A Review of 3D Shape Descriptors for Evaluating Fidelity Metrics in Digital Twin

Abstract

Digital Twin (DTw) technology is a cornerstone of Industry 4.0, enabling real-time monitoring, predictive maintenance, and performance optimization across diverse industries. A key requirement for effective DTw implementation is high geometric fidelity—ensuring the digital model accurately represents the physical counterpart. Fidelity metrics provide a quantitative means to assess this alignment in terms of geometry, behavior, and performance. Among these, 3D shape descriptors play a central role in evaluating geometric fidelity, offering computational tools to measure shape similarity between physical and digital entities. This paper presents a comprehensive review of 3D shape descriptor methods and their applicability to geometric fidelity assessment in DTw systems. We introduce a structured taxonomy encompassing classical, structural, texture-based, and deep learning-based descriptors, and evaluate each in terms of transformation invariance, robustness to noise, computational efficiency, and suitability for various DTw applications. Building upon this analysis, we propose a conceptual fidelity metric that maps descriptor properties to the specific fidelity requirements of different application domains. This metric serves as a foundational framework for shape-based fidelity evaluation and supports the selection of appropriate descriptors based on system needs. Importantly, this work aligns with and contributes to the emerging ISO 30138 standardization initiative by offering a descriptor-driven approach to fidelity assessment. Through this integration of taxonomy, metric design, and standardization insight, this paper provides a roadmap for more consistent, scalable, and interoperable fidelity measurement in digital twin environments—particularly those demanding high precision and reliability.

1. Introduction

Industry 4.0 marks a transformative shift in manufacturing and industrial operations, driven by the integration of cyber-physical systems (CPS), the Internet of Things (IoT), cloud computing, and artificial intelligence (AI) [1]. Central to this ecosystem is the Digital Twin (DTw), a dynamic virtual representation of a physical asset continuously updated with real-time sensor data [2]. DTws enable virtual testing, operational forecasting, and predictive maintenance, and are increasingly adopted across industries including aerospace, healthcare, manufacturing, and automotive [3]. A critical factor in DTw effectiveness is fidelity—how accurately the digital model replicates the physical system. Fidelity assessment is essential for validating DTw performance and ensuring consistency across applications [4]. Metrics for fidelity evaluation are typically categorized into geometric, behavioral, and performance dimensions [5]. Among these, geometric fidelity is foundational, particularly for domains relying on accurate spatial modeling and structural simulations. To evaluate geometric fidelity, 3D shape descriptors are employed to quantify the similarity between the shapes of physical and digital models. These descriptors, which encode geometric features invariant to translation, rotation, and scale, are widely used in image processing, computer vision, and DTw applications [6,7]. Despite their importance, the existing literature lacks a comprehensive review connecting shape descriptors directly to fidelity assessment within DTw systems. This paper addresses this gap by centering its focus on 3D shape descriptors as a core fidelity assessment tool. DTws and fidelity metrics are presented as foundational context, while the main contribution lies in categorizing, comparing, and analyzing shape descriptor methods—ranging from boundary-based and region-based descriptors to deep learning models. This study proposes a fidelity metric that maps descriptor capabilities to DTw fidelity requirements and offers recommendations to strengthen emerging standardization frameworks such as ISO 30138 [8]. In this way, this paper provides a new analytical lens for understanding and improving geometric fidelity in DTw applications. Unlike prior surveys (e.g., [7]), this work bridges shape descriptors with ISO 30138 [8] standardization, proposes a domain-agnostic fidelity metric, and introduces a descriptor-aware benchmarking protocol—enabling cross-industry fidelity scoring. Moreover, the absence of standardized fidelity metrics presents a significant barrier. Without them, industries face severe interoperability failures (e.g., incompatible geometric data preventing seamless integration of an aerospace component’s DTw into a manufacturing assembly line DTw) and unacceptable safety risks (e.g., a surgical DTw with inaccurate geometric representations leading to flawed preoperative planning). These critical challenges underscore the urgent need for a unified approach to fidelity assessment, motivating our development of a framework explicitly aligned with the emerging ISO 30138 [8] standard.

This paper provides a comprehensive review of fidelity metrics in Digital Twin (DTw) technology, with a particular emphasis on 3D shape descriptors and standardization challenges. Fidelity assessment in DTw applications is critical to ensuring that digital models accurately replicate their physical counterparts in terms of geometry, behavior, and functionality. However, the lack of standardized evaluation methods presents a significant challenge for cross-industry adoption. To address these concerns, this study aims to analyze existing fidelity assessment methodologies used in DTw applications, examine the role of 3D shape descriptors in evaluating geometric accuracy, and identify key challenges in standardizing fidelity metrics to achieve cross-industry interoperability. Another key focus of this review is the examination of current challenges in standardizing fidelity metrics and exploring potential solutions to achieve industry-wide standardization. The absence of universally accepted evaluation frameworks, data integration protocols, and validation techniques has resulted in inconsistencies across different DTw implementations. By identifying common limitations and proposing standardized fidelity assessment methodologies, this study aims to contribute to the development of a unified framework for assessing Digital Twin fidelity, ensuring greater accuracy, efficiency, and interoperability across industrial domains. Establishing such a framework will facilitate more reliable DTw implementations, enhancing their utility in sectors such as manufacturing, healthcare, aerospace, and smart infrastructure.

Historical Development of Digital Twin Technology

The concept of Digital Twins originated in the early 2000s when Michael Grieves first introduced the idea as part of Product Lifecycle Management (PLM) research at the University of Michigan [9]. He proposed a three-part DTw model (Figure 1), consisting of the following:

• The physical object (real-world system).
• The virtual representation (Digital Twin).
• The data connection (bidirectional flow of information between the physical and virtual environments).

This framework allowed industries to integrate real-time data streams from physical assets into digital models, enabling predictive maintenance, process optimization, and lifecycle analysis [10,11] (Figure 2). NASA was among the early adopters of Digital Twin technology, employing DTws to simulate spacecraft conditions for mission planning and maintenance [12]. The ability to analyze real-time spacecraft telemetry data using DTws helped predict failures and optimize system performance in extreme environments. Over the past two decades, the advancement of IoT, AI, and cloud computing has significantly expanded the applications of DTws beyond aerospace. In manufacturing, DTws are widely used to monitor production lines, optimize supply chains, and improve quality control [2]. In healthcare, patient-specific DTws allow for personalized treatment simulations, reducing risks and improving medical outcomes [13]. The automotive and smart infrastructure industries have also adopted DTws to enhance design processes, simulate real-world conditions, and enable predictive analytics [14].

With the increasing adoption of Industry 4.0 technologies, DTws are now being used in complex, multi-scale systems that require high-fidelity modeling of physical assets. However, assessing the fidelity of DTws remains a challenge, as there is no universally accepted standard for evaluating geometric, functional, and behavioral accuracy [5]. The lack of standardized fidelity metrics can lead to inconsistencies in performance evaluation and cross-industry interoperability.

