Indoor-oriented three-dimensional gaussian diffusion model point cloud repairing method
By introducing directional adaptive modeling of the point cloud centroid and axis-by-axis distance components into the three-dimensional Gaussian diffusion model, the problems of insufficient local structural stability and overall spatial distribution consistency in indoor point cloud restoration in existing technologies are solved, and higher quality point cloud restoration results are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- XI'AN POLYTECHNIC UNIVERSITY
- Filing Date
- 2026-04-14
- Publication Date
- 2026-05-29
AI Technical Summary
Existing 3D point cloud restoration methods are insufficient in terms of local structural stability and overall spatial distribution consistency in indoor environments. In particular, isotropic diffusion models have difficulty in taking into account both structural preservation in different directions and restoration diversity.
A three-dimensional Gaussian diffusion model for indoor environments is adopted. By introducing the centroid of the point cloud as the spatial reference center, an axis-wise distance component and a second-order statistic are constructed to form a direction-adaptive three-dimensional Gaussian forward diffusion model in the form of diagonal covariance. A denoising network is used to regulate the axis-wise diffusion intensity. The model is trained by combining observation consistency constraints and diffusion standard loss function to optimize the repair process.
It improves the structural consistency, spatial distribution rationality and usability of point cloud restoration results, enhances the robustness and generalization ability to complex occlusion, sparse sampling and non-uniform missing patterns, and reduces structural drift and excessive smoothing of details.
Smart Images
Figure CN122115803A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of 3D point cloud processing and generation modeling technology, and relates to a method for repairing 3D Gaussian diffusion model point clouds for indoor applications. Background Technology
[0002] With the development of technologies such as indoor 3D reconstruction, robot navigation, and augmented reality, 3D point clouds, as an important data form for describing indoor geometry, are widely used in tasks such as scene understanding, object recognition, pose estimation, and map building. However, in actual data acquisition, indoor point clouds often suffer from problems such as local missing points, sparse and uneven distribution, or structural fragmentation due to factors such as sensor viewpoint occlusion, reflective materials, uneven sampling density, field of view limitations, and interference from dynamic objects. This reduces the robustness and accuracy of downstream tasks. Therefore, how to effectively repair missing point clouds to restore complete, continuous indoor structures that conform to real geometric constraints is a key focus of existing technologies.
[0003] Existing point cloud restoration methods mainly include rule-based or geometric prior-based methods and deep learning-based methods. Rule-based or statistical modeling methods typically rely on strategies such as plane fitting, structural hole filling, or probability distribution assumptions. While simple to implement, they have limited ability to represent complex interior structures (such as multi-layered furniture, slender supports, and concave-convex decorations), and are prone to problems such as overly smoothed restoration results, loss of details, or structural discontinuities. Deep learning methods based on autoencoders, generative adversarial networks, and other technologies achieve restoration by learning the latent representation of training data. They can achieve certain results under specific data distributions, but these methods are often heavily dependent on training data. When faced with unseen interior layouts or complex occlusions, they are prone to local structural distortion, unreasonable restoration shapes, or inconsistencies with the observed point cloud, affecting the reliability of the restoration.
[0004] In recent years, diffusion models have been introduced into the field of 3D point cloud generation and completion due to their stable training mechanism and strong generative capabilities. Existing diffusion models in 3D space... In general, noise of the same intensity is used for diffusion modeling in all directions, assuming consistent perturbation and denoising characteristics across spatial directions, i.e., isotropic diffusion assumption. However, in real-world indoor scenes, the spatial unfolding scale, geometric constraints, and missing patterns of point clouds are often inconsistent in different directions: for example, the ground and walls in the vertical direction... It has strong geometric constraints in the horizontal direction It has a larger unfolding scale; the furniture structure is in The direction may exhibit a broad and continuous distribution, while... The direction is concentrated within a limited height range. Isotropic diffusion cannot simultaneously take into account the structural preservation and completion diversity in different directions, which can easily lead to drift in structurally sensitive directions or deviations in overall distribution consistency. Therefore, how to introduce a direction-adaptive modeling method that better conforms to the differences in indoor geometric directions in point cloud repair diffusion modeling, so as to improve the performance of repair results in terms of structural consistency, spatial distribution rationality and usability, remains an urgent problem to be solved by existing technologies. Summary of the Invention
[0005] The purpose of this invention is to provide a method for repairing point clouds in a 3D Gaussian diffusion model for indoor applications, addressing the shortcomings of existing point cloud repair diffusion models. The problem that the completion results caused by using consistent noise control in all directions are insufficient in terms of local structural stability and overall spatial distribution consistency.
