Intelligent restoration expert system design for Jingdezhen export porcelain via improved denoising diffusion probabilistic model

As a millennium-old “Porcelain Capital” and a key departure point of the Maritime Silk Road, Jingdezhen has produced ceramics renowned for their exquisite craftsmanship and profound cultural significance, representing a vital legacy of cultural exchange between China and the world¹. Since the Song and Yuan dynasties, Jingdezhen’s export porcelain has been traded via the Maritime Silk Road to Asia, Europe, Africa, and the Americas, becoming a model for East-West cultural interaction^2,3. These wares (Fig. 1) not only preserve traditional Chinese craftsmanship but also incorporate Western aesthetic preferences, exemplifying cross-cultural innovation in world art history and earning recognition in museum collections worldwide⁴. However, due to the inherent fragility of porcelain and environmental factors such as light exposure, the patterns on these artifacts are prone to damage, resulting in the loss of artistic essence. Traditional manual restoration processes are complex and technically demanding, typically requiring skilled professionals to assess, clean, bond, and fill damaged areas⁵. While conventional digital restoration tools, such as Photoshop software, can fill blurred or missing image regions, they often yield unnatural edges and aesthetically unsatisfactory results after retouching⁶. To more effectively recover the original features and historical value of damaged porcelain, intelligent restoration technologies, characterized by high efficiency and precision-offer promising solutions to the limitations of traditional restoration methods.

The pictures of exquisite export porcelain.

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Traditional porcelain restoration techniques can be broadly categorized into manual restoration and conventional image-based restoration, both of which involve repairing missing sections of the artifact or removing specific defects. Manual restoration directly addresses the physical object and is guided by the principles of “restoration to original appearance”, “minimum intervention”, and “reversibility”⁷. However, manual methods are often time-consuming and costly, and the cultivation of skilled restoration professionals remains challenging, presenting significant obstacles to the conservation of ancient porcelain.

Conventional image-based restoration refers to the digital repair of damaged porcelain artifacts, utilizing pixel-level inpainting techniques to recover their original appearance. For example, Fang et al.⁸ proposed a digital image processing model for the restoration of cracks in ancient ceramics, which has improved the accuracy of crack repair. Zheng et al.⁹ developed a method for blue-and-white porcelain image processing based on multi-scale Retinex and histogram multi-threshold segmentation. The main advantage of traditional image-based restoration lies in its non-contact approach, which prevents secondary damage to the artifact. However, the process remains highly dependent on manual intervention to ensure restoration accuracy and visual naturalness.

Intelligent restoration technologies for ancient porcelain primarily encompass two aspects: (1) the application of deep learning techniques to repair damaged areas. For instance, Lamb et al.¹⁰ proposed an automated method based on deep learning to predict and restore the shapes of damaged 3D objects, aiming for the automated restoration of ancient Greek ceramics. (2) Restoration techniques based on digital technologies. Liu et al.¹¹ achieved reversible restoration of Song dynasty gilt black Ding ware by employing digital acquisition, 3D printing, and virtual reconstruction. Intelligent restoration technologies for ancient porcelain offer significant advantages, including high restoration accuracy and detail recovery, improved efficiency in fragment classification, and reduced need for manual intervention.

