A sparse-view three-dimensional reconstruction method for cultural relics, a storage medium and a computer device

Abstract

The application discloses a kind of sparse view angle cultural relic three-dimensional reconstruction method, storage medium and computer equipment, wherein method includes: obtaining cultural relic multi-view image and camera parameter;Radiation is constructed and space point sampling is carried out on radiation;The uncertainty of space point is jointly modeled, and color, body density and evidence uncertainty parameter are simultaneously output in implicit neural radiance field model;Introduce uncertainty-driven progressive sinusoidal position encoding method, preferentially activate low-frequency channel in the early training, and with uncertainty feedback dynamic unfreezing high-frequency feature;After unfreezing is completed, using uncertainty perception's partition self-supervised consistency mechanism, reliable and unreliable area are continuously weighted optimization, and potential geometric information in unreliable area is fully utilized;High-fidelity three-dimensional reconstruction image and confidence evaluation result of cultural relic are generated by volume rendering.The application effectively improves the accuracy and stability of cultural relic three-dimensional reconstruction under the condition of sparse view angle.

Description

Technical Field

[0001] This invention relates to the field of computer vision technology, and more specifically to a sparse-view 3D reconstruction method for cultural relics based on progressive position coding and partitioned self-supervision. Background Technology

[0002] 3D reconstruction technology is now widely used in industrial inspection, virtual reality, robot perception, and the digital preservation and display of cultural heritage. Traditional 3D reconstruction methods typically rely on multi-view stereo vision (MVS), structured light scanning, and laser scanning to recover the 3D shape of objects through multi-angle acquisition and geometric reconstruction. However, these methods often require intensive, stable, and controllable acquisition conditions, placing high demands on imaging equipment, lighting environment, and object accessibility. In the context of cultural relic preservation, the surface of artifacts may contain highly reflective materials, complex fine lines, localized damage, and other detailed features. Furthermore, artifacts are usually not repeatedly touched or freely rotated to acquire multi-angle images, making it difficult to obtain sufficient observation perspectives. Limited perspectives directly lead to problems such as structural loss, texture blurring, and incomplete details in traditional reconstruction methods, making it difficult to meet the needs of high-fidelity digital archiving and restoration analysis.

[0003] In recent years, Neural Radiance Field (NeRF) has proposed an implicit representation framework based on Multilayer Perceptron (MLP). It takes 3D spatial location and viewpoint direction as input and uses volume rendering to generate images from arbitrary viewpoints. It has demonstrated high-quality capabilities for novel viewpoint synthesis and geometric reconstruction under dense multi-view conditions. However, standard NeRF relies on sufficient multi-view observations for supervised learning. Under sparse view conditions, it introduces high uncertainty in insufficiently observed areas, manifesting as geometric shape collapse, loss of surface details, and enhanced artifacts. This particularly affects the reliable reconstruction of high-frequency details such as local cracks and engravings in cultural relics.

[0004] Regarding the problem of sparse view reconstruction, existing research has proposed various improvement approaches within the NeRF framework. These improved methods have alleviated the degradation caused by sparse views to some extent, but still have significant shortcomings in two key aspects, especially in typical sparse acquisition-constrained scenarios such as cultural relics. On the one hand, traditional NeRF uses fixed high-frequency position encoding, introducing all frequency components at once, which easily leads to premature fitting of noise or pseudo-details when observations are insufficient, and lacks a mechanism to gradually introduce high-frequency information during the training process. On the other hand, pseudo-new views generated based on geometric warps are often directly used for consistency supervision, but this supervision usually simply removes unreliable regions through hard threshold masks, and cannot perform fine-grained weighting based on region credibility. It neither fully utilizes weak supervision information nor can it maintain stable learning in areas with highlights, occlusion, or material changes. Therefore, in the context of cultural relic scenes, which are typical applications with "few acquisitionable viewpoints and high requirements for detail fidelity," a 3D reconstruction method oriented towards sparse view conditions is still urgently needed. Summary of the Invention

[0005] The present invention provides a method, storage medium, and computer equipment for sparse-view 3D reconstruction of cultural relics based on progressive position coding and partition self-supervision, which can stably restore the overall geometry and detailed texture of cultural relics under few viewing angles and provide a highly reliable 3D basis for cultural relic preservation and restoration decisions. It can solve at least one of the above-mentioned technical problems.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A sparse perspective method for 3D reconstruction of cultural relics includes the following steps:

[0008] S1. Obtain sparse multi-view images of cultural relics and corresponding camera internal and external parameters, construct rays by pixels and sample within the ray range to obtain a set of three-dimensional sampling points for neural radiation field training.

[0009] S2. Construct a neural radiation field model based on a set of three-dimensional sampling points, introduce an evidence uncertainty modeling framework, perform implicit representation learning on the three-dimensional radiation field, and output the color of the sampling points and their uncertainty.

[0010] S3. Introduce an uncertainty-driven progressive position coding method to perform multi-frequency sinusoidal position coding on the spatial coordinates of the sampling points. In the early stage of training, only the low-frequency channel is activated. As the uncertainty of the model decreases, the high-frequency channel is gradually unfrozen to achieve progressive feature learning from low frequency to high frequency.

[0011] S4. Interpolate the camera extrinsic parameters of adjacent source viewpoints to obtain the new viewpoint pose. On the one hand, backproject the source viewpoint and remap it to the new viewpoint to generate a pseudo new viewpoint. On the other hand, input the camera parameters of the new viewpoint into the neural radiation field model to render the predicted viewpoint.

[0012] S5. Compare the consistency between the pseudo-new view and the predicted view, calculate the depth consistency between the two at the corresponding pixel positions, and adaptively adjust the pixel supervision intensity according to the consistency result and data uncertainty. Divide the new view into reliable or unreliable regions, apply strong supervision training to reliable regions, and apply weak supervision to unreliable regions.

[0013] S6. Construct a joint optimization objective function that includes color principal loss and partition loss, perform end-to-end training in conjunction with differentiable rendering specification constraints, optimize global radiation field parameters, and output the 3D reconstruction results of cultural relics and uncertainty assessment results.

[0014] Furthermore, S1 and S2 further include:

[0015] Based on sparse multi-view images of cultural relics and corresponding camera intrinsic and extrinsic parameters, layered sampling is performed along pixel rays to form three-dimensional sampling points. The layered sampling includes coarse sampling and fine sampling based on resampling.