2. Literature Search Methodology

To ensure a rigorous, transparent, and reproducible review process, we adopted a systematic literature search and screening methodology consistent with PRISMA [15,16] guidelines. Our initial database search yielded a total of 389 articles (Figure 3), retrieved from leading academic databases such as IEEE Xplore, ScienceDirect, ACM Digital Library, and Google Scholar. These databases were selected for their comprehensive coverage of research related to digital twins (DTw), fidelity assessment, and 3D shape descriptors. The initial records were screened to remove duplicates, resulting in 181 unique articles. These articles underwent a title and abstract screening to determine their relevance to the core topics of our study—specifically, digital twin systems, shape descriptors, and fidelity metrics. During this phase, 83 articles were excluded for not aligning with the scope of the study. The most common reasons for exclusion at this stage included articles that lacked technical content on digital twins or fidelity evaluation and those that were conceptually unrelated despite containing overlapping keywords.

The remaining 98 articles progressed to the full-text review stage, where a more detailed evaluation was conducted. Articles were excluded if they did not meet the language requirement (English only), did not directly relate to digital twin systems, or did not include substantive discussion or application of fidelity metrics—particularly in the context of geometric, behavioral, or performance fidelity. These exclusion criteria were applied to ensure that only the most relevant and technically informative studies were retained. Ultimately, 60 articles were identified as meeting all inclusion criteria and were selected for the final synthesis. These articles form the foundational corpus of this review and were analyzed in depth to develop the proposed taxonomy of shape descriptors, establish links to ISO 30138 [8] standardization, and inform the development of a conceptual fidelity mapping framework for digital twin applications.

3. Digital Twin Technology

Digital Twins (DTws) are virtual representations of physical objects or systems that are continuously updated with real-time data to reflect the current operational status and predict future behavior [17]. These models integrate advanced technologies such as the Internet of Things (IoT), Artificial Intelligence (AI), and Big Data analytics to enable a two-way flow of information between the physical and digital domains [2]. DTws provide an interactive and dynamic platform where system performance can be monitored, analyzed, and optimized without directly affecting the physical entity. One of the key features of DTws is their ability to create high-fidelity simulations that help organizations make informed decisions by forecasting potential failures, optimizing operations, and improving resource utilization [18].

One of the primary advantages of DTws is their application in predictive maintenance. Unlike traditional maintenance strategies that rely on either reactive or scheduled maintenance, predictive maintenance leverages DTws to anticipate failures based on real-time data from embedded sensors [19]. By analyzing operational patterns, DTws allow organizations to intervene before a failure occurs, thus reducing unplanned downtimes and enhancing system longevity. Moreover, DTws facilitate system optimization by continuously analyzing and adjusting operational parameters to improve efficiency and reduce energy consumption. The ability of DTws to perform “what-if” scenario analyses allows businesses to assess different operational strategies and select the most effective approach without disrupting the real-world system [20].

3.1. Applications of Digital Twins in Various Industries

The adoption of DTws spans multiple industries, including aerospace, healthcare, manufacturing, and automotive, where they have been instrumental in improving operational efficiency, reducing costs, and enhancing safety. DTws play a crucial role in the aerospace sector by enabling real-time monitoring of aircraft components and predicting maintenance requirements. Rolls-Royce, for instance, employs DTws to model the performance of jet engines, using real-time data to assess wear and tear, predict potential failures, and optimize maintenance schedules [19].

Table 1. Industry applications of Digital Twin technology.

Industry	Key Applications	Primary Benefits	Real-World Example
Aerospace	-Real-time component monitoring -Predictive maintenance -Engine performance modeling	-Reduced failures -Lower maintenance costs -Enhanced flight safety	Rolls-Royce jet engine monitoring and failure prediction [19]
Healthcare	-Organ modeling -Treatment simulation -Disease progression prediction	-Non-invasive interventions -Personalized medicine -Reduced treatment risks	Cardiac intervention planning for personalized treatment [21]
Manufacturing	-Production line optimization -Quality control -Supply chain management	-Operational cost reduction -Defect prevention -Enhanced efficiency	Factory digital replica for workflow testing and bottleneck prediction [20]
Automotive	-Vehicle performance simulation -Crash testing -Autonomous driving development	-Improved safety standards -Fuel efficiency gains -Reduced R&D costs	Virtual testing environments for self-driving algorithms [22]

summarizes the industry-based applications of digital twin technology. By integrating DTws into aircraft systems, manufacturers and airline operators can minimize unexpected failures, reduce maintenance costs, and improve overall flight safety. In the healthcare sector, DTws have been applied to model human organs, providing a non-invasive method to predict disease progression and optimize treatment plans [21]. Personalized digital twins of patients enable doctors to simulate different treatment approaches and predict their effectiveness before administering them in real life. For example, in cardiology, DTws help physicians simulate how different interventions might affect a patient’s heart condition, thus aiding in personalized treatment plans. The manufacturing sector benefits significantly from DTws by optimizing production lines, improving supply chain management, and reducing operational costs [20]. By creating a digital replica of a factory, manufacturers can test new workflows, predict bottlenecks, and enhance production efficiency. Additionally, DTws support quality control by identifying defects in products before they reach the market, thereby improving overall product reliability. In the automotive industry, DTws are extensively used to simulate vehicle performance and improve safety standards. Automotive manufacturers use DTws to test different design configurations and assess their impact on vehicle dynamics, fuel efficiency, and crashworthiness [22]. Furthermore, DTws are used in autonomous vehicle development, allowing engineers to create virtual environments where self-driving algorithms can be trained and tested before deployment in real-world conditions.

3.2. Challenges in Digital Twin Implementation

Despite their numerous advantages, the implementation of DTws presents several challenges that must be addressed to unlock their full potential.

Table 2. Cross-industry implementation challenges.