[0006] The technical solution adopted in this invention is a point cloud repair method for a three-dimensional Gaussian diffusion model for indoor use. It represents the missing point cloud as a three-dimensional point set, introduces the centroid of the point cloud as a spatial reference center, constructs the axial distance components of each point relative to the centroid, and calculates the second-order statistics of each axis direction as the directional scale signal. Based on the deviation between the directional scale signal and the reference scale, the noise intensity is recalibrated axially to form a directional adaptive three-dimensional Gaussian forward diffusion model in the form of diagonal covariance. A denoising network is used to predict the noise components at each diffusion step and update them according to the axial diffusion intensity, while introducing observation consistency constraints. Finally, the diffusion standard loss function is used to train the forward diffusion model on the error between the injected real noise and the predicted noise to obtain an optimized diffusion model. Specifically, as follows:
[0007] Step 1: Represent the missing point cloud data and model its orientation, and construct the axial distance components and their second-order axial distance statistics under the centroid reference. Step 2: Based on the second-order statistics obtained in Step 1, construct a three-dimensional Gaussian forward diffusion model with directional adaptive noise control, form independent noise intensity parameters for each axis, and construct a diagonal covariance matrix. Step 3: Construct a direction-adaptive reverse denoising sampling process that matches Step 2. Initialize from standard Gaussian noise and gradually reverse sample to obtain the repaired point cloud. In the reverse sampling process, introduce observation consistency constraints to ensure that the generated result is consistent with the missing point cloud in the observed area. Step 4: Train the diffusion model using the diffusion standard loss function based on noise prediction, so that it can learn to predict the noise injected during the forward diffusion process under the axial diffusion schedule in Step 2, thereby achieving the stable reverse denoising repair in Step 3.
[0008] The invention is further characterized in that, Step 1 specifically includes: The missing point cloud in the indoor space is represented as a point set. , Given the point cloud coordinates of the nth point; calculate the centroid of the point cloud. And construct the axis-wise distance component relative to the centroid for each point: (1) Then, for each point, define its distance components relative to the centroid in three directions: (2) Finally, construct the second-order distance statistics in the three directions: (3) in, Points; Representing point clouds in The spatial unfolding scale and degree in the direction are used as the directional scale signal for step 2, which is controlled by noise on each axis.
[0009] Step 2 specifically involves: first constructing a reference scale using second-order statistics along each axis. Or axis-by-axis reference scale And define the relative deviation: ,in (4) in, It is a directional scale constructed based on second-order statistics of axis-by-axis distance. , It represents the distance components of each point relative to the centroid in three directions; For reference scale; Then, based on the relative deviation, the parameters for controlling the noise intensity at time step t are... Perform axis-by-axis recalibration to obtain axis-by-axis noise intensity: (5) in, This is the sensitivity coefficient. The range of values is ; For the clipping function to make ; The range of values is , The range of values is ; t For time steps, , This represents the total time step; structure A three-dimensional diagonal matrix: (6).
[0010] The reference scale The determination method includes any of the following: Method 1: Set as a fixed hyperparameter constant before training. ,and Take 0.5 to 2 times the mean of the second-order statistics for the corresponding direction in the training set; Method 2: Obtain the axis-by-axis reference scale separately. ;
[0011] in, This indicates calculating the average.
[0012] The three-dimensional Gaussian forward diffusion process in step 2 adopts a diagonal covariance form, and its one-step transition distribution is as follows: (7) in, This is the current state. This indicates scaling the previous state along the axis. The diagonal covariance matrix injected for axis-by-axis noise, thereby... The noise intensity in the three directions is independent of each other and is matched with the directional scale signal.