The rapid advancement of Artificial Intelligence (AI) is emerging as a cutting-edge technology in the field of cultural heritage restoration. By leveraging big data analytics, image recognition, and 3D modeling¹², AI provides precise and efficient support for porcelain restoration¹³. In recent years, AI, particularly GAN, has achieved remarkable progress in computer-based image restoration and has become a research hotspot in cultural heritage restoration worldwide. Many researchers have successfully applied GAN to the restoration of lacquerware¹⁴, textiles¹⁵, images¹⁶, and murals^17,18, among other areas. The application of GAN in artistic image restoration offers notable advantages, such as high flexibility and low resource requirements. However, GAN also has limitations, including large data requirements, challenges in content inference, and model instability. Compared with GAN, DDPM presents a distinct technical approach and exhibits considerable potential in the field of image restoration. The concept of the Diffusion Model was first introduced in 2015 by Sohl-Dickstein et al.¹⁹. DDPM²⁰ demonstrates significant advantages in image generation, including stable training processes and straightforward inference, and is suitable for a wide range of image generation tasks. They can generate images of varying resolutions and styles by controlling noise levels and even support text-to-image generation based on textual descriptions²¹. Nevertheless, in image restoration tasks, DDPM often encounters difficulties with complex textures and semantic content, leading to inconsistencies between generated images and known regions, as well as limited generalization capabilities, which can affect restoration outcomes. Consequently, numerous researchers have proposed innovative improvements to conventional DDPM to enhance their performance in image restoration tasks. For example, Lu et al.²² developed a DDPM-based method for underwater image enhancement (UW-DDPM). In addition, numerous image restoration approaches based on Transformer architectures have been reported. For example, Xu et al.²³ proposed a diversified image inpainting method that integrates the Transformer and DDPM frameworks, aiming to address the challenge of generating diverse and realistic restoration results. In the cultural heritage field, Zheng et al.²⁴ introduced a method for ancient ceramic restoration based on texture stitching using image processing techniques. Hu et al.²⁵ developed the GuidePaint approach, which leverages a lossless image-guided diffusion model to tackle the restoration of ancient murals. Compared to the aforementioned restoration methods, the improved DDPM proposed in this study offers several advantages in the restoration of ancient porcelain. Relative to GuidePaint, the improved DDPM more effectively addresses the restoration of complex surface textures and patterns on porcelain through conditional generation and multi-timestep information fusion. Unlike the texture-stitching-based method for ceramic restoration, the improved DDPM does not rely on traditional texture matching but instead learns the image distribution to generate restoration content directly from noise. This allows for semantically informed restoration in areas where textures are indistinct, minimizing matching errors and yielding superior results for damaged porcelain surfaces. Compared with the Diversified Image Inpainting method, the improved DDPM is specifically optimized for porcelain restoration tasks: by sampling unmasked regions and performing conditional generation during the reverse diffusion process, it can more accurately recover the original features of porcelain, better meeting the high standards of detail and authenticity required for ceramic restoration.

Although the improved DDPM has demonstrated considerable potential in various fields, its application in ceramic restoration remains relatively unexplored. This study represents a pioneering effort to apply the improved DDPM to the restoration and design of ceramic art, opening new possibilities for ceramic creation²⁶. At present, several unresolved challenges persist in the field of image restoration for cultural heritage. For example, semantic consistency remains a critical issue, as restored image textures and structures often fail to match those of the original artifact. To address these challenges, the improved DDPM proposed in this study samples unmasked regions and performs conditional generation during the reverse diffusion process, thereby enhancing semantic consistency in image restoration. This approach enables the precise reconstruction of porcelain textures, colors, and patterns. The intelligent restoration expert system integrates this algorithm to achieve automated and intelligent restoration, thereby improving both efficiency and applicability. As discussed earlier, traditional methods are limited in maintaining semantic consistency, and early AI-based techniques have struggled with texture recovery and structural matching. In response to these limitations, the improved DDPM enhances semantic consistency through its conditional generation mechanism, while the intelligent restoration expert system translates this capability into a practical engineering solution, effectively addressing challenges in restoration efficiency and applicability.

Compared with previous research on porcelain restoration, this study achieves several innovative breakthroughs. In terms of restoration technology, the improved DDPM simulates natural pattern generation, enabling the effective recovery of textures and motifs on Jingdezhen export porcelain, particularly when dealing with complex damage, thus yielding more authentic restoration results. Regarding system development, the proposed intelligent restoration expert system integrates the improved DDPM algorithm, streamlining the workflow and reducing reliance on specialized personnel. As a result, non-experts can efficiently perform high-quality restoration. In terms of technological application and cultural dissemination, the use of deep learning for digital porcelain restoration avoids physical damage to artifacts and supports digital documentation and archiving. This approach facilitates the digital transformation of cultural heritage conservation and broadens avenues for the dissemination of porcelain culture. The innovations presented in this study offer new perspectives for the restoration of ancient porcelain and the protection of cultural heritage, contributing to the transmission and creative development of cultural legacies.