Challenge	Key Issues	Impact	Mitigation Approaches
Interoperability	-Non-standardized data formats -Incompatible communication protocols	-Limited system integration -Reduced collaboration efficiency	Universal framework development [23]
Scalability	-Massive IoT/sensor data volumes -Computational resource limitations	-System responsiveness issues -Performance degradation at scale	High-performance computing infrastructure [5]
Standardization Gap	-Absence of unified frameworks -Inconsistent implementation methodologies	-Benchmarking difficulties -Validation challenges	Industry-wide standards adoption [24]
Security & Privacy	-Cyber-attack vulnerability -Data breach risks -IP theft threats	-Critical infrastructure disruptions -Loss of sensitive data	Encryption and continuous monitoring [25]
Implementation Costs	-High IoT/cloud infrastructure investment -Specialized training requirements	-Limited SME adoption -ROI achievement delays	Modular deployment strategies [18]

summarizes the cross-industry implementation challenges of Digital Twin technology. One of the significant barriers to DTw adoption is the lack of standardized data formats and communication protocols. Different industries and organizations use various software platforms, making it challenging to integrate DTw solutions seamlessly across different systems [23]. The absence of a universally accepted DTw framework limits data sharing and collaboration, thereby reducing the efficiency of DTw deployments. DTws generate vast amounts of data from embedded sensors and IoT devices, making scalability a critical concern [18]. As organizations expand their use of DTws, managing the increasing data volume becomes more complex, requiring advanced computational resources and robust data processing capabilities. Ensuring that DTws remain responsive and efficient at scale necessitates the development of high-performance computing infrastructures. The digital twin ecosystem currently lacks comprehensive standardization, making it difficult for industries to develop interoperable solutions [24]. Unlike traditional engineering models that follow specific guidelines, DTw frameworks vary widely, leading to inconsistencies in implementation. Without standardized methodologies, organizations face challenges in benchmarking performance, validating models, and ensuring compatibility across different platforms. As DTws rely heavily on real-time data exchange between physical and digital systems, they are susceptible to cyber threats. Unauthorized access to a DTw system can lead to data breaches, intellectual property theft, and potential disruptions in critical infrastructure [25]. Ensuring robust cybersecurity measures, such as encryption, access controls, and continuous monitoring, is essential to safeguard DTw applications. Developing and deploying DTws require significant investment in IoT devices, cloud computing, and data analytics infrastructure [18]. Small and medium-sized enterprises (SMEs) often struggle to afford the upfront costs associated with DTw implementation. Additionally, organizations must invest in workforce training to equip employees with the necessary skills to manage and maintain DTw systems effectively.

Digital Twins are transforming industries by enabling predictive maintenance, optimizing operations, and improving decision-making processes. From aerospace and healthcare to manufacturing and automotive, DTws are driving efficiency and innovation. However, challenges such as interoperability issues, scalability constraints, lack of standardization, cybersecurity risks, and high implementation costs must be addressed to maximize the benefits of DTws. As technology continues to evolve, the development of standardized frameworks and advancements in AI-driven analytics will play a crucial role in overcoming these challenges and expanding the adoption of DTws across industries.

4. Fidelity Metrics in Digital Twins

4.1. Definition and Importance of Fidelity Metrics

Fidelity in Digital Twins (DTws) refers to the degree of accuracy and completeness with which a digital representation mirrors its physical counterpart. It focuses on how well the digital model replicates the geometry, motion, and functional behaviors of the physical system—distinct from simulation or predictive analytics, which are downstream applications rather than intrinsic components of fidelity [8]. A high-fidelity DTw ensures that its digital counterpart accurately represents the physical object’s structure and behavior, enabling reliable analysis and decision-making [4]. Fidelity metrics thus provide quantitative means to evaluate this representational accuracy under defined conditions [5].

4.2. Categorization of Fidelity Metrics

To align with the structure proposed by ISO 30138 and to clearly separate fidelity from simulation-based outputs, this paper adopts the following categorization (see Figure 4).

Geometric Fidelity—Measures how closely the DTw’s shape, structure, and spatial dimensions correspond to the physical system. This is particularly relevant in CAD models, additive manufacturing, and 3D surface matching applications [26].

Motion Fidelity—Refers to the accuracy with which the DTw captures the movement characteristics of the physical system, including kinematics, displacement, and velocity profiles. It is essential in domains where mechanical or biomechanical motion play a role [27].

Functional Fidelity—Evaluates whether the DTw replicates the functional output or operational behavior of the physical system under specific tasks or scenarios. This includes force responses, fluid flows, or electrical outputs, depending on the application context [3].

By structuring fidelity along these three dimensions, this paper provides a focused framework for assessing and improving shape-based accuracy in DTws, particularly in the context of emerging standardization efforts such as ISO 30138 [8].

High-fidelity DTws require continuous data synchronization, real-time updates, and multi-domain integration, making fidelity assessment an essential component in design validation, process optimization, and system reliability [2]. High-fidelity Digital Twins serve as the foundation for physics-based simulations such as CFD (for fluid dynamics) and FEM (for structural stress and thermal response). However, these simulations depend on the fidelity of the digital representation—they are applications that follow the construction of a validated, high-accuracy DTw model, not components of fidelity itself.

While fidelity metrics and simulation are conceptually distinct, they are inherently interlinked in Digital Twin (DTw) systems. Specifically, simulation-based outputs often serve as reference benchmarks for assessing fidelity: functional fidelity is evaluated by comparing the DTw’s simulated outputs against the real system’s functional responses under equivalent conditions, while motion fidelity assesses how closely dynamic simulations replicate the actual kinematic or behavioral trajectories of the physical system. In this sense, simulations are not separate from fidelity metrics but are instrumental in defining and validating them. Therefore, high-fidelity simulation becomes a tool for fidelity assessment, providing target states or behaviors that fidelity metrics aim to quantify and compare. This interpretation aligns with ISO 30138 [8], where simulation is positioned as a downstream validation mechanism that draws upon a high-fidelity digital representation.

4.3. Importance of Fidelity in Critical Applications

The fidelity of a Digital Twin is particularly critical in high-stakes industries such as aerospace, healthcare, and advanced manufacturing, where even minor deviations in accuracy can lead to significant operational risks, safety hazards, or financial losses [14] .

4.3.1. Aerospace Industry

In aerospace applications, DTws are used to model aircraft components, flight dynamics, and predictive maintenance systems. Aircraft manufacturers, such as Boeing and Rolls-Royce, leverage high-fidelity DTws to simulate jet engine performance, material fatigue, and system failures [19]. The accuracy of these DTws directly impacts flight safety, fuel efficiency, and maintenance scheduling. Poor fidelity in a DTw could result in incorrect failure predictions, leading to unplanned downtime or catastrophic system failures [12].

4.3.2. Healthcare Industry

In the healthcare sector, patient-specific DTws are used to simulate organ functions, disease progression, and treatment outcomes. High-fidelity DTws assist in personalized medicine, surgical planning, and drug testing, reducing the risks associated with real-world medical interventions [13]. For example, cardiovascular DTws help predict how a patient’s heart will respond to a specific treatment, ensuring that procedures are tailored to individual needs [21]. Inaccurate DTw representations in healthcare can lead to misdiagnosis, ineffective treatment plans, or surgical complications.

4.3.3. Manufacturing and Smart Infrastructure

In smart manufacturing, fidelity metrics help maintain precision in automated assembly lines, quality control, and supply chain optimizations. DTws are used to simulate production workflows, enabling manufacturers to detect defects and optimize resource utilization before full-scale implementation [26]. Similarly, in civil engineering and infrastructure management, DTws are used to model structural integrity, energy efficiency, and smart grid operations, ensuring that digital replicas provide reliable predictions for maintenance and sustainability [4].