[0013] In step 3, the denoising network is at least in the current diffusion state. The time step t and conditional information are used as inputs and outputs as prediction noise, wherein the conditional information includes any one or a combination of the following: (1) Conditional features c extracted from the missing point cloud by the point cloud feature encoder; (2) Missing point cloud And its observation mask M.
[0014] Step 3 is as follows: Backdiffusion is used to progressively generate point clouds from random noise. Let the backdiffusion distribution be a diagonal Gaussian independent of each axis: (8) in, c These are partial point cloud conditional features extracted in step 1. These are the parameters for the denoising network. reverse mean for: (9) Inverse covariance : (10) Among them, the noise intensity of each axis The centroid-axis distance statistics from step 2 are given; , , , To predict noise; The specific process of backsampling is as follows: ① Initialization: The generation phase begins with sampling the initial point cloud using standard Gaussian sampling. ; ②Stepwise denoising sampling: for Execute sequentially; a. Input The noise is then fed into a denoising network to obtain the predicted noise. ; b. Calculation and ; c. Sampling random variables ,get: ; d. Observation Consistency Backfilling: Obtaining the next state at each time step. Then, based on the observation mask M, the observed area is backfilled with the corresponding values of the input point cloud to obtain the final result. : (11) Here, ⊙ represents element-wise multiplication to ensure that the generated point cloud is consistent with the input missing point cloud in the observed area.
[0015] Step 4 employs a diffusion standard loss function based on noise prediction. The specific method for defining the loss function is as follows: Let time step t The noisy point cloud sample is: (12) in, This indicates the initial step with a noisy cloud. Standard Gaussian noise, ; , , ; It is a unit diagonal matrix; the denoising network outputs predicted noise. And define the standard noise prediction loss for the diffusion model: (13) in, It expresses expectation.
[0016] Step 1 also includes conditional encoding of the missing point cloud: using a point cloud feature encoder to extract global shape features and local context features from the missing point cloud, which are then used as conditional features c and input into the denoising network in step 3 to constrain the repair result to be consistent with the missing point cloud in terms of geometric shape and local structure.
[0017] Compared with the prior art, the beneficial effects of the present invention are: This invention explicitly introduces a spatially orientation-dependent anisotropic modeling mechanism during point cloud modeling and diffusion. Through centroid reference and axis-by-axis scale statistics-driven orientation-adaptive noise control, it enables point clouds to... The model exhibits differentiated diffusion perturbation and denoising recovery behaviors along different coordinate axes, effectively avoiding problems such as structural drift, boundary blurring, and excessive smoothing of details that are prone to occur in existing isotropic diffusion models for indoor point cloud restoration. The restored point cloud is more consistent with the real geometric characteristics of the interior in terms of overall geometry, local structural continuity, and directional constraints (such as planar structures like walls, floors, and tabletops, as well as furniture support structures), thereby improving the structural stability and spatial rationality of the point cloud restoration results.
[0018] Because the forward diffusion and backward denoising processes of this invention employ axis-by-axis independent diagonal covariance three-dimensional Gaussian modeling, and differentiate the diffusion intensity in each direction using directional scale signals, the model can adapt to changes in different indoor structural types and scale ratios (e.g., open areas versus narrow areas, planar structures versus slender support structures, low furniture versus tall facades, etc.). Compared to existing technologies that rely on fixed geometric priors, regular hole filling, or a single uniform noise assumption, this invention is less constrained by a single distribution assumption when filling in missing areas, and can cover a richer variety of indoor spatial structural forms, thereby improving the robustness and generalization ability of the repair results to complex occlusion, sparse sampling, and non-uniform missing patterns.