This study focuses on the restoration of Jingdezhen export porcelain, with the workflow illustrated in Fig. 2. Data collection: Images of export porcelain were collected through web scraping, scanning of ceramic literature, and field investigations. High-quality images were selected and uniformly processed to 256 × 256 pixels to construct the experimental dataset. Model development and optimization: The improved DDPM was employed to restore damaged patterns, and its performance was compared with that of the FMM and GAN. By introducing an enhanced PatchMatch Stereo Estimation (PSE) module and incorporating information from known image regions, the reverse diffusion and resampling processes were adjusted to optimize the model, resulting in a significant improvement in restoration accuracy. Intelligent restoration system construction: Advanced technologies were integrated to design the front-end and back-end architecture, with the back-end developed using the Flask framework to handle requests and data, forming a digital web platform. Evaluation protocol: Porcelain plate samples were selected for restoration experiments. The performance of various methods was quantitatively compared using the Structural Similarity Index (SSIM), Peak Signal-to-Noise Ratio (PSNR), and Learned Perceptual Image Patch Similarity (LPIPS) metrics. SSIM quantifies structural consistency between restored and original images by computing similarities in structural information, luminance, and contrast. PSNR, based on the root mean square error of pixel differences, measures noise suppression after image restoration. LPIPS utilizes pre-trained neural networks to extract high-level semantic features, assessing the perceptual similarity between the restored region and the original image. Together, these metrics enable a comprehensive evaluation of restoration quality at the pixel, structural, and semantic-perceptual levels.

The proposed research framework.

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Extensive images of Jingdezhen export porcelain were collected through multiple channels, including web image scraping using Python and scanning images from historical porcelain catalogs. To ensure image quality and integrity, the collected materials were filtered and cleaned: images with low resolution, cluttered backgrounds, or distorted patterns were removed before constructing the porcelain image database. Given the limited sample size, data augmentation techniques such as rotation and flipping were employed to increase dataset diversity and alleviate the constraints of insufficient samples. In addition to complete porcelain plate images, two categories of damaged types, generally damaged and severely damaged, were included, each accounting for 5% of the total training set. By introducing diverse damage scenarios, the model’s generalization ability for samples with varying degrees of damage was enhanced. In total, 2574 qualified images were collected, with 2000 images used for training and 574 for testing (Fig. 3).

Partial porcelain plate data.

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At this stage, the focus was on addressing the restoration needs of damaged export porcelain images to identify the optimal restoration model. Analysis revealed the unique advantages of the improved DDPM in the context of export porcelain restoration, as it enhances restoration outcomes by optimizing texture, color, and damage features in porcelain images. Ultimately, an efficient restoration solution was established, providing technical support for the conservation of cultural heritage.

DDPM achieves image generation through a forward diffusion and a reverse denoising process^27,28. In the forward diffusion process, the original image \({x}_{0}\) is gradually transformed into Gaussian noise \({x}_{T}\) over \(T\) time steps, with noise incrementally added at each step as described by the following equation:

Where \({{\rm{\alpha }}}_{{\rm{t}}}=1-{\beta }_{t}\),\(\,{\beta }_{t}\) is the predefined noise variance, and \({\epsilon }_{t-1}\) is noise sampled from a standard normal distribution \({\mathcal{N}}\left(0,{\rm{I}}\right)\), which is added to \({x}_{t-1}\).

In the reverse denoising process, a neural network \({\epsilon }_{\theta }\left({x}_{t},t\right)\) is used to predict the noise at each time step, thereby progressively reconstructing the image. Here, \(\bar{{\alpha }_{t}}={\prod }_{i=1}^{t}{\alpha }_{i}\) denotes the cumulative product of \({a}_{i}\) from \(i\) = 1 to \(t\). The function \({\epsilon }_{\theta }\left({x}_{t},t\right)\) represents the noise predicted by the neural network based on the noisy image \({x}_{t}\) and time step \(t\), while \(z\) is noise sampled from the standard normal distribution \({\mathcal{N}}\left(0,{\rm{I}}\right)\), which introduces stochasticity into the denoising process. The forward diffusion and reverse denoising processes of DDPM can be seen in Fig. 4.

Schematic diagram of forward diffusion and reverse denoising process in DDPM.