Across these industries, the need for high-fidelity DTws is imperative for ensuring safety, efficiency, and cost-effectiveness. The ability to accurately model, analyze, and predict system behavior is dependent on the effectiveness of fidelity metrics, necessitating robust assessment frameworks.

4.4. Existing Approaches to Fidelity Assessment

Numerous approaches have been developed to assess the fidelity of Digital Twins (DTws), tailored to the complexity of the system, application domain, and precision requirements. While traditional frameworks often blend geometric validation with simulation-based predictions, recent standards—such as ISO 30138 [8]—emphasize the need to separate fidelity assessment from simulation outcomes. Several standardization initiatives have emerged to guide the development and integration of digital twin systems. ISO/TR 24464:2020 [28] outlines visualization elements critical to digital twin interfaces, particularly for industrial data representation. Additionally, ISO/AWI TS 25271 [29] proposes a reference architecture for digital twin interfaces that ensures interoperability and scalability within industrial automation systems. Accordingly, fidelity in DTws can be understood through three primary dimensions: Geometric Fidelity, Motion Fidelity, and Functional Fidelity.

Geometric fidelity pertains to how accurately the DTw replicates the physical object’s shape, structure, and spatial characteristics. This is typically assessed using 3D shape descriptors such as Fourier descriptors [30], Zernike moments, and curvature-based techniques that capture invariant geometric features across transformations [7]. Additionally, point cloud comparisons derived from 3D scanning or LiDAR are frequently used to measure surface deviation, curvature consistency, and volumetric accuracy [6]. Quantitative geometric metrics like Hausdorff distance and Chamfer distance are applied to calculate deviation between corresponding surface points of the digital and physical models, providing precise indicators of geometric mismatch [31]. Recent advancements in 3D shape descriptors have significant implications for enhancing the fidelity of Digital Twin systems. One study evaluated various global and local shape descriptors using Kinect-like depth images and found that spin-images were particularly effective for class-based object recognition, while shape distributions were better suited for distinguishing between object instances—insights directly applicable to Digital Twins reliant on real-time sensor data for object recognition and model updates [32]. Complementing this, the ShapeBench framework introduced a standardized approach to benchmarking local 3D descriptors by proposing the Descriptor Distance Index (DDI), offering improved evaluation of point-wise correspondence and scalability, which are critical for ensuring accurate digital replication of complex surfaces [33].

Motion fidelity evaluates the extent to which a DTw replicates the kinematic or dynamic movement behavior of its physical counterpart. It is especially important in domains such as biomechanics, robotics, or aerospace systems. Fidelity metrics in this category may include displacement tracking, velocity profile matching, or time-synchronized comparison of motion sequences. While these assessments may rely on motion capture or sensor fusion, the focus remains on the faithful reproduction of movement rather than prediction. These metrics ensure the DTw preserves the time-resolved physical behavior of the system under realistic operating conditions [27].

Functional fidelity, meanwhile, measures the DTw’s ability to reproduce the output performance of the physical system when executing specific tasks. This could include pressure distribution in a valve, load-bearing capacity in a structural component, or energy output in an electromechanical system. Metrics used in this domain focus on comparing functional outputs between the physical and digital systems under matching input conditions. Functional fidelity does not include predictive modeling but emphasizes task-oriented alignment—how closely the DTw mimics the system’s operational functionality in measurable ways [3]. The assessment of DTw fidelity requires a structured and physically grounded approach that distinguishes representation quality (fidelity) from predictive analytics (simulation). The separation of fidelity into geometric, motion, and functional components enables more precise evaluation and aligns the assessment process with the architecture proposed by ISO 30138 [8].

4.5. Limitations of Traditional Shape Fidelity Metrics

While shape fidelity metrics are essential tools for evaluating the accuracy of geometric representations in Digital Twins (DTws), traditional approaches present several limitations. It is important to clearly distinguish between the simulation process—which aims to predict or reproduce system behavior—and the fidelity assessment process, which evaluates the accuracy of the digital representation based on comparison with the physical entity. This section addresses limitations specifically related to shape fidelity assessment, not simulation-based modeling.

4.5.1. Lack of Standardization

There is no universally accepted fidelity metric that applies uniformly across industries or DTw applications. As a result, shape fidelity assessments are often domain-specific, limiting cross-industry interoperability and benchmarking. Existing standards, including those under development, such as ISO 30138, recognize this gap and seek to define consistent frameworks for evaluating shape-based fidelity using standardized descriptors [1,34].

4.5.2. Inability to Capture Multi-Scale Features

Traditional geometric fidelity metrics, such as point cloud comparisons or surface deviation analysis, are often limited to macro-level shape differences and may fail to capture micro-scale or hierarchical features relevant in complex domains like biomedical modeling or microelectronics. This limitation is especially apparent when using surface-based metrics that overlook internal structures or volumetric consistency [27,35]

4.5.3. Computational Complexity—Clarifying Simulation vs. Assessment

A common misinterpretation is to conflate the computational burden of dynamic DTw simulations with that of fidelity assessment tools. Simulations, particularly those involving Multiphysics or time-dependent behaviors, often require high-performance computing resources due to their complexity and real-time processing demands [4,27]. However, shape fidelity metrics, especially descriptor-based methods—are generally computationally lightweight, particularly when used for post-processing or batch evaluation. Traditional shape descriptors, such as Fourier-based or Zernike moments [36,37], can be implemented efficiently and are well-suited for real-time or large-scale evaluations. Deep learning-based descriptors (e.g., CNNs) may involve greater computational costs, but primarily during the training phase. Once trained, their inference efficiency is comparable to traditional methods [38]. Therefore, it is essential to distinguish simulation complexity from descriptor evaluation, especially when proposing standardized fidelity scoring systems such as those envisioned by ISO 30138.

4.5.4. Data Heterogeneity and Integration Challenges

Digital Twin systems rely on continuous input from heterogeneous data sources—ranging from sensors, SCADA systems, and IoT devices to engineering databases and simulation outputs. These sources often differ in data structure, granularity, and semantics, creating significant integration challenges [2,23]. Inconsistent units, sampling rates, and metadata standards can degrade the accuracy of the DTw’s internal representation and, in turn, reduce shape fidelity. Addressing these issues requires standardized data schemas, ontology alignment, and preprocessing pipelines capable of normalizing incoming data streams.

4.5.5. Network and Latency-Induced Synchronization Issues

In real-time Digital Twin applications—especially those involving physical systems with dynamic states—latency between the physical entity and its digital counterpart introduces temporal inconsistencies. These may result from network congestion, limited bandwidth, or protocol delays in cloud-edge architectures [4]. For example, in manufacturing or smart grid systems, even a few milliseconds of delay can lead to mismatches in state estimation, affecting the DTw’s effectiveness in real-time control or monitoring. While not strictly a shape fidelity issue, such delays compromise the synchronous accuracy of the DTw and thus require mitigation through edge computing, timestamp alignment, or adaptive update cycles.