[0019] This invention employs a standard noise prediction training objective that matches the directional adaptive diffusion mechanism, enabling the network to directly learn the noise injected during the axis-by-axis independent diffusion process during the training phase. This achieves collaborative optimization of the training objective and the generation mechanism within the same technical framework, reducing convergence instability and quality fluctuation issues caused by inconsistencies between the objective function and the diffusion process in existing technologies. Attached Figure Description
[0020] Figure 1 This is a flowchart of the directional adaptive three-dimensional Gaussian diffusion model method of the present invention; Figure 2 This is a schematic diagram of the overall structure of the conditional diffusion network of the present invention; Figure 3 This is a schematic diagram of the forward diffusion and reverse denoising process of the present invention; Figure 4 This is a flowchart of the construction process for axis-wise directional scale and noise intensity under the centroid reference. Detailed Implementation
[0021] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.
[0022] Example 1 This invention provides a method for repairing point clouds in a 3D Gaussian diffusion model for indoor applications. The specific steps are as follows: Step 1: Represent the missing point cloud data and model its orientation, and construct the axial distance components and their second-order axial distance statistics under the centroid reference. Step 2: Based on the second-order statistics obtained in Step 1, construct a three-dimensional Gaussian forward diffusion model with directional adaptive noise control, form independent noise intensity parameters for each axis, and construct a diagonal covariance matrix. Step 3: Construct a direction-adaptive reverse denoising sampling process that matches Step 2. Initialize from standard Gaussian noise and gradually reverse sample to obtain the repaired point cloud. In the reverse sampling process, introduce observation consistency constraints to ensure that the generated result is consistent with the missing point cloud in the observed area. Step 4: Train the diffusion model using the diffusion standard loss function based on noise prediction, so that it can learn to predict the noise injected during the forward diffusion process under the axial diffusion schedule in Step 2, thereby achieving the stable reverse denoising repair in Step 3.
[0023] Note: The term "direction adaptive" as used in this article refers to... Three-dimensional Gaussian diffusion modeling is performed by setting different noise intensity parameters for each of the three coordinate axes and using a diagonal covariance matrix.
[0024] The missing point cloud for indoor spaces specifically includes tables, chairs, computers, keyboards, lamps, cups, walls, bookshelves, etc.
[0025] Example 2 Based on Example 1, Step 1 aims to establish an accurate data foundation that conforms to the real-world radar acquisition characteristics for the directional adaptive noise-controlled 3D Gaussian diffusion process. The core idea is to abstract the radar point cloud distribution characteristics in 3D space into differences in directional geometric scale and dispersion around the spatial center: in a real indoor scene, different objects and structures... The spatial extent, point cloud sparsity, and geometric constraints in the three directions are usually not consistent. Taking a chair and a table as examples, the point cloud of a chair is in the horizontal direction. It typically exhibits a "narrow and dispersed" distribution characteristic, and in the vertical direction The point clouds are mainly concentrated in the height range of chair legs and seat; table point clouds often exhibit a "wide and continuous" distribution in the horizontal direction, with the tabletop forming a large area of planar structure, while in the vertical direction they are concentrated in the range of tabletop thickness and table leg height. These differences result in different statistical scales of the point clouds in the three directions, and it will be difficult to simultaneously take into account the preservation of structure and the diversity of generation in different directions if a single uniform noise control is used.
[0026] Therefore, this invention introduces the centroid of the point cloud as the spatial reference origin and defines the distance components of each point relative to the centroid in the three coordinate axes and the second-order statistics of the axis-by-axis distance. It establishes three-directional independent directional modeling parameters, providing an interpretable, stable and spatially consistent control basis for the subsequent three-dimensional Gaussian diffusion process of axis-by-axis noise injection. This improves the structural consistency and morphological rationality of point cloud restoration of indoor objects (such as chairs, tables, etc.) in different directions.
[0027] Meanwhile, to reduce background noise interference in the original radar point cloud and improve the target structure modeling capability of the subsequent conditional diffusion network, a pre-processing point cloud segmentation module is introduced at the input. This pre-processing point cloud segmentation module can employ point cloud segmentation networks such as RandLA-Net to perform semantic segmentation or foreground segmentation on the original radar point cloud, extract the target foreground point cloud, and then feed it into the conditional encoder and diffusion network for subsequent modeling.