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Conventional DDPM often struggles to reconcile semantic information between known and generated regions during image synthesis, resulting in semantic inconsistency and an inability to handle extreme occlusions and random masks. Lugmayr et al.²⁹ proposed RePaint, which samples unmasked regions and applies conditional generation during the reverse diffusion process for image inpainting. This approach effectively addresses the challenges of free-form image restoration and produces high-quality, semantically consistent images. Therefore, the method presented in this study is developed based on the RePaint framework (GitHub: git.io/RePaint).

We define the ground truth image as \(x\), and introduce a binary mask matrix \(m\in \{{{0,1}}\}^{H\times W}\), where \(m\) = 1 denotes regions to be inpainted and \(m\)=0 denotes intact known regions. The symbol \(\odot\) represents element-wise multiplication. Accordingly, the unknown pixels are represented by \(m\odot x\), while the known pixels are represented by \((1-m)\odot x\). During the reverse process from \({x}_{t}\) to \({x}_{t-1}\), we rely only on \({x}_{t}\), performing conditional generation on the known region \((1-m)\odot {x}_{t}\), while ensuring the correctness of the distribution²⁹. For the mask \(m\), the pixels at time step \(t-1\) are divided into known regions (\(m=0\)) and unknown region (\(m=1\)), denoted as \({x}_{t-1}^{\text{known}}\) and \({x}_{t-1}^{\text{unknown}}\). Here, \({\bar{\alpha }}_{t}\) represents the cumulative product coefficient, \(I\) denotes the identity matrix, \({\mu }_{\theta }\left({x}_{t},t\right)\) and \({\Sigma }_{\theta }\left({x}_{t},t\right)\) are the mean and variance predicted by the model, respectively.

For the known region:

For the unknown region:

Finally, we obtain:

During the sampling process of the improved DDPM, for the known region \({x}_{t-1}^{{known}}\), we sample using the known pixels \({\rm{m}}\odot {x}_{0}\) in the given image. Meanwhile, \({x}_{t-1}^{{\rm{known}}}\) is sampled from the model based on the previous iteration \({x}_{t}\). Then, we use a mask to combine these into the new sample \({x}_{t-1}\), as shown in the Fig. 5.

The improved DDPM sampling process diagram.

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The objective of DDPM is to generate images that are consistent with the underlying data distribution. In our improvement, we sample from \({x}_{t}\sim {\mathcal{N}}(\sqrt{1-{\beta }_{t}}{x}_{t-1},{\beta }_{t}I)\), diffusing the output \({x}_{t-1}\) back to \({x}_{t}\). This approach produces a new \({x}_{t}^{{\rm{unknown}}}\) that is better aligned with \({x}_{t}^{{\rm{known}}}\) and incorporates conditional information from \({x}_{t}^{{\rm{known}}}\). To incorporate more semantic information from multiple time steps during the denoising process, we introduce the concept of “jump length”, which refers to the interval between time steps in the denoising process. By fusing information across multiple time steps, semantic consistency is enhanced, enabling the model to more effectively utilize information from different time steps during denoising, thereby improving restoration performance.

We adopt the mask-based conditional sampling mechanism and the jump length strategy from the RePaint framework. The conditional sampling mechanism introduces spatial constraints, enforcing the preservation of intact regions while enabling reasonable reconstruction of damaged areas during the sampling process. Specifically, at each time step \(t\), the model receives two key inputs: the original image mask (where intact regions are labeled as 1 and damaged regions as 0) and the original image \({x}_{0}\). During sampling, the algorithm first uses the diffusion model to predict the latent variable \({x}_{t}\) at the current time step, and then performs spatial fusion on the prediction according to the mask \(M\):

Here, \({\mathcal{N}}\left({x}_{0},{\sigma }_{t}^{2}I\right)\) denotes the sampling result from a Gaussian distribution with the original image as the mean and the current noise level as the variance. This design ensures that the model strictly preserves the intact information during the restoration process, while generating unknown regions in accordance with statistical principles. In particular, when applied to the restoration of blue-and-white porcelain, this mechanism enables the precise retention of undamaged decorative patterns and color information, filling in only the missing areas and thereby significantly enhancing the fidelity of the restoration.

