecting the broader structural aspects of writing style. In contrast, for signatures, where individual letterforms carry more weight and variation is often more pronounced, the congruence score is prioritized. In all cases, the total similarity score lies within the interval [0,1], ensuring interpretability and consistency across different examination contexts. This score serves as the primary quantitative indicator guiding the expert’s conclusion regarding authorship. 2.11. Expert Decision The total similarity score serves as the primary basis for the expert’s decision regarding authorship. While the score provides a quantitative measure of similarity between the questioned and known handwriting samples, it should not be interpreted as a direct probability. Such an interpretation, especially at higher score levels, risks oversimplifying the nuanced nature of handwriting comparison. Instead, the similarity score functions as a threshold indicator within a broader evaluative framework. Based on extensive empirical observations from casework, it can be stated with reasonable confidence that a score below 0.8 generally supports a rejection of the hypothesis that the questioned handwriting was produced by the known author. In other words, such a score indicates insufficient similarity to justify identification. However, reaching a positive conclusion of authorship requires careful consideration of contextual factors identified during the pre-assessment stage. Thus, the expert decision should not be solely score-driven but rather result from a holistic integration of quantitative analysis and qualitative judgment within the forensic context. The total similarity score strengthens the objectivity and reproducibility of the process and supports expert interpretation. 2.12. Databank All acquired, processed, and calculated data is stored in the system’s databank. This information is also utilized for statistical research in an anonymized form—real cases, personal names, and authentic handwriting samples are not accessible for this purpose. The databank serves as a valuable resource for the ongoing refinement of the examination procedures and the development of new methodological adaptations.