These limitations—ranging from semantic inconsistencies in data integration to latency-driven synchronization errors—highlight the need for robust, scalable data management and communication architectures that preserve fidelity in both static and real-time DTw applications.

4.6. Comparative Analysis of Related Studies

While several prior studies have explored aspects of fidelity in Digital Twins (DTws), their coverage is often fragmented across geometric modeling, behavioral simulation, and system performance evaluation. Table 3 provides a comparative summary of prominent studies, organized by their focus on fidelity dimensions—Geometric, Motion, and Functional—and whether they address standardization concerns, particularly alignment with ISO 30138.

Early works, such as Tangelder & Veltkamp [7] (Table 3), provide detailed reviews of shape descriptors but lack a DTw context. More recent studies, like those by Tao et al. [2] and Fuller et al. [4], examine fidelity from a conceptual or system design perspective, yet without proposing structured fidelity metrics. Other contributions (e.g., [26,39]) address domain-specific applications or propose modeling improvements but fall short of integrating fidelity assessments with evolving ISO standardization efforts. In contrast, the current study offers a novel synthesis of 3D shape descriptor methods, introduces a fidelity metric, and aligns ISO 30138’s scope by distinguishing shape fidelity from simulation-based predictive applications. The table below helps contextualize this contribution within the broader DTw research landscape. Desai et al. [40] propose a fidelity taxonomy that complements ISO efforts, although it is not explicitly standardized. Similarly, Agapaki & Brilakis [39] focus on DL-based geometric retrieval in industrial contexts, offering insight into descriptor-based fidelity assessment.

Table 3. Comparative Analysis of Major Studies on Digital Twin Fidelity Assessment.

Study	Year	Focus Area	Geometric Fidelity	Motion Fidelity	Functional Fidelity	Standardization Insight	Key Contribution
Tangelder & Veltkamp [7]	2008	3D shape retrieval methods	✔ In-depth	✖ Not addressed	✖ Not addressed	✖ Not discussed	Comprehensive survey of 3D shape descriptors for retrieval purposes.
Tao et al. [2]	2019	DTw architecture and applications	✔ Broad concepts	✔ General behaviors	✔ General behaviors	✖ Not specific	Proposed a conceptual framework for DTws, including fidelity considerations.
Negri et al. [26]	2017	DTw in manufacturing	✔ Point cloud, geometry	✔ Simulated behavior	✔ Simulated behavior	✖ No ISO link	Discussed shape and simulation fidelity in manufacturing contexts.
Fuller et al. [4]	2020	DTw enabling technologies	✔ Mentioned	✔ Latency and synchronization	✔ Latency & synchronization	✖ General observations	Identified challenges and open questions in DTw standardization.
Kim et al. [23]	2023	Fidelity design model for DTws	✔ Detailed	✔ Detailed	✔ Detailed	✔ ISO-aligned	Introduced concepts of similarity, correspondence, and fidelity in DTws.
Desai et al. [40]	2023	Multi-fidelity modeling and uncertainty quantification	✔ Surrogate models	✔ Surrogate models	✔ Surrogate models	✖ Not discussed	Proposed a framework for enhanced multi-fidelity modeling in DTws.
Agapaki & Brilakis [39]	2022	Geometric DTws for industrial facilities	✔ Deep learning-based	✖ Not addressed	✖ Not addressed	✖ Not discussed	Developed a method for retrieving industrial shapes for geometric DTws.
Sharma et al. [41]	2022	State of the art in DTw theory and practice	✔ Overview	✔ Overview	✔ Overview	✖ Not specific	Reviewed DTw features, challenges, and open research questions.
ISO/IEC AWI TR 30138 [8]	2025	Fidelity metric standard for DTw systems	✔ Under development	✔ Under development	✔ Under development	✔ ISO standard	Establishing a standardized approach to DTw fidelity metrics.
This paper (Current Study)	2025	Shape fidelity evaluation in DTws	✔ Deep comparison, taxonomy	✔ Motion/functional reclassification	✔ Motion/functional reclassification	✔ Linked to ISO 30138	Proposes a fidelity metric centered on 3D shape descriptor evaluation, aligned with ISO 30138.

Where: ✔ (Full support), ✖ (Not supported).

Table 3. Comparative Analysis of Major Studies on Digital Twin Fidelity Assessment.

Study	Year	Focus Area	Geometric Fidelity	Motion Fidelity	Functional Fidelity	Standardization Insight	Key Contribution
Tangelder & Veltkamp [7]	2008	3D shape retrieval methods	✔ In-depth	✖ Not addressed	✖ Not addressed	✖ Not discussed	Comprehensive survey of 3D shape descriptors for retrieval purposes.
Tao et al. [2]	2019	DTw architecture and applications	✔ Broad concepts	✔ General behaviors	✔ General behaviors	✖ Not specific	Proposed a conceptual framework for DTws, including fidelity considerations.
Negri et al. [26]	2017	DTw in manufacturing	✔ Point cloud, geometry	✔ Simulated behavior	✔ Simulated behavior	✖ No ISO link	Discussed shape and simulation fidelity in manufacturing contexts.
Fuller et al. [4]	2020	DTw enabling technologies	✔ Mentioned	✔ Latency and synchronization	✔ Latency & synchronization	✖ General observations	Identified challenges and open questions in DTw standardization.
Kim et al. [23]	2023	Fidelity design model for DTws	✔ Detailed	✔ Detailed	✔ Detailed	✔ ISO-aligned	Introduced concepts of similarity, correspondence, and fidelity in DTws.
Desai et al. [40]	2023	Multi-fidelity modeling and uncertainty quantification	✔ Surrogate models	✔ Surrogate models	✔ Surrogate models	✖ Not discussed	Proposed a framework for enhanced multi-fidelity modeling in DTws.
Agapaki & Brilakis [39]	2022	Geometric DTws for industrial facilities	✔ Deep learning-based	✖ Not addressed	✖ Not addressed	✖ Not discussed	Developed a method for retrieving industrial shapes for geometric DTws.
Sharma et al. [41]	2022	State of the art in DTw theory and practice	✔ Overview	✔ Overview	✔ Overview	✖ Not specific	Reviewed DTw features, challenges, and open research questions.
ISO/IEC AWI TR 30138 [8]	2025	Fidelity metric standard for DTw systems	✔ Under development	✔ Under development	✔ Under development	✔ ISO standard	Establishing a standardized approach to DTw fidelity metrics.
This paper (Current Study)	2025	Shape fidelity evaluation in DTws	✔ Deep comparison, taxonomy	✔ Motion/functional reclassification	✔ Motion/functional reclassification	✔ Linked to ISO 30138	Proposes a fidelity metric centered on 3D shape descriptor evaluation, aligned with ISO 30138.