The jump length mechanism is an efficient sampling strategy designed to accelerate the inference process of diffusion models while maintaining restoration quality. The Traditional Diffusion Model typically requires hundreds or even thousands of time steps to generate high-quality samples. In contrast, the jump length mechanism dynamically adjusts the sampling trajectory, substantially reducing the required computational steps. In our implementation, we developed a non-uniform time-step scheduling algorithm, where the granularity of the jumps is controlled by the parameter \(\lambda\):

Here, \(T\) denotes the total number of time steps, and jump length represents the base interval for each jump. In the context of blue-and-white porcelain restoration, this mechanism effectively reduces the average number of sampling steps while maintaining high visual quality. Experimental results demonstrate that this adaptive sampling strategy is particularly well-suited for processing cultural heritage images characterized by complex textures and fine structures.

The combination of mask-based conditional sampling and the jump length mechanism achieves precise restoration of Jingdezhen porcelain images through a three-tier collaborative design, addressing the semantic and structural complexity inherent in these artifacts: (1) Motif structure constraints: A binary mask strictly distinguishes between intact and damaged regions, enforcing the continuity of critical decorative motifs-such as entwined patterns and blue-and-white landscapes during the diffusion process and preventing misaligned generation. (2) Color fidelity strategy: By integrating the original color statistics using a Gaussian distribution \({\mathcal{N}}\left({x}_{0},{\sigma }_{t}^{2}I\right)\), the model ensures a natural gradation of blue-and-white tones. (3) Multi-scale sampling optimization: The jump length mechanism employs an exponentially decaying step schedule, enabling rapid recovery of macroscopic composition in the early stages and refined depiction of microscopic textures in later stages. As the sampling approaches the true image, the step size is automatically reduced, preserving the structural integrity of fragile areas-such as rims and decorative handles-with thin or easily fractured glaze. This design not only enhances restoration efficiency but also guides sampling with the mask to avoid unnecessary computation, making it particularly suitable for the restoration of Jingdezhen porcelain with highly regular motifs, delicate glaze structures, and complex historical traces.

Within the system, the mask-based conditional sampling mechanism enables controlled generation according to mask information; for example, in image generation, the mask can specify which regions should be preserved. The jump length mechanism accelerates sampling and reduces the computational cost by skipping certain sampling steps, which can be flexibly adjusted in the diffusion model by modifying the number of sampling steps. Working in tandem, mask constraints ensure spatial consistency in restoration, while jump sampling enhances efficiency. Together, these mechanisms provide robust technical support for the efficient and high-quality restoration of intricate artifacts such as blue-and-white porcelain, optimizing both restoration accuracy and inference speed.

In this study, we adopted a U-Net architecture as the backbone of the Diffusion Model. Model training was performed using the Adam optimizer, with a learning rate set to 1e−4, a batch size of 16, and a total of 100 training epochs. The loss function was based on the standard Diffusion Model objective, which combines reconstruction loss (e.g. mean squared error, MSE) and a regularization term (e.g., Kullback–Leibler divergence, KL divergence), to ensure that the model effectively learns the data distribution and generates high-quality samples. For data preprocessing, all training images were resized to 256 × 256 pixels, and data augmentation techniques were applied to expand the dataset, thereby enhancing the model’s generalization capability and robustness. These training details ensure both the effectiveness and reproducibility of the model.

Given the unique color distribution characteristics and intricate texture structures of blue-and-white porcelain images, as well as the high requirements for detail preservation in the restoration process, this study introduces targeted optimizations for the algorithm architecture and core processing mechanisms based on the conventional RePaint algorithm. By incorporating an improved PSE algorithm, this study has achieved notable progress in color fidelity and texture feature preservation. This enhancement improves the model’s ability to capture the complex patterns of porcelain, thereby improving image restoration outcomes.