[0016] Using the spatial coordinates of the sampling points and the direction of the line of sight as input to the neural radiation field model, the three-dimensional radiation properties are implicitly represented and the color estimate is output.

[0017] An evidence uncertainty modeling framework is embedded in the neural radiation field model to simultaneously provide color prediction and its uncertainty.

[0018] Sine position coding is applied to the spatial coordinates of the sampling points to form a multi-frequency representation, which supports the subsequent gradual unfreezing.

[0019] Furthermore, S3 further includes:

[0020] S3.1 Calculate uncertainty based on evidence parameters;

[0021] Model uncertainty measures whether the neural radiation field model has learned well enough at the current location, while data uncertainty measures whether a sampling point itself is difficult to observe stably due to external factors. For the i-th pixel in the training batch, model uncertainty and data uncertainty are calculated, and the resulting uncertainty is used as a scheduling signal during the training process. Its calculation expression is as follows:

[0022]

[0023]

[0024] in, This represents the model uncertainty at the i-th pixel. This indicates the uncertainty of the data at the i-th pixel. This represents the scale parameters after volume rendering and blending. This represents the shape parameters after volume rendering and blending. This represents the precision parameters after volume rendering and blending.

[0025] S3.2 Constructing a progressive location coding strategy based on model uncertainty;

[0026] To avoid the neural radiation field model prematurely fitting local noise from a sparse perspective, a frequency weight mask is constructed based on model uncertainty and training progress, expressed as:

[0027]

[0028] in, The frequency weight mask coefficients for progressive position coding are the dynamic scheduling factors. This is the training progress coefficient, representing a gradual increase in the overall proportion of high-frequency frequencies being exposed as training progresses. This is used to ensure that not all high frequencies are exposed during early training. This is a hyperparameter used to adjust the amplification factor of model uncertainty during high-frequency channel unfreezing;

[0029] S3.3, Gradual unfreezing of the location coding channel;

[0030] The dynamic scheduling factor obtained using S3.2 By controlling the activation level of different frequency components in position coding, a practical application of progressive position coding is formed, which involves the three-dimensional spatial coordinates of the sampling points. Perform multi-frequency sinusoidal position encoding, where, Let j represent the j-th sampling point on the i'-th ray, where j is the index of the sampling point. This index is used to distinguish different sampling positions on the same ray or pixel, and a gating weight is introduced for each high-frequency component. and combine this weight with Binding is used to adjust the effective strength of different frequency channels in the current stage. The weighted position encoding expression is:

[0031]

[0032]

[0033] in, Indicates the gating weight Sampling points obtained under action The weighted multi-frequency sinusoidal position-coded feature vector, This is a frequency-specific allocation function used to ensure that the weights of high-frequency components vary. Monotonous rise, This function restricts array elements to a specified range, used to limit weights within a reasonable range, where k represents the frequency channel.

[0034] Furthermore, S4 further includes:

[0035] S4.1 Generate new camera view parameters based on the extrinsic parameter interpolation of adjacent source view cameras;

[0036] In the existing sparse multi-view artifact image sequence, two adjacent source views are selected. and The corresponding camera external poses are respectively and ,in, Represents the rotation matrix. This represents the translation vector. To generate new target viewpoint camera parameters, the poses of adjacent source viewpoints are interpolated to obtain the new target viewpoint. position The target new perspective camera parameters are expressed as follows:

[0037]

[0038] in, This represents the target's new perspective camera parameters, where K represents the camera intrinsic parameter matrix;

[0039] S4.2 Generate a pseudo-truth view with a new perspective based on geometric warp operations;

[0040] The target new perspective camera parameters obtained using S4.1 and any source perspective Observational images Its pixel depth estimation A geometric projection transformation, or geometric warp operation, is performed on the source view image to synthesize a pseudo-true view under the new viewpoint. ;

[0041] S4.3 Prediction of neural radiation field model based on new perspective parameters;

[0042] The target new perspective camera parameters obtained in S4.1 The volume density of the i-th pixel is obtained by inputting the data into the neural radiation field model. and color distribution parameters By accumulating the sampling points along the ray through volume rendering integral, the predicted radiation results under this new perspective are obtained. and the corresponding depth estimation .

[0043] Furthermore, in S5, based on the self-supervised learning of partitions with consistency and uncertainty, the new perspective radiation prediction results obtained in S4 are applied. With pseudo-truth view A consistency comparison is performed, and continuous weights are generated based on the uncertainty of the evidence to complete the region division. Further, step S5 includes the following steps:

[0044] S5.1, Deep consistency comparison and adaptive threshold adjustment based on data uncertainty;

[0045] From the new perspective of the target, the predicted depth is compared with the remapping reference depth to obtain the depth consistency error, which is expressed as:

[0046]

[0047] in, Represents the pixel coordinates of the target from a new perspective. Depth consistency error at the location This represents the predicted depth value obtained by the neural radiation field model rendered from this new perspective. This represents the pseudo-true value reference depth obtained by geometrically remapping the source view to the new viewpoint of the target;

[0048] An adaptive threshold is determined for each pixel location or the corresponding position of the ray sampling. This adaptive threshold is used to determine whether the consistency at that location is reliable. Data uncertainty at each pixel Set an adaptive threshold for uncertainty, expressed as follows:

[0049]

[0050] in, Indicates the first An adaptive threshold for uncertainty at each pixel. Based on the threshold, This is the scaling factor;

[0051] Define a consistency indicator function with the following expression:

[0052]

[0053] in, This represents the pixel coordinates of the target from a new perspective. The depth consistency indicator function at that location When the value is 1, it indicates that the geometric projection at that location is consistent, and the reliability is high. When =0, it indicates that the geometric projection at that location is unstable and has low reliability;

[0054] according to The value of is used to divide the pixels in the new viewpoint of the target into reliable regions with consistent depth and unreliable regions with inconsistent depth, denoted as and respectively. and The expressions are as follows:

[0055]

[0056]

[0057] in, This represents the set of pixels with consistent depth and reliable geometric relationships within the new perspective of the target. This represents a set of pixels with inconsistent depth and unreliable geometric relationships in a new perspective of the target.