Where: ✔ (Full support), ✖ (Not supported).

5. Shape Descriptors: A Key Component for Fidelity Metrics

A shape descriptor is a mathematical or computational representation that captures the essential geometric features of a 2D or 3D object in a compact and transformation-invariant form. In the context of Digital Twins (DTws), shape descriptors are used to quantify the similarity between the physical object and its digital counterpart based on structural, spatial, and surface characteristics. They are widely used in domains such as computer vision, pattern recognition, and Digital Twin technology to compare, classify, and retrieve shapes based on geometric properties [6,7]. Effective shape descriptors exhibit invariance to translation, rotation, and scale, and demonstrate robustness to noise, occlusion, and geometric distortion. These descriptors can be broadly categorized into several types, including boundary-based, region-based, texture-based, structural, Fourier-based, and deep learning-based descriptors, each with specific strengths and limitations, depending on the application domain [6,7,31,42].

5.1. Historical Development and Types of Shape Descriptors

Shape descriptors are mathematical constructs that encode the geometric characteristics of objects into compact, computationally usable forms. In the context of Digital Twin (DTw) systems, shape descriptors are foundational to quantifying geometric fidelity—the degree to which a digital model replicates the shape and structural attributes of its physical counterpart [6,7]. Effective descriptors enable accurate assessment of how closely a DTw aligns with the form, surface, and structure of real-world objects, supporting core validation tasks in manufacturing, healthcare, and infrastructure modeling.

Shape descriptors are systematically categorized based on the geometric and structural features they capture, as illustrated in Figure 5. These descriptors play a foundational role in evaluating geometric fidelity in Digital Twin (DTw) systems, aligning with ISO 30138, which emphasizes geometric fidelity as a prerequisite for validating the digital-physical correspondence. Classical descriptors are broadly divided into boundary-based, region-based, and texture-based categories. Boundary-based descriptors analyze the outer contour of a shape and are especially efficient for clean, well-defined geometries. Notable examples include Chain Codes [43], Shape Contexts [31], and Curvature Scale Space [42]. Region-based descriptors, on the other hand, extract information from the entire shape interior, making them more robust against noise and deformation. Prominent methods in this group include Moment Invariants [44], Zernike Moments [36], Geometric Moments, and the Radial Basis Function [45]. Texture-based descriptors, such as the Gray Level Co-occurrence Matrix [46] and Local Binary Patterns [47], focus on surface pattern features and are particularly valuable when texture plays a significant role in shape characterization.

Beyond classical methods, structural descriptors model the topological and relational aspects of shapes, offering insight into internal organization and connectivity. These include skeleton-based approaches such as Shock Graphs [48,49], and graph-based techniques like Attributed Relational Graphs [50] and Reeb Graphs. Contextual representations like Shape Contexts [31] provide a bridge between structural and statistical information, allowing for more comprehensive fidelity evaluation. With the emergence of modern learning paradigms, deep learning-based descriptors have become increasingly influential. These include Convolutional Neural Networks [34], Recurrent Neural Networks [51], and unsupervised learning techniques such as the Descriptor Distance Index (DDI) based on autoencoders [52]. These methods automatically learn hierarchical, task-specific shape features from data, enabling them to adapt effectively to diverse application domains, including autonomous systems and medical imaging [53]. Hybrid descriptors are also gaining prominence by combining characteristics from multiple descriptor families to improve robustness and adaptability. Examples include Combined Boundary and Region Descriptors and Combined Shape and Texture Descriptors [6]. These hybrids reflect a broader trend toward flexible, context-aware geometric fidelity evaluation methods that can accommodate complex real-world variability. While shape descriptors do not directly assess temporal or functional behaviors, they provide the necessary geometric baseline for higher-level simulation, behavioral modeling, and predictive analytics in DTw systems [2,4].

In alignment with ISO 30138, which emphasizes geometric fidelity as the foundation for broader DTw validation, this paper leverages shape descriptors as a core tool for evaluating the accuracy of digital-physical shape correspondence. While descriptors do not directly capture temporal or functional behaviors, they provide the geometric baseline necessary for advanced simulation and predictive modeling, thus supporting the multi-layered architecture of DTw systems [2,4].

Figure 5. Technology tree for shape descriptor methods [6,7,31,36,42,43,44,45,46,47,49,51,52].

Figure 5. Technology tree for shape descriptor methods [6,7,31,36,42,43,44,45,46,47,49,51,52].

5.2. Comparative Evaluation of Shape Descriptors

Table 4. Comparison of different methods.

Criterion	Boundary-Based	Region-Based	Texture Based	Structural	Fourier-Based	Deep Learning Based (3D Shape Descriptor)	Hybrid
Translation Invariance	✔	✔	✔	✔	✔	✔	✔
Rotation Invariance	✔	✔	✔	✔	✔	✔	✔
Scale Invariance	✔	✔	✔	✔	✔	✔	✔
Handling of Noise and Distortion	✖	✖	⭘	⭘	✖	✔	⭘
Representation of Complex Shapes	⭘	✔	✔	✔	✖	✔	✔
Computational Efficiency	✔	✔	⭘	✖	✔	✔	⭘
Robustness of Occlusion	✖	✖	✖	⭘	✖	✔	⭘
Ability to Learn from Data	✖	✖	✖	✖	✖	✔	✔
Generalization to Unseen Data	✖	✖	✖	✖	✖	✔	⭘
Flexibility for different domains	✖	✔	✔	✔	✖	✔	⭘

Where: ✔ (Full support), ✖ (Not supported), ⭘ (partially supported).

provides a comparative analysis of various shape descriptors used in image processing and computer vision, evaluated across several performance criteria. The descriptors are categorized into Boundary-Based, Region-Based, Texture-Based, Structural, Fourier-Based, Deep Learning-Based (3D Shape Descriptor), and Hybrid types. Each descriptor type is assessed for its effectiveness in meeting specific criteria such as translation invariance, rotation invariance, scale invariance, handling of noise and distortion, representation of complex shapes, computational efficiency, robustness to occlusion, ability to learn from data, generalization to unseen data, and flexibility for different domains. The criteria were selected according to ISO 30138’s fidelity pillars (invariance, robustness) and industry requirements (computational efficiency, occlusion handling). The scores are derived from consensus in the literature [6,33,38].

All descriptor types exhibit strong translation, rotation, and scale invariance, suggesting their robustness in maintaining consistent shape representations despite changes in position, orientation, or size of the object within the image. However, they vary significantly in their ability to handle noise and distortion; most types struggle, except for Deep Learning-Based and Hybrid descriptors, which show partial resilience. In terms of representing complex shapes, the Region-Based, Texture-Based, and Structural descriptors excel, providing detailed and accurate representations, whereas Boundary-Based and Hybrid types show moderate capabilities.