[0028] The specific steps are as follows: (1) Conditional input and target: Receive local, sparse, non-uniform 3D radar point cloud data collected from the real world or generated by simulation as conditional input, denoted as a point set. ,in For the number of points. Each point Represented by three-dimensional Cartesian coordinates, i.e. The goal of this invention is to generate a corresponding, complete, and realistic 3D point cloud that conforms to the characteristics of real radar detection. .
[0029] (2) Use "centroid-axis distance statistics" to characterize the uncertainty and structural differences in each axis direction: In order to accurately model point clouds in different spatial directions ( To address the different generation uncertainties and structural characteristics on the axes, this invention uses the centroid of the point cloud as the spatial reference center and characterizes the spatial scale differences in the three directions by the axial distance components of each point relative to the centroid and their statistics.
[0030] First, the point set Calculate the centroid:
[0031]
[0032] Then, for each point Define its axis-by-axis distance components:
[0033] Further construct the second-order statistic for axis-by-axis distance:
[0034] in, Representing point clouds in The spatial extent and dispersion in a direction; a larger value indicates a more dispersed distribution of point clouds in that direction. Therefore, a relatively stronger noise injection (a larger value) can be used in that direction during subsequent diffusion. This is to match its statistical characteristics, and vice versa. The second-order statistic of range per axis can reflect the differences in structural constraints of real radar point clouds in different directions. For example, in many radar configurations, the spatial distribution characteristics in the range direction and the angular direction are different, resulting in point clouds exhibiting different scales and sparsity in the horizontal and vertical directions. Therefore, using... It can provide three independent control criteria for the subsequent diffusion process, enabling the model to use different noise injection intensities and training weights in different directions, thereby improving the spatial rationality and structural consistency of the generated point cloud.
[0035] (3) Conditional encoder: Use a point cloud feature encoder (e.g., a PointNet-based neural network) to process the input partial point cloud. The global shape features and local context features are extracted and denoted as conditional features c. The conditional features c will participate in the subsequent diffusion process as conditional information, guiding the generated complete point cloud to maintain consistency with the input part in terms of geometric shape and local structure, thereby realizing point cloud generation oriented to conditional input.
[0036] (4) During the training phase, the forward diffusion process uses a real, complete point cloud as the initial state, that is, let This represents the complete point cloud of the training samples. To integrate with the diffusion model framework, this invention employs a Markov chain with progressively increasing noise. exist The noise is gradually perturbed to an approximately standard Gaussian distribution within a time step. During the generation phase, the inverse denoising sampling is initialized with standard Gaussian noise, i.e., from... An initial point cloud is obtained through sampling, and then gradually reverse-sampled to generate... .
[0037] Step 1 constructs a three-dimensional scaling statistical model based on a centroid reference: using second-order statistics of the distances between the centroid and each axis. Representation point cloud in The spatial extent and dispersion in three directions. Simultaneously, step one yields the conditional feature c and the initial point cloud required for the diffusion process. This provides data and parameter preparation for the three-dimensional Gaussian forward diffusion process with direction-adaptive noise control in step 2.
[0038] Example 3 Building upon Example 2, step 2 aims to define and simulate a physically plausible, axis-independent noise addition process, progressively perturbing the complete radar point cloud into a noise distribution approaching a standard Gaussian, thus providing a stable statistical path for the reverse generation process. The key innovation of this invention lies in: axis-by-axis noise intensity. Instead of directly fixing the noise level, the point cloud is adaptively controlled by the three-directional geometric scale statistics around its centroid, so that the noise injection intensity in different coordinate axis directions matches the actual spatial distribution characteristics of the point cloud. The specific steps are as follows: (1) Definition of Spatial Center Reference and Distance Components of Each Axis: Continuing the directional modeling idea from step 1, this invention abstracts the distribution pattern of point clouds in three-dimensional space as "directional scale differences around the spatial reference center." The point cloud state at any time step t during the diffusion process... ,in First, calculate its centroid (space reference center):
[0039]
[0040] And define the axis-wise distance components of each point relative to the centroid:
[0041] Note: The distance components mentioned above are purely geometric quantities used to provide directional scale signals. Their function is solely to allow different statistical scales to be obtained in different directions, thereby driving... Directional adaptive control.