[0058] S5.2 To suppress noise and highlight geometric boundaries, pixel weights are defined as follows:

[0059]

[0060] in, This represents any pixel position within the new perspective of the target. This indicates the pixel weight at that pixel location, derived from data uncertainty. This indicates the uncertainty of the data at that pixel location. It is the numerical stability constant. ;

[0061] For reliable regions, photometric consistency loss is used. Then, normalization is performed. The expression for this process is:

[0062]

[0063]

[0064] in, Indicates loss of photometric uniformity The normalization factor, For the normalized smoothing term, ;

[0065] To avoid treating incorrect reprojection as label learning, in Use depth-order consistency to obtain for The local neighborhood is defined, and the depth order of the prior and prediction is given by the following expressions:

[0066]

[0067]

[0068] in, For the neighborhood pixel position, This indicates the prior depth order symbol calculated from the pseudo-ground value depth, used to characterize the pixel position in the pseudo-ground value. with neighboring pixel positions The relationship between the preceding and following parts, This indicates the order of predicted depths calculated based on the predicted depth, used to characterize the sequential relationship between the two pixel positions in the current model's prediction. and These represent the depth values ​​of the pseudo-ground truth depth map at these two pixel positions, respectively. and These represent the depth values ​​of the predicted depth map at these two pixel locations, respectively, sign( ) is a sign function that outputs three discrete values: {-1, 0, 1}.

[0069] if and If the symbols are different, it means the order has been reversed, which requires a penalty. The expression is:

[0070]

[0071]

[0072] in, Indicates pixel position With the neighborhood pixel position The relative depth order consistency penalty function between them;

[0073] This results in the unreliable area loss. Then, normalization is performed. The expression for this process is:

[0074]

[0075]

[0076] in, Indicates loss in unreliable areas The normalization factor;

[0077] Combining equations (13)-(20), the partition loss Defined as:

[0078]

[0079] in, and Both are tradeoff coefficients, and both are greater than 0.

[0080] Furthermore, in step S6, the partition loss obtained in step S5 is jointly optimized with the base loss of the evidence modeling NeRF to obtain the overall loss. The expression is:

[0081]

[0082] in, This indicates damage to the base. This indicates the partition loss.

[0083] A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the above-described sparse perspective artifact 3D reconstruction method.

[0084] A computer device includes a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the sparse perspective artifact 3D reconstruction method described above.

[0085] The beneficial effects of this invention are reflected in:

[0086] This invention proposes a sparse-view 3D reconstruction method for cultural relics based on progressive position coding and partition self-supervision. It is designed for scenarios where the digital acquisition of cultural relics is limited by perspective. The method aims to stably restore the overall geometry and detailed texture of cultural relics under sparse-view conditions, and simultaneously provide pixel-level uncertainty quantification, providing a highly reliable 3D basis for cultural relic preservation and restoration decisions.

[0087] Specifically, the uncertainty-guided positional encoding unfreezing module introduced in this method adjusts the high-frequency components of the sinusoidal positional encoding through dynamic frequency masks. This allows the model to focus on the stable learning of low-frequency geometric structures in the early stages of training, and gradually open the high-frequency channels as model uncertainty decreases. This achieves a progressive high-frequency feature capture from coarse to fine, and this mechanism significantly suppresses noise overfitting and pseudo-high-frequency texture generation under sparse sampling. Furthermore, the partitioned self-supervised module combined with this method can automatically divide reliable and unreliable regions without external labels. It applies strong supervision constraints to high-confidence regions and relative depth consistency constraints to low-confidence regions, thereby fully utilizing potential weak supervision information while maintaining geometric continuity. Attached Figure Description

[0088] The accompanying drawings, which are provided to further illustrate this application and form part of this application, illustrate exemplary embodiments of this application and are used to explain this application, but do not constitute an undue limitation of this application.

[0089] Figure 1 This is a detailed flowchart illustrating the sparse perspective method for 3D reconstruction of cultural relics according to an embodiment of the present invention.

[0090] Figure 2 It is a schematic diagram of a real image.

[0091] Figure 3 It is about Figure 2 An enlarged diagram of the mouth of a dinosaur fossil.

[0092] Figure 4 It is about Figure 2 A magnified diagram showing the details of the railings.

[0093] Figure 5 This is a schematic diagram of the visualization rendering result of the original ENERF method.

[0094] Figure 6 It is about Figure 5 Enlarged schematic diagram of the mouth of a dinosaur fossil.

[0095] Figure 7 It is about Figure 5 A magnified diagram showing the details of the railings.

[0096] Figure 8 This is a schematic diagram of the visualization rendering result of the uncertainty-driven progressive position coding module of this invention performing three-dimensional reconstruction of cultural relics under sparse view conditions.

[0097] Figure 9 It is about Figure 8 Enlarged schematic diagram of the mouth of a dinosaur fossil.

[0098] Figure 10 It is about Figure 8 A magnified diagram showing the details of the railings.

[0099] Figure 11 This is a schematic diagram of the visualization rendering result of the partition self-supervised module of this invention performing three-dimensional reconstruction of cultural relics under sparse view conditions.

[0100] Figure 12 It is about Figure 11 Enlarged schematic diagram of the mouth of a dinosaur fossil.

[0101] Figure 13 It is about Figure 11 A magnified diagram showing the details of the railings.

[0102] Figure 14 A schematic diagram of the visualization rendering result of the sparse perspective cultural relic 3D reconstruction method according to an embodiment of the present invention.

[0103] Figure 15 It is about Figure 14 Enlarged schematic diagram of the mouth of a dinosaur fossil.

[0104] Figure 16 It is about Figure 14 A magnified diagram showing the details of the railings.

[0105] Figure 17 This is a structural block diagram of a computer device according to an embodiment of the present invention. Detailed Implementation

[0106] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0107] It should be noted that the meaning of "and / or" throughout the text includes three parallel solutions. Taking "A and / or B" as an example, it includes solution A, solution B, or a solution that simultaneously satisfies A and B. Furthermore, "multiple" refers to two or more. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0108] See Figure 1 This invention provides a method for 3D reconstruction of cultural relics from a sparse perspective, comprising the following steps:

[0109] S1. Obtain sparse multi-view images of cultural relics and corresponding camera internal and external parameters, construct rays by pixels and sample within the ray range to obtain a set of three-dimensional sampling points for neural radiation field training.