Computational efficiency is another critical factor, with Boundary-Based descriptors (Table 4) noted for their efficiency. In contrast, Texture-Based and Fourier-Based descriptors are less efficient, and Hybrid and Deep Learning-Based types are moderately efficient. Robustness to occlusion is challenging for most descriptors; however, Hybrid and Deep Learning-Based descriptors show some capability to manage occlusions, likely due to their comprehensive learning and feature integration strategies. A unique strength of Deep Learning-Based descriptors is their ability to learn from data, which allows these models to continuously improve and adapt through exposure to more examples. This learning capability also aids in generalizing new, unseen data, a significant advantage in practical applications in which data variability is common. In terms of flexibility across different domains, Region-Based Descriptors stand out as particularly adaptable, which is crucial for analyzing diverse image types. Hybrid descriptors also offer some flexibility, benefiting from the integration of multiple descriptor features. This analysis underscores the diverse strengths and limitations of each descriptor type, guiding the selection of appropriate methods for specific applications in image processing and computer vision. The use of Deep Learning-Based and Hybrid descriptors is particularly notable for their advanced capabilities in learning and adapting to new data and conditions.

6. Digital Twin Standardization and ISO 30138

As Digital Twin (DTw) systems continue to proliferate across various industries, there is a growing demand for standardized methodologies to evaluate and benchmark fidelity. Standardization plays a crucial role in ensuring interoperability, consistency, and trust in DTw implementations, particularly when these systems span heterogeneous data sources and application contexts. In response to this need, the ISO/IEC AWI TR 30138 [8] technical report aims to establish a framework for assessing Digital Twin fidelity, with an emphasis on geometric accuracy and shape-based representation. Although ISO/IEC 30138 has not yet been finalized or made publicly accessible, it offers a forward-looking structure that distinguishes shape fidelity from application-layer functions such as simulation, behavioral modeling, or predictive analytics. This delineation is consistent with the ISO “onion model,” which positions simulation as an outcome built upon a validated high-fidelity core [2,4].

Rather than treating ISO/IEC 30138 as a prescriptive requirement, this paper uses its proposed fidelity framework as a conceptual guide to organize and inform shape fidelity assessment. Specifically, our work focuses on geometric fidelity, evaluated through 3D shape descriptors—computational methods that quantify structural similarity between the physical object and its digital counterpart [6,7]. In line with the goals outlined in the draft standard, we present a fidelity metric that aligns descriptor attributes—such as transformation invariance, computational efficiency, and robustness to noise—with domain-specific fidelity requirements. While the ISO/IEC 30138 standard is expected to expand its scope to encompass motion and functional fidelity in future iterations, its current focus on geometric fidelity offers a timely and relevant foundation for shaping best practices. This study contributes to this evolving landscape by (1) identifying limitations in conventional shape fidelity methods, (2) classifying descriptor types based on performance criteria proposed in ISO 30138, and (3) offering application-driven guidance for integrating shape descriptors into scalable fidelity assessment frameworks [17].

6.1. Ongoing Standardization Efforts

Several organizations are actively involved in DTw standardization. The Digital Twin Consortium (DTC) is a global initiative that includes industry leaders, government bodies, and academic institutions working to establish interoperability frameworks, reference architectures, and security standards for DTw systems (Digital Twin Consortium [54]). The consortium aims to create a common foundation that allows DTws from different vendors and industries to function seamlessly.

The International Organization for Standardization (ISO) has also contributed significantly to DTw standardization. Through its ISO/IEC JTC 1/SC 41 initiative, ISO is developing standards for DTw data management, integration methodologies, and validation frameworks (ISO [8]). These efforts aim to enhance the compatibility of DTws with existing enterprise systems, such as manufacturing execution systems (MESs) and enterprise resource planning (ERP) platforms [55]. Similarly, the Institute of Electrical and Electronics Engineers (IEEE) P2806 working group is working on a standard framework for DTw systems, outlining best practices for data modeling, real-time synchronization, and predictive analytics [2].

These standardization efforts are critical for ensuring cross-platform interoperability and promoting the broader adoption of DTws. However, despite ongoing progress, achieving universal standardization remains a challenge.

6.2. Challenges to Achieving Universal Standardization

Several obstacles hinder the establishment of universal DTw standards. One of the primary challenges is the complexity of interconnected systems, as DTws often integrate heterogeneous data sources, diverse software environments, and varying computational models [17]. This complexity makes it difficult to develop a single, universally applicable standard that can cater to the diverse needs of industries such as aerospace, healthcare, and manufacturing [20]. Another major challenge is the variability in fidelity measurement approaches. Different industries require varying levels of geometric, behavioral, and performance fidelity, making it difficult to establish a unified framework for fidelity assessment [2]. For instance, aerospace DTws require precise geometric and structural accuracy for flight simulations, while manufacturing DTws prioritize process optimization and efficiency over physical replication [55]. This variation complicates efforts to define universal fidelity metrics that are applicable across all domains.

Furthermore, fragmentation among standardization bodies poses a significant hurdle. Organizations such as ISO, IEEE, and the Digital Twin Consortium often operate independently, leading to overlapping or conflicting standards. This lack of coordination can result in inconsistent implementation guidelines, making it difficult for companies to adopt a unified approach to DTw development and deployment. Security and data privacy also play a role in limiting standardization. Because DTws often process sensitive operational and proprietary data, standardization must address cybersecurity challenges, including encryption, authentication, and access control. Without robust security measures in place, industries may be reluctant to fully integrate standardized DTw frameworks into their operations. Overcoming these challenges will require greater collaboration among industry stakeholders, regulatory bodies, and researchers. Developing flexible and adaptive standardization frameworks that accommodate industry-specific needs while maintaining cross-platform interoperability is key to unlocking the full potential of DTws in smart manufacturing, infrastructure management, and predictive maintenance.

7. Future Directions in Digital Twin Research

7.1. Innovations in Fidelity Metrics

Emerging trends in fidelity metrics are shaping the evolution of Digital Twin (DTw) technology by enhancing accuracy and reliability through advanced computational techniques. One of the most promising developments is the integration of advanced 3D shape descriptors, which allow for precise geometric representations of physical objects in a digital environment. These descriptors, including Fourier-based, curvature-based, and machine learning-enhanced shape descriptors, improve DTw fidelity by ensuring more accurate surface reconstruction, structural validation, and object recognition [35]. Such advancements enhance the ability of DTws to capture complex physical attributes, making them more effective for applications such as precision manufacturing and biomedical simulations.