PSE enhances the final output by integrating the predictions of multiple sub-models. Suppose there are \(n\) sub-models, and each sub-model produces a prediction \({y}_{i}\) for the input \(x\). The output of PSE can thus be represented as:

In terms of algorithm optimization, this study introduces the ColorAwarePSE class, which enhances the original PSE algorithm by constructing a framework for improved color information preservation. This framework integrates both structural consistency and color fidelity constraints. By selecting samples with higher color fidelity and applying a boundary color correction strategy, the overall quality of porcelain image restoration is improved. Let \({y}_{{\rm{Structure}}}\) denote the structure-enhanced result, \({y}_{{\rm{Color}}}\), the sample with the highest color fidelity, \(\lambda\) the color weight, and \(M\) the restoration region mask. The output of the improved ColorAwarePSE can be represented as:

To address the processing of texture features in porcelain plate images, this study introduces the CeramicTexturePreservation module. Based on the analysis of ceramic texture characteristics, this module extracts local texture features and constructs a texture similarity guidance map, effectively preserving and enhancing the texture features of porcelain while reducing the loss or distortion of texture information during restoration. In the enhancement of porcelain plate texture preservation, the calculation of texture similarity is a critical step. Let \({F}_{{\rm{original}}}\) denote the feature vector of the original image, \({F}_{{\rm{sample}}}\) the feature vector of the sample image, and \(N\) denote the number of elements involved in the calculation (i.e., the number of pixels in the masked region). The formula can be expressed as:

In the sample selection stage, this study employs an improved PSE algorithm combined with a multi-path sampling strategy, which maintains sample diversity while reducing the number of integrated samples. This approach provides a new means of enhancing algorithmic efficiency, enabling a balanced optimization between algorithm performance and restoration quality. A comparison of the proposed method and the RePaint approach in terms of relevant image restoration characteristics is presented in Table 1.

To clearly illustrate the algorithmic structure and key parameter configurations of the improved PSE module, Fig. 6 presents a flowchart of the algorithm that integrates multi-path sampling and color-aware mechanisms. Table 2 lists the core hyperparameters used in the algorithm implementation along with their specific values.

Algorithm flowchart.

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During the system implementation phase, this study developed a technical platform that integrates algorithmic models with interactive functionality to meet the intelligent restoration needs of Jingdezhen export porcelain. The system adopts a decoupled front-end and back-end architecture to achieve efficient data exchange and separation of business logic. The user interface is designed to cover the entire restoration workflow, supporting both visualized user operations and quantitative evaluation of restoration outcomes. Usability testing demonstrates that the system performs well in terms of restoration efficiency, user experience, and functional practicality, providing a solution that balances professionalism and ease of use for digital porcelain restoration.

The system front end was developed using the modern JavaScript framework Next.js, leveraging its component-based architecture and efficient server-side rendering capabilities to enable rapid construction of a responsive web interface. Structured data exchange between the front and back ends is facilitated by the Axios client, which also optimizes the handling of asynchronous requests to enhance the smoothness of user operations.

We adopted the Flask framework to build the system back end, which is renowned for its lightweight nature and flexibility. Flask enables efficient handling of front-end requests by routing them to the appropriate view functions for business logic processing. The results are then returned to the front end, and relevant data updates are mapped to the database to ensure data persistence and consistency. This design not only maintains code simplicity but also meets the requirements for system maintainability and scalability.

The overall system architecture adopts a decoupled front-end and back-end model, with API design following RESTful standards and data transmission in JSON format. This separation allows for parallel development of the front and back ends, reduces server load, and enhances system maintainability. It also effectively ensures the openness of the technology stack and supports the flexible reuse of functional modules.

The workflow of the porcelain plate image restoration system begins with user interaction. Users first upload an image of a porcelain plate and then create a damaged mask to accurately identify the regions requiring restoration. Next, users select a restoration model from improved DDPM, FMM, or GAN, and submit the restoration request. Upon receiving the request, the system back end performs inference using the selected model to generate the restored image and computes evaluation metrics such as SSIM, PSNR, and LPIPS. In the final result interaction stage, users can download the restored image and view a comparison between the original and restored images, allowing for an intuitive assessment of restoration outcomes. The complete system workflow is illustrated in Fig. 7.

System flowchart.

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On the image upload page (Fig. 8), users can upload images requiring restoration directly from their local folders. They are then directed to the mask drawing page (Fig. 9), where they can use the mouse to draw a mask on the uploaded image and select a restoration model from the available options. Finally, on the results and analysis page (Figs. 10 and 11), the system displays the restoration outcomes, presenting the restored image, the original image, and the masked image side by side to facilitate comparison of restoration effects. In addition, the page displays calculated evaluation metrics such as SSIM, PSNR, and LPIPS, enabling users to conduct comparative analyses of the restoration results.

The image upload page.