[0110] S2. Based on the set of three-dimensional sampling points, a neural radiation field model is constructed. An evidence uncertainty modeling framework is introduced to perform implicit representation learning on the three-dimensional radiation field and output the color of the sampling points and their uncertainty, so as to stabilize the geometric structure and improve the ability to reconstruct high-frequency details.

[0111] S2 specifically includes the following steps:

[0112] S2.1 Input multi-view cultural relic image data The corresponding camera pose is input into the neural radiation field model, where the image data is RGB three-channel, with width and height of [missing information]. and The input image data is further subdivided into coarse sampling and fine sampling during the input construction stage, where: coarse sampling , This represents the number of coarse samples. Represents the three-dimensional coordinates of coarse sampling points; fine sampling , The number of fine samples, The three-dimensional coordinates representing the coarse sampling points;

[0113] The neural radiation field model receives spatial coordinates X and viewpoint direction d as inputs to estimate the radiation properties of the sampling point in three-dimensional space.

[0114] This step lays the foundation for subsequent uncertainty modeling and rendering.

[0115] S2.2, Evidence deep learning module embedded in network;

[0116] An evidence-based deep learning module is embedded in the neural radiation field model to model the uncertainty of each spatial sampling point, assuming the color of the sampling point. Let j be the sampling points on the light ray, each following an independent normal distribution, i.e. ,in, This represents the expected radiation value at that sampling point. This represents the variance of the sampling point, used to characterize instability or noise level. To ensure the network outputs not only a single predicted value but also confidence information, [the following is added:] ... Introducing the Normal–Inverse-Gamma (NIG) distribution as prior evidence, its mean... and variance Controlled by the parameters of the normal inverse gamma distribution: mean Precision parameters Shape parameters Scale parameters Then its probability density function p is defined as:

[0117]

[0118] The fused evidence model will output the following parameters:

[0119] Color Mean : Output by the neural radiation field model, representing the mean of the color prediction;

[0120] Precision parameters : Used to reflect the model's confidence in color predictions, defined as the reciprocal of accuracy. ,in, To predict the variance of color;

[0121] Shape parameters : Indicates the model's predictive stability for that spatial sampling point; a higher stability indicates better performance. The value indicates that the model has higher stability at this sampling point;

[0122] Scale parameters Used to control the range of color distribution, combined with It reflects the degree of dispersion of the predicted distribution;

[0123] At each sampling point, the color prediction follows a normal inverse gamma distribution. These parameters are used to quantify the uncertainty of the model.

[0124] S2.3, Sine wave position coding network structure setting;

[0125] In the neural radiation field model, sinusoidal positional encoding (SPE) is used to expand the spatial coordinates in the frequency domain. This involves dividing the three-dimensional coordinates of the sampling points... The input is directly fed into a set of front-end mapping layers that use sine functions as activation, so that the activation function of the first layer of the network is a sine function instead of the conventional ReLU or other monotonic activation functions.

[0126] Specifically, let the first layer of the network be... ,in, and These are the learnable weights and biases of this layer, respectively. The sinusoidal activation function explicitly introduces a set of learnable spatial frequency bases in the coordinate space, enabling the subsequent multilayer perceptron (MLP) to represent spatial variation patterns in different frequency bands, including the overall geometric contours at low frequencies and the local detail textures at high frequencies, through linear combination and subsequent hidden layer transformations.

[0127] By using the sinusoidal activation function as the activation function of the first layer, the neural radiation field model can naturally represent the multi-frequency spatial basis without explicitly splicing fixed high-frequency Fourier features from the beginning. These sinusoidal high-frequency components can be selectively amplified or suppressed during training to describe high-frequency details such as cracks, engravings, and wear boundaries on the surface of cultural relics.

[0128] More importantly, this structure provides a controllable entry point for the subsequent uncertainty-driven progressive frequency unfreezing mechanism (see step details in S3): the frequency weight mask coefficients of the subsequent progressively position-encoded frequency. This will directly determine the actual activation intensity of these sinusoidal high-frequency components in different training stages and different spatial regions.

[0129] S3. An uncertainty-driven progressive position coding method is introduced to perform multi-frequency sinusoidal position coding on the spatial coordinates of the sampling points. In the early stage of training, only the low-frequency channels are activated, and the high-frequency channels are gradually unfrozen as the uncertainty of the model decreases, so as to achieve progressive feature learning from low frequency to high frequency.

[0130] S3 specifically includes the following steps:

[0131] S3.1 Calculate uncertainty based on evidence parameters;

[0132] Epistemic uncertainty measures whether the neural radiation field model has learned well enough at the current location, while aleatoric uncertainty measures whether a sampling point itself is difficult to observe stably due to external factors (such as reflection, occlusion, material wear, etc.).

[0133] For the i-th pixel in the training batch, calculate the model uncertainty and data uncertainty, and use the resulting uncertainty as a scheduling signal during the training process. The calculation expression is as follows:

[0134]

[0135]

[0136] in, This represents the model uncertainty at the i-th pixel. This indicates the uncertainty of the data at the i-th pixel. This represents the scale parameters after volume rendering and blending. This represents the shape parameters after volume rendering and blending. This represents the precision parameters after volume rendering and blending.

[0137] In this embodiment, the aforementioned uncertainty index is used as a scheduling signal during the training process for subsequent progressive position encoding unfreezing (see S3.2 and S3.3), and further for partition self-supervised weight allocation (see S5).

[0138] S3.2 Constructing a progressive location coding strategy based on model uncertainty;

[0139] Based on the sinusoidal positional encoding network structure introduced in S2, to avoid the neural radiation field model prematurely fitting local noise or pseudo-high-frequency details under sparse perspectives, this embodiment proposes a progressive positional encoding strategy driven by model uncertainty to control the frequency range of spatial positional encoding input to the neural radiation field model. Specifically, a frequency weight mask is constructed based on model uncertainty and training progress, expressed as:

[0140]

[0141] in, The frequency weight mask coefficients for progressive position coding are the dynamic scheduling factors. ' is a hyperparameter used to adjust the amplification factor of model uncertainty during high-frequency channel unfreezing. The training progress coefficient represents the gradual increase in the overall proportion of high-frequency frequencies as training progresses, used to ensure that not all high frequencies are exposed in the early stages of training. It is defined as:

[0142]

[0143] Where step is the current training step number, and end_step is the preset maximum number of steps to fully unfreeze at a given frequency.