Additionally, machine learning (ML) and artificial intelligence (AI)-driven techniques are increasingly being integrated into fidelity assessment frameworks. Deep learning models, such as convolutional neural networks (CNNs) and generative adversarial networks (GANs), are being employed to refine DTw representations by automatically learning and reconstructing high-fidelity models from sensor data [56]. These AI-enhanced approaches reduce the dependency on manual model calibration and increase the adaptability of DTws to real-time operational changes. Furthermore, unsupervised learning methods are being explored to autonomously detect discrepancies between physical and digital counterparts, thereby improving predictive maintenance and anomaly detection in industrial applications [23].

Another notable innovation is the use of probabilistic modeling for dynamic fidelity assessment. Traditional fidelity metrics focus primarily on static shape accuracy; however, probabilistic approaches enable the evaluation of behavioral fidelity by predicting variations in performance over time [57]. These models enhance DTw functionality by accounting for uncertainty in operational conditions, making them highly valuable for industries such as aviation, energy, and autonomous systems.

7.2. Focused Research Directions in Shape Fidelity

This review identifies key opportunities to advance shape fidelity assessment in Digital Twins (DTws) through targeted research and standardization strategies, particularly in alignment with the scope of ISO 30138, which focuses exclusively on shape fidelity using 3D shape descriptors. Broader fidelity types, such as motion and behavioral fidelity, are expected to be addressed in future standards and are outside the scope of this paper.

7.2.1. Fidelity Metric for Shape Descriptor Mapping

We propose a fidelity metric that aligns 3D shape descriptor types—such as Fourier-based, Zernike moments, and deep learning-based descriptors—with application-specific shape fidelity requirements. This metric enables systematic selection of descriptors based on factors like transformation invariance, noise resistance, and computational efficiency. It provides a standardized and scalable framework for descriptor selection across domains such as manufacturing, medical imaging, and smart infrastructure, fully within the context of shape-based geometric fidelity.

7.2.2. ISO 30138-Informed Fidelity Classification Framework

ISO 30138 calls for metric development grounded in shape descriptors. Building on this, we propose a descriptor-based classification system in which shape fidelity levels are defined by descriptor capabilities. For instance, high-fidelity use cases may demand AI-based descriptors robust to deformation and occlusion, while lower-fidelity applications may rely on region-based methods. This approach supports adaptive shape fidelity scoring and offers a standardized path for integration into ISO 30138 validation processes.

7.2.3. Descriptor-Aware Benchmarking Protocols and Datasets

A key gap in current practice is the absence of standardized benchmarking resources tailored to shape fidelity. We advocate for the creation of descriptor-aware datasets and evaluation protocols that test descriptor performance under controlled geometric transformations, noise, and resolution constraints. These tools will enable consistent fidelity scoring across platforms and support ISO-compliant validation workflows.

7.2.4. Domain-Specific Shape Fidelity Profiles

Shape fidelity requirements vary significantly across application domains. For instance, implant modeling in biomedical engineering may necessitate micro-level resolution to capture fine anatomical detail, whereas infrastructure-oriented Digital Twins (DTws) often prioritize broader geometric conformity and structural integrity. In this context, we outline the conceptual basis for developing domain-specific fidelity profiles—modular configurations that define descriptor performance thresholds, accuracy tolerances, and geometric resolution requirements tailored to specific sectors. These profiles are intended to guide the selection and calibration of shape descriptors within the fidelity metric framework introduced earlier in this paper. Full implementation of these profiles, including validation procedures and sector-specific benchmarks, will be presented in a companion study [58], which operationalizes the proposals outlined here. By focusing exclusively on shape fidelity, this section remains aligned with the scope and intent of ISO 30138 and provides a foundation for future integration into evolving standardization efforts.

7.2.5. Implementation Workflow Overview

The proposed fidelity assessment workflow begins with acquiring both the physical 3D object and its corresponding digital twin model [59,60]. For the physical asset, a 3D scanner is employed to capture its geometry (Figure 6), while the digital counterpart is obtained from a CAD-based virtual model [61]. Both inputs undergo depth image generation through multi-view rendering, which produces multiple 2D projections from varying perspectives. These depth images are then processed by a 3D shape descriptor—implemented using convolutional neural network (CNN) architectures such as ResNet50 or VGG19—to extract robust feature vectors. The extracted features from both the physical and digital models are compared within the fidelity computation stage, where Descriptor Distance Index (DDI) (Appendix A.1) and Optimal Support Radius (OSR) (Appendix A.2) are evaluated to quantify the fidelity between the two representations. Finally, the computed metrics are aggregated into an evaluation report, which summarizes the fidelity level and provides insight into potential deviations between the physical asset and its digital twin. This condensed version ensures that essential methodological details, computational steps, and metric definitions are accessible within the current review, reducing reliance on the companion paper for conceptual understanding.

8. Conclusions

This study advances the field of Digital Twin (DTw) fidelity assessment through a systematic examination of 3D shape descriptors and their role in quantifying geometric correspondence between physical assets and their digital counterparts. By establishing a clear taxonomy that distinguishes geometric fidelity from motion and functional dimensions, we provide a crucial framework for standardized evaluation aligned with emerging ISO/IEC AWI TR 30138 guidelines. Our primary contributions include the following: (1) the development of a descriptor-based fidelity metric that correlates transformation invariance, noise robustness, and computational efficiency with application-specific requirements; (2) a comprehensive classification of shape descriptor families that informs optimal selection for different DTw use cases; and (3) concrete recommendations for integrating these approaches into evolving standardization efforts. The practical implications of this work extend across multiple domains, from enabling sub-millimeter accuracy in medical imaging applications to supporting real-time quality control in smart manufacturing environments and ensuring structural integrity in large-scale infrastructure projects. In aerospace applications, the framework facilitates mission-critical part validation, while in autonomous vehicle development, it supports precise virtual testing of safety-critical components.

While this study provides foundational insights, several limitations must be acknowledged. The current focus on geometric fidelity represents an essential but incomplete picture of DTw validation, as behavioral and functional dimensions require complementary assessment methodologies. Additionally, the computational requirements for real-time implementation of high-fidelity descriptors warrant further optimization studies, particularly for resource-constrained environments. The rapid evolution of deep learning-based approaches also necessitates ongoing framework updates to maintain relevance. These limitations notwithstanding, the proposed methodology establishes a critical baseline for future research directions, including the development of integrated multi-modal fidelity frameworks and domain-specific implementation profiles. As Digital Twin technology continues to mature across industries, the geometric fidelity foundation established in this work will serve as an indispensable component of comprehensive validation protocols, ensuring the reliability and interoperability of DTw systems in increasingly complex Industry 4.0 applications. Future efforts should build upon this foundation by incorporating temporal metrics for motion fidelity and performance indicators for functional validation, while standardization bodies may leverage our classification system to develop sector-specific implementation guidelines.