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The mask drawing page.

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The restoration result page.

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The result analysis page.

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To verify the operational feasibility of the system, we conducted a small-scale usability evaluation. The basic demographic information of the respondents is summarized in Table 3. The usability study involved ten participants, including six restoration experts and four students, thus covering both professionals and non-professionals with varying years of experience using restoration tools, ensuring the representativeness of the sample. In terms of task completion efficiency, 80% of participants completed a single restoration task within 5–10 min, and 90% reported that the time required was noticeably or somewhat reduced compared to previous tools. Only one participant felt that the duration was “about the same”, and no one reported increased time, which intuitively reflects the system’s positive impact on restoration efficiency.

In terms of satisfaction ratings, the system performed exceptionally well across all evaluated dimensions, including ease of use, quality of restoration results, response speed, and willingness to recommend. The average scores were 4.1 for ease of use, 4.4 for restoration quality, 4.3 for response speed, and 4.6 for willingness to recommend (all on a five-point scale), with each metric scoring above 4. Notably, the willingness to recommend score was close to full marks, indicating a high level of participant satisfaction with the system’s functionality and a strong inclination to recommend it to others.

In open-ended feedback, participants widely affirmed the system’s performance in terms of visual effects, the rationality of the restoration workflow, response speed, and user interface friendliness. Core strengths frequently highlighted included precise image recognition (enabling rapid localization of fractures and patterns in blue-and-white porcelain) and the stability of the intelligent reassembly algorithm (which reduces the manual burden of fragment recombination). Participants also provided constructive suggestions for improvement, such as enhancing the accuracy of blue shade recognition and increasing the clarity of system prompts.

Experimental results demonstrate that the blue-and-white porcelain restoration system shortens restoration time and improves accuracy through intelligent functionalities, while its intuitive interface lowers the threshold for use by non-professionals. Its robust stability and data management capabilities offer reliable support for both heritage conservation and academic research.

In this section, sixteen well-known blue-and-white porcelain export plates were selected as experimental subjects to compare the restoration performance of the three aforementioned models, thereby demonstrating that the intelligent restoration system based on the improved DDPM achieves high-quality restoration results on the porcelain plate dataset. Furthermore, this is substantiated by quantitative comparisons using SSIM, PSNR, and LPIPS metrics. The following outlines the operational workflow of applying this method to the restoration of blue-and-white porcelain plates.

First, pre-restoration porcelain plate images are preprocessed to ensure background cleanliness and saved in .jpg or .png format. Subsequently, by running the system code to access the website’s default page, users can upload locally stored image files. By clicking the “Select Image” button, users can import images into the system for subsequent restoration. On the restoration page, users can choose FMM, GAN, or improved DDPM as the image restoration method in the editor located in the upper right corner. After a random mask is applied to the imported image, users may select any model for restoration and wait for the results to be generated. Upon completion, users can compare the original, masked, and restored images on the result analysis page. Additionally, the values of SSIM, PSNR, and LPIPS evaluation metrics are displayed at the bottom of the page, providing a quantitative basis for objectively assessing the restoration performance of the three models.

To ensure the rigor and scientific validity of the experimental design, this study employs two representative types of masks (central rectangular masks and randomly distributed masks) to comprehensively evaluate model performance. The central rectangular mask focuses on simulating regular damage scenarios in the center of the image, while the randomly distributed mask emulates the irregular damage patterns commonly observed in actual artifacts. By covering different types of defect patterns, these approaches more precisely highlight the advantages of the improved DDPM model in complex restoration scenarios. The quantitative evaluation results for the central rectangular mask are presented in Table 4, with visual comparisons shown in Fig. 12. Quantitative metrics and visual comparisons for the randomly distributed mask are provided in Table 5 and Fig. 13, respectively.

The comparison of porcelain plate restoration effects by various models (rectangular mask).

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The comparison of porcelain plate restoration effects by various models (random mask).