[0144] S3.3, Gradual unfreezing of the location coding channel;

[0145] The dynamic scheduling factor obtained using S3.2 By controlling the activation level of different frequency components in position coding, a practical application of Sine Positional Encoding (SPE) is formed.

[0146] Three-dimensional spatial coordinates of the sampling points Perform multi-frequency sinusoidal position encoding, where, This represents the three-dimensional spatial coordinates of the j-th sampling point, and a gating weight is introduced for each high-frequency component. and combine this weight with Binding is used to adjust the effective strength of different frequency channels in the current stage. The weighted position encoding expression is:

[0147]

[0148]

[0149] in, Indicates the gating weight The three-dimensional spatial coordinates of the sampling points obtained under the action The weighted multi-frequency sinusoidal position-coded feature vector is as follows. This is a frequency-specific allocation function used to ensure that the weights of high-frequency components vary. Monotonous rise, This function restricts array elements to a specified range, used to limit weights within a reasonable range, such as [0,1], where k represents the frequency channel.

[0150] As the number of training steps increases, the training progress coefficient... It will gradually increase; that is, globally, high-frequency features will gradually become more open, but different spatial regions will experience variations due to model uncertainties. Different locations will acquire high-frequency components at different speeds and intensities. This scheduling mechanism of "unfreezing by region and by time" means that location coding is not uniform linear annealing, but rather spatially adaptive unfreezing driven by uncertainty.

[0151] S4. Interpolate the camera extrinsic parameters of adjacent source viewpoints to obtain the new viewpoint pose. On the one hand, backproject the source viewpoint and remap it to the new viewpoint to generate a pseudo-new viewpoint. On the other hand, input the camera parameters of the new viewpoint into the neural radiation field model to render the predicted viewpoint. This realizes the synthesis of new viewpoints without external labels and provides input basis for subsequent self-supervised partitioning and region division.

[0152] S4 specifically includes the following steps:

[0153] S4.1 Generate new camera view parameters based on the extrinsic parameter interpolation of adjacent source view cameras;

[0154] In the existing sparse multi-view artifact image sequence, two adjacent source views are selected. and The corresponding camera external poses are respectively and ,in, Represents the rotation matrix. This represents the translation vector. To generate new target viewpoint camera parameters, the poses of adjacent source viewpoints are interpolated to obtain the new target viewpoint. position ;

[0155] Specifically, let the interpolation coefficients be denoted as The rotation matrix can be obtained using, for example, spherical linear interpolation (Slerp).

[0156]

[0157] And perform linear interpolation on the translation vector:

[0158]

[0159] If the camera intrinsic parameter matrix K can be considered constant or calibrated between adjacent viewpoints, then the target new viewpoint camera parameters are expressed as follows:

[0160]

[0161] in, This indicates the camera parameters for the new perspective of the target.

[0162] The result of this step is the generation of a new camera perspective that was not actually captured. This provides conditions for subsequent pseudo-truth value synthesis and self-supervised constraints. This new perspective can be regarded as being between the source perspective and the actual source perspective. and The "intermediate perspective" between these two perspectives can construct additional monitoring signals without the need for additional data acquisition.

[0163] S4.2 Generate a pseudo-truth view with a new perspective based on geometric warp operations;

[0164] The target new perspective camera parameters obtained using S4.1 and any source perspective Observational images Its pixel depth estimation A geometric projection transformation, or geometric warp operation, is performed on the source view image to synthesize a pseudo-true view under the new viewpoint. .

[0165] The aforementioned geometric warp operation essentially involves using known source viewpoint images and geometric estimations to reproject information into a new, un-captured viewpoint, thus constructing a "pseudo-true" monitoring signal. and And no additional manual labeling is required;

[0166] S4.3 Prediction of neural radiation field model based on new perspective parameters;

[0167] The target new perspective camera parameters obtained in S4.1 The volume density of the i-th pixel is obtained by inputting the data into the neural radiation field model. and color distribution parameters By accumulating the sampling points along the ray through volume rendering integral, the predicted radiation results under this new perspective are obtained. and the corresponding depth estimation .

[0168] The prediction result, along with the pseudo-true value obtained in S4.2, is used in S5 below for partition self-supervised consistency constraints and region division.

[0169] S5. Compare the consistency between the pseudo-new view and the predicted view, calculate the depth consistency between the two at the corresponding pixel positions, and adaptively adjust the pixel supervision intensity according to the consistency result and data uncertainty. Divide the new view into reliable or unreliable regions, apply strong supervision training to reliable regions, and apply weak supervision (or regular constraints) to unreliable regions to improve the reliability and robustness of the overall reconstruction.

[0170] In S5, based on partition self-supervised learning with consistency and uncertainty, the new perspective radiation prediction results obtained in S4 are applied. With pseudo-truth view A consistency comparison is performed, and continuous weights are generated based on the uncertainty of the evidence to complete the region division. Further, S5 specifically includes the following steps:

[0171] S5.1, Deep consistency comparison and adaptive threshold adjustment based on data uncertainty;

[0172] The new perspective of the same target obtained in S4 Below, the pseudo-ground value depth map generated by warp will be displayed. Depth map predicted by neural radiation field model Pixel-by-pixel alignment comparison yields the depth consistency error, expressed as:

[0173]

[0174] in, Represents the pixel coordinates of the target from a new perspective. Depth consistency error at the location This represents the predicted depth value obtained by the neural radiation field model rendered from this new perspective. This represents the pseudo-true value reference depth obtained by geometrically remapping the source view to the new viewpoint of the target;

[0175] An adaptive threshold is determined for each pixel location or the location corresponding to a ray sample. This adaptive threshold is used to determine whether the consistency at that location is reliable. This threshold is not a fixed constant, but rather incorporates the data uncertainty corresponding to that location, i.e., the noise-type uncertainty derived from the evidence parameters output by the neural radiation field model in the previous step. As described in S3.1 above, the data uncertainty can be determined based on... Evidence parameters are calculated, and based on this, according to Data uncertainty at each pixel Set an adaptive threshold for uncertainty, expressed as follows:

[0176]

[0177] in, Indicates the first An adaptive threshold for uncertainty at each pixel. Based on the threshold, This is the scaling factor;

[0178] This step means that if a region itself is very noisy due to highlights, occlusion, texture defects, etc., this method allows for a larger depth error and still considers it as "usable information" instead of directly classifying it as an error. Then, using this adaptive threshold as a criterion, a consistency indicator function is defined to mark the consistency status of pixels as follows:

[0179]

[0180] in, This represents the pixel coordinates of the target from a new perspective. The depth consistency indicator function at that location When the value is 1, it indicates that the geometric projection at that location is consistent, and the reliability is high. When =0, it indicates that the geometric projection at that location is unstable (usually due to occlusion, pseudo-alignment, warp artifacts, or noisy regions), and the confidence level is low.