[0042] Constructing orientation scale based on second-order statistics of axis-by-axis distance :
[0043] (2) Set target reference scale
[0044] Method 1: Constant setting Set as a hyperparameter constant, fixed before training, and use the same value in all three directions. The range of the constant's value is... .
[0045] Method 2: Setting each axis in different directions Set separately Each corresponds to a target scale in three directions, enhancing expressive ability.
[0046]
[0047] in, This indicates calculating the average.
[0048] (3) Define relative deviation:
[0049] This indicates that the current scale in this direction is larger than the target reference scale, therefore a larger diffusion intensity (greater) is used in this direction. β (values) to match its larger spatial range and degree of dispersion; This indicates that the scale in this direction is lower than the target reference scale, therefore a relatively small diffusion intensity is used in this direction.
[0050] Note: This relative deviation is used to adjust the diffusion intensity of each axis. The diffusion intensity of the axis is adaptively adjusted according to this deviation.
[0051] (4) The diffusion intensity of each axis is controlled by the relative deviation.
[0052] Parameters for controlling noise intensity at time step t Based on this, the noise intensity of each axis is obtained:
[0053] in, This is the sensitivity coefficient. The range of values is ; For the clipping function to make ; The range of values is , The range of values is ; t For time steps, , This represents the total time step; structure A three-dimensional diagonal matrix:
[0054] Example 4 Based on Example 3, a three-dimensional Gaussian forward diffusion model with adaptive noise control is constructed: Since each subsequent step in the diffusion process depends only on the preceding step, it conforms to the process of a Markov chain; this invention defines a forward Markov chain:
[0055] Each subsequent step transforms into a diagonal Gaussian:
[0056] in, The mean term is used to scale the point cloud state of the previous time step along one axis to preserve the main information of the original geometry. The covariance term is used to inject Gaussian noise along each of the three coordinate axes, and its magnitude is determined by the axial diffusion intensity. Therefore, this step can be understood as: while preserving the main structure of the previous state, adaptively adding noise perturbations of different intensities along each direction. The axial noise intensity... The noise is automatically adjusted by the second-order statistic of the centroid distance, so the noise in different directions is more in line with the real spatial scale characteristics of the point cloud.
[0057] definition: Then you can directly from Sampling :
[0058] The output of the second step includes: 1. Sequence definition of forward diffusion ; 2. Axial diffusion intensity driven by centroid distance statistics The calculation method; 3. Training using closed-loop sampling ; 4. Final Noise Status (Approximately standard Gaussian noise distribution).
[0059] Step 3 is the core generation process of the model. It learns how to gradually remove noise from the noise distribution obtained in Step 2 along the backward diffusion path, and generates a complete and reliable radar point cloud under the guidance of optional conditional feature c. Consistent with Step 2, this step adopts a three-dimensional Gaussian backward diffusion process with diagonal covariance, and performs axis-by-axis noise intensity... The denoising intensity in different directions is adaptively determined by the centroid-by-axis distance statistics, thus matching the spatial scale characteristics of the point cloud and ultimately generating a complete and reliable radar point cloud. The specific steps are as follows: (1) Backdiffusion is used to generate point clouds stepwise from random noise. Its goal is to learn the conditional distribution: and from the initial noise Stepwise sampling .in c These are partial point cloud conditional features extracted in step 1, used to constrain the generated result to maintain geometric consistency with the input. The overall definition of the reverse process is written as:
[0060] in: This represents the initial noise distribution. These are the parameters of the denoising network, which are obtained through training.
[0061] (2) Independent reversed conditional Gaussians for each axis, with mean and covariance in diagonal form (from...). (Decision). Let the inverse distribution be a diagonal Gaussian independent of each axis:
[0062] Among them, reverse mean for:
[0063] Inverse covariance :
[0064] Among them, the noise intensity of each axis The centroid-axis distance statistics from step 2 are given.
[0065] The key point is that the covariance is a diagonal structure for each axis and is consistent with the definition of noise intensity for each axis in step 2, so as to ensure independent modeling in three directions throughout