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The evaluation of restoration performance utilized three quantitative metrics: SSIM, PSNR, and LPIPS. To accurately evaluate the damaged regions of porcelain requiring restoration, several key improvements were made to the assessment methodology. A binary mask mechanism was introduced, ensuring that metrics were calculated exclusively within the masked damaged areas, thereby eliminating interference from the background and irrelevant regions. The mask was further dilated to enlarge the edge areas, to incorporate the transition zone between the restored region and its surroundings and ensure that the evaluation covered the continuity at restoration boundaries. When calculating SSIM and PSNR, we extracted only the Region of Interest (ROI) defined by the mask to enable precise quantification of pixel-level similarity and structural fidelity within the restoration area. For LPIPS evaluation, a VGG feature extraction network was employed (as opposed to traditional pixel-wise metrics), and color space correction as well as mask constraints were applied to enhance the model’s ability to capture semantic consistency and visual coherence in the restored region. These improvements render the evaluation process more targeted, to significantly increase the accuracy and relevance of restoration effect comparisons. Experimental results indicate that the improved assessment method clearly highlights the superiority of the improved DDPM model in restoring image details and achieving high-similarity restorations.

To address the limitations of traditional manual restoration and existing algorithms in complex restoration scenarios, this study proposes an intelligent restoration method based on an improved DDPM. By optimizing the diffusion model architecture, this approach enables semantically-aware restoration of arbitrarily shaped damaged regions, overcoming the constraints of fixed mask training and significantly enhancing both structural detail and semantic consistency in restoration. The accompanying intelligent restoration expert system integrates multiple algorithms for user comparison and adopts a front-end and back-end architecture built with Next.js and Flask. The system allows users to customize damage masks and generates restoration results in real-time. It intuitively displays the original image, masked image, and restored image, while simultaneously providing key quantitative evaluation metrics to facilitate scientific assessment of restoration outcomes. Through technological innovation and interactive optimization, the proposed method and system effectively balance restoration accuracy, efficiency, and user operability, providing a reusable technical solution and application paradigm for digital porcelain restoration.

Comparative experiments applying both central rectangular and random masks to porcelain plate samples, reveal several differences among the models. The FMM model exhibits rigid boundary handling and insufficient restoration of texture details in the masked regions at the pattern edges, failing to reconstruct the original decorative motifs and color gradations of the porcelain plates. While the GAN model achieves a visually seamless transition at the edges (making restoration traces nearly imperceptible), it suffers from loss of detail in the restoration of complex patterns within the masked area and does not precisely reproduce the intricate structures of the original design. In contrast, the improved DDPM model not only achieves natural color and texture blending at the boundaries but also accurately restores fine features within complex masked areas, such as the directionality of lines and gradient glaze transitions. The restored colors and lines are highly consistent with those of the original samples. These visual differences are corroborated by the superior average values of SSIM, PSNR, and LPIPS for the improved DDPM model, as presented in Tables 4 and 5, jointly validating its effectiveness in complex mask scenarios from both qualitative and quantitative perspectives.

In summary, the intelligent restoration expert system for Jingdezhen export porcelain proposed in this study, which is based on the improved DDPM, enables precise identification of damaged regions in blue-and-white porcelain plate images. During the restoration process, the model leverages its powerful generative capabilities to produce highly realistic restoration content that incorporates the distinctive textures, colors, and patterns of blue-and-white porcelain. Compared with traditional manual restoration methods, the automated workflow significantly reduces the restoration cycle, enabling a broader range of valuable ceramic artifacts to be restored in a timely and effective manner. This approach not only alleviates the challenges associated with training skilled manual restorers and the technical complexity of restoration but also opens new avenues for the digital preservation and dissemination of cultural heritage.

Although this study has made progress in the intelligent restoration of Jingdezhen export porcelain, several challenges remain in terms of practical application and model performance. First, the complexity of damage poses a significant challenge. The current experimental design, which simulates damage using simple manual masks, struggles to address real-world restoration needs involving irregular, severe, or even missing fragments. Second, there are limitations in ___domain adaptability. As the model is trained solely on blue-and-white porcelain, the substantial differences in texture, pattern, and color across various types of ceramics introduce a risk of ___domain bias when restoring other ceramic types. Third, there are issues regarding adaptation to physical restoration scenarios. The present study is confined to digital image experiments, lacking validation on physically damaged artifacts, and the restoration fidelity and resemblance to original objects still have room for improvement. Future work should focus on optimizing complex damage simulation, adaptation to multiple ceramic types, and joint validation with physical restoration efforts.