[0181] according to The value of is used to divide the pixels in the new viewpoint of the target into reliable regions with consistent depth and unreliable regions with inconsistent depth, denoted as and respectively. and The expressions are as follows:

[0182]

[0183]

[0184] in, This represents the set of pixels with consistent depth and reliable geometric relationships within the new perspective of the target. This represents a set of pixels with inconsistent depths and unreliable geometric relationships in a new perspective of the target.

[0185] This step makes the threshold adaptive, depending on the noise environment of the pixel itself, rather than a fixed threshold. This makes the comparison process more robust to areas of high reflectivity, wear, and noise in dark areas of the artifact's surface.

[0186] S5.2 To suppress noise and highlight geometric boundaries, pixel weights are defined as follows:

[0187]

[0188] in, This represents any pixel position within the new perspective of the target. This indicates the pixel weight at that pixel location, derived from data uncertainty. This indicates the uncertainty of the data at that pixel location. It is the numerical stability constant. ;

[0189] For reliable regions, photometric consistency loss is used. Then, normalization is performed. The expression for this process is:

[0190]

[0191]

[0192] in, Indicates loss of photometric uniformity The normalization factor, For the normalized smoothing term, ;

[0193] To avoid treating incorrect reprojection as label learning, in Use depth-order consistency to obtain for The local neighborhood is defined, and the depth order of the prior and prediction is given by the following expressions:

[0194]

[0195]

[0196] in, For the neighborhood pixel position, This indicates the prior depth order symbol calculated from the pseudo-ground value depth, used to characterize the pixel position in the pseudo-ground value. with neighboring pixel positions The relationship between the preceding and following parts, This indicates the order of predicted depths calculated based on the predicted depth, used to characterize the sequential relationship between the two pixel positions in the current model's prediction. and These represent the depth values ​​of the pseudo-ground truth depth map at these two pixel positions, respectively. and These represent the depth values ​​of the predicted depth map at these two pixel locations, respectively, sign( ) is a sign function that outputs three discrete values: {-1, 0, 1}.

[0197] if and If the symbols are different, it means the order has been reversed, which requires a penalty. The expression is:

[0198]

[0199]

[0200] in, Indicates pixel position With the neighborhood pixel position The relative depth order consistency penalty function between them;

[0201] This results in the unreliable area loss. Then, normalization is performed. The expression for this process is:

[0202]

[0203]

[0204] in, Indicates loss in unreliable areas The normalization factor;

[0205] Combining equations (13)-(20), the partition loss Defined as:

[0206]

[0207] in, and Both are tradeoff coefficients, and both are greater than 0.

[0208] The above steps achieve dynamic partitioning guided by both consistency and uncertainty. The reliable region adopts strong supervision of photometric alignment, while the unreliable region is weakly supervised by relative depth order. It naturally possesses scale invariance and is more robust to specular highlights and occlusions.

[0209] S6. Construct a joint optimization objective function that includes color principal loss and partition loss, perform end-to-end training in conjunction with differentiable rendering specification constraints, optimize global radiation field parameters, and output the 3D reconstruction results of cultural relics and uncertainty assessment results.

[0210] In step S6, the partitioning loss obtained in step S5 is combined with the pedestal loss of the evidence modeling NeRF (e.g., NIG negative log-likelihood and canonical term; in this embodiment, the pedestal loss can be selected as color normal inverse gamma negative log-likelihood loss) to jointly optimize the model and obtain the overall loss. The expression is:

[0211]

[0212] in, This indicates damage to the base. This indicates the partition loss.

[0213] To further verify the effectiveness and superiority of this method in the task of reliable modeling of complex surface defects, this invention constructs an experimental scenario based on the LLFF public dataset, and compares and evaluates the performance of the original ENeRF method with that of this method and its sub-modules (uncertainty-driven progressive position encoding module and partition self-supervised module). During the experiment, all models were optimized under the same data partitioning and training conditions, with the training steps set to 100k steps to ensure sufficient model fit. Model performance was evaluated using three commonly used metrics: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity (SSIM), and Perceptual Distance Indicator (LPIPS). PSNR and SSIM are used to measure the pixel-level differences and structural consistency between the predicted image and the real image, while LPIPS is used to evaluate the perceptual similarity between the generated image and the real image.

[0214] Table 1. Model Performance Evaluation Indicators

[0215]

[0216] As can be seen from the experimental results in Table 1, the uncertainty-driven progressive location coding and partitioned self-supervised collaborative optimization method proposed in this invention outperforms the comparative methods in all three metrics. Compared with the original ENeRF, PSNR increased from 21.185 to 21.926, SSIM increased from 0.772 to 0.797, and LPIPS decreased from 0.316 to 0.267, indicating that this method can effectively improve image reconstruction quality and detail restoration under sparse perspectives.

[0217] like Figures 2-16 The visualization results show that in several key areas (such as fossil skeleton edges, railing details, and background structures), the rendering results generated by this invention are significantly superior to the original ENERF method in terms of edge sharpness, texture integrity, and microstructure coherence. Specifically, this method can more clearly recover the curved structure and contour continuity of the skeleton edges, and the interval texture of the railings is clearly discernible, while the original method usually exhibits obvious blurring, jitter, or artifacts in such high-frequency areas. In addition, under complex materials such as glass reflections and specular edges in the background area, the rendering results of this method are closer to the geometry and lighting distribution of the real image, presenting a more believable ability to model details.

[0218] Experimental results fully demonstrate that the method proposed in this invention can achieve more stable and reliable reconstruction of cultural relic surfaces under sparse viewing conditions. Through an uncertainty-driven progressive frequency unfreezing mechanism and partitioned self-supervised collaborative optimization, this method can still maintain high structural consistency and texture fidelity in modeling complex surface areas such as high reflectivity, fine cracks, and wear of photographed cultural relics under sparse conditions.

[0219] This invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the sparse perspective artifact 3D reconstruction method described above.

[0220] See Figure 17 The present invention also provides a computer device, including a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the sparse perspective artifact 3D reconstruction method described above.

[0221] This invention also provides a computer program product containing instructions that, when run on a computer, cause the computer to perform the steps of the sparse perspective artifact 3D reconstruction method described above.

[0222] It is understood that the systems, devices and storage media provided in the embodiments of the present invention correspond to the methods provided in the embodiments of the present invention, and the explanations, examples and beneficial effects of the relevant content can be referred to the corresponding parts of the above-mentioned sparse perspective cultural relic three-dimensional reconstruction method.

[0223] It should be noted that those skilled in the art will understand that all or part of the steps implemented in the embodiments of the present invention can be implemented entirely or partially by software, hardware, firmware, or any combination thereof. When implemented in hardware, it can be implemented entirely or partially by purchasing standard parts or modifications. When implemented in software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available media may be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid state disks (SSDs)).

[0224] In summary, this invention addresses the problems of low reliability and poor stability in existing image processing technologies when faced with limited viewing angles. It provides a sparse-view 3D reconstruction method for cultural relics based on evidence uncertainty-driven progressive positional encoding of neural radiation fields and partitioned self-supervision. This method, through the collaborative design of evidence uncertainty-driven progressive positional encoding and warp-guided partitioned self-supervision, effectively suppresses premature high-frequency fitting and cross-surface erroneous supervision in sparse-view scenarios, significantly improving the overall geometric stability and detail texture restoration of cultural relics. It also provides pixel-level uncertainty assessment, offering highly reliable 3D reconstruction support for the digital archiving and restoration decisions of cultural relics.

[0225] It should be understood that the examples and embodiments described herein are for illustrative purposes only and are not intended to limit the invention. Those skilled in the art can make various modifications or changes based on them. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the protection scope of the invention.

Claims

1. A method for 3D reconstruction of cultural relics from a sparse perspective, characterized in that, Includes the following steps: S1. Obtain sparse multi-view images of cultural relics and corresponding camera internal and external parameters, construct rays by pixels and sample within the ray range to obtain a set of three-dimensional sampling points for neural radiation field training. S2. Construct a neural radiation field model based on a set of three-dimensional sampling points, introduce an evidence uncertainty modeling framework, perform implicit representation learning on the three-dimensional radiation field, and output the color of the sampling points and their uncertainty. S3. Introduce an uncertainty-driven progressive position coding method to perform multi-frequency sinusoidal position coding on the spatial coordinates of the sampling points. In the early stage of training, only the low-frequency channel is activated. As the uncertainty of the model decreases, the high-frequency channel is gradually unfrozen to achieve progressive feature learning from low frequency to high frequency. S4. Interpolate the camera extrinsic parameters of adjacent source viewpoints to obtain the new viewpoint pose. On the one hand, backproject the source viewpoint and remap it to the new viewpoint to generate a pseudo new viewpoint. On the other hand, input the camera parameters of the new viewpoint into the neural radiation field model to render the predicted viewpoint. S5. Compare the consistency between the pseudo-new view and the predicted view, calculate the depth consistency between the two at the corresponding pixel positions, and adaptively adjust the pixel supervision intensity according to the consistency result and data uncertainty. Divide the new view into reliable or unreliable regions, apply strong supervision training to reliable regions, and apply weak supervision to unreliable regions. S6. Construct a joint optimization objective function that includes color principal loss and partition loss, perform end-to-end training in combination with differentiable rendering specification constraints, optimize global radiation field parameters, and output the 3D reconstruction results of cultural relics and uncertainty assessment results. S3 further includes: S3.1 Calculate uncertainty based on evidence parameters; Model uncertainty measures whether the neural radiation field model has learned well enough at the current location, while data uncertainty measures whether a sampling point itself is difficult to observe stably due to external factors. For the i-th pixel in the training batch, model uncertainty and data uncertainty are calculated, and the resulting uncertainty is used as a scheduling signal during the training process. Its calculation expression is as follows: in, This represents the model uncertainty at the i-th pixel. This indicates the uncertainty of the data at the i-th pixel. This represents the scale parameters after volume rendering and blending. This represents the shape parameters after volume rendering and blending. This represents the precision parameters after volume rendering and blending. S3.2 Constructing a progressive location coding strategy based on model uncertainty; To avoid the neural radiation field model prematurely fitting local noise from a sparse perspective, a frequency weight mask is constructed based on model uncertainty and training progress, expressed as: in, The frequency weight mask coefficients for progressive position coding are the dynamic scheduling factors. This is the training progress coefficient, representing a gradual increase in the overall proportion of high-frequency frequencies being exposed as training progresses. This is used to ensure that not all high frequencies are exposed during early training. This is a hyperparameter used to adjust the amplification factor of model uncertainty during high-frequency channel unfreezing; S3.3, Gradual unfreezing of the location coding channel; The dynamic scheduling factor obtained using S3.2 By controlling the activation level of different frequency components in position coding, a practical application of progressive position coding is formed, which controls the three-dimensional spatial coordinates of the sampling points. Perform multi-frequency sinusoidal position encoding, where, Let j represent the j-th sampling point on the i'-th ray, where j is the index of the sampling point. This index is used to distinguish different sampling positions on the same ray or pixel, and a gating weight is introduced for each high-frequency component. and combine this weight with Binding is used to adjust the effective strength of different frequency channels in the current stage. The weighted position encoding expression is: in, Indicates the gating weight Sampling points obtained under action The weighted multi-frequency sinusoidal position-coded feature vector, This is a frequency-specific allocation function used to ensure that the weights of high-frequency components vary. Monotonous rise, This function restricts array elements to a specified range, used to limit weights within a reasonable range, where k represents the frequency channel.

2. The sparse perspective method for three-dimensional reconstruction of cultural relics as described in claim 1, characterized in that, S1 and S2 further include: Based on sparse multi-view images of cultural relics and corresponding camera intrinsic and extrinsic parameters, layered sampling is performed along pixel rays to form three-dimensional sampling points. The layered sampling includes coarse sampling and fine sampling based on resampling. Using the spatial coordinates of the sampling points and the direction of the line of sight as input to the neural radiation field model, the three-dimensional radiation properties are implicitly represented and the color estimate is output. An evidence uncertainty modeling framework is embedded in the neural radiation field model to simultaneously provide color prediction and its uncertainty. Sine position coding is applied to the spatial coordinates of the sampling points to form a multi-frequency representation, which supports the subsequent gradual unfreezing.

3. The sparse perspective method for three-dimensional reconstruction of cultural relics as described in claim 1, characterized in that, S4 further includes: S4.1 Generate new camera view parameters based on the extrinsic parameter interpolation of adjacent source view cameras; In the existing sparse multi-view artifact image sequence, two adjacent source views are selected. and The corresponding camera external poses are respectively and ,in, Represents the rotation matrix. This represents the translation vector. To generate new target viewpoint camera parameters, the poses of adjacent source viewpoints are interpolated to obtain the new target viewpoint. position The target new perspective camera parameters are expressed as follows: in, This represents the target's new perspective camera parameters, where K represents the camera intrinsic parameter matrix; S4.2 Generate a pseudo-truth view with a new perspective based on geometric warp operations; The target new perspective camera parameters obtained using S4.1 and any source perspective Observational images Its pixel depth estimation A geometric projection transformation, or geometric warp operation, is performed on the source view image to synthesize a pseudo-true view under the new viewpoint. ; S4.3 Prediction of neural radiation field model based on new perspective parameters; The target new perspective camera parameters obtained in S4.1 The volume density of the i-th pixel is obtained by inputting the data into the neural radiation field model. and color distribution parameters By accumulating the sampling points along the ray through volume rendering integral, the predicted radiation results under this new perspective are obtained. and the corresponding depth estimation .

4. The sparse perspective method for three-dimensional reconstruction of cultural relics as described in claim 1, characterized in that, In step S5, based on self-supervised learning of partitions with consistency and uncertainty, the new perspective prediction radiation results obtained in step S4 are used to predict the radiation results. With pseudo-truth view A consistency comparison is performed, and continuous weights are generated based on the uncertainty of the evidence to complete the region division. Further, step S5 includes the following steps: S5.1, Deep consistency comparison and adaptive threshold adjustment based on data uncertainty; From the new perspective of the target, the predicted depth is compared with the remapping reference depth to obtain the depth consistency error, which is expressed as: in, Represents the pixel coordinates of the target from a new perspective. Depth consistency error at the location This represents the predicted depth value obtained by the neural radiation field model rendered from this new perspective. This represents the pseudo-true value reference depth obtained by geometrically remapping the source view to the new viewpoint of the target; An adaptive threshold is determined for each pixel location or the corresponding position of the ray sampling. This adaptive threshold is used to determine whether the consistency at that location is reliable. Data uncertainty at each pixel Set an adaptive threshold for uncertainty, expressed as follows: in, Indicates the first An adaptive threshold for uncertainty at each pixel. Based on the threshold, This is the scaling factor; Define a consistency indicator function with the following expression: in, This represents the pixel coordinates of the target from a new perspective. The depth consistency indicator function at that location When the value is 1, it indicates that the geometric projection at that location is consistent, and the reliability is high. When =0, it indicates that the geometric projection at that location is unstable and has low reliability; according to The value of is used to divide the pixels in the new viewpoint of the target into reliable regions with consistent depth and unreliable regions with inconsistent depth, denoted as and respectively. and The expressions are as follows: in, This represents the set of pixels with consistent depth and reliable geometric relationships within the new perspective of the target. This represents a set of pixels with inconsistent depth and unreliable geometric relationships in a new perspective of the target. S5.2 To suppress noise and highlight geometric boundaries, pixel weights are defined as follows: in, This represents any pixel position within the new perspective of the target. This indicates the pixel weight at that pixel location, derived from data uncertainty. This indicates the uncertainty of the data at that pixel location. It is the numerical stability constant. ; For reliable regions, photometric consistency loss is used. Then, normalization is performed. The expression for this process is: in, Indicates loss of photometric uniformity The normalization factor, For the normalized smoothing term, ; To avoid treating incorrect reprojection as label learning, in Use depth-order consistency to obtain for The local neighborhood is defined, and the depth order of the prior and prediction is given by the following expressions: in, For the neighborhood pixel position, This indicates the prior depth order symbol calculated from the pseudo-ground value depth, used to characterize the pixel position in the pseudo-ground value. with neighboring pixel positions The relationship between the preceding and following parts, This indicates the order of predicted depths calculated based on the predicted depth, used to characterize the sequential relationship between the two pixel positions in the current model's prediction. and These represent the depth values ​​of the pseudo-ground truth depth map at these two pixel positions, respectively. and These represent the depth values ​​of the predicted depth map at these two pixel locations, respectively, sign( ) is a sign function that outputs three discrete values: {-1, 0, 1}. if and If the symbols are different, it means the order has been reversed, which requires a penalty. The expression is: in, Indicates pixel position With the neighborhood pixel position The relative depth order consistency penalty function between them; This results in the unreliable area loss. Then, normalization is performed. The expression for this process is: in, Indicates loss in unreliable areas The normalization factor; Combining equations (13)-(20), the partition loss Defined as: in, and Both are tradeoff coefficients, and both are greater than 0.

5. The sparse perspective method for three-dimensional reconstruction of cultural relics as described in claim 1, characterized in that, In step S6, the partition loss obtained in step S5 is jointly optimized with the base loss of the evidence modeling NeRF to obtain the overall loss. The expression is: in, This indicates damage to the base. This indicates the partition loss.

6. A computer-readable storage medium, characterized in that, The device contains a computer program that, when executed by a processor, causes the processor to perform the steps of the sparse perspective artifact 3D reconstruction method as described in any one of claims 1-5.

7. A computer device, characterized in that, It includes a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the sparse perspective artifact 3D reconstruction method as described in any one of claims 1-5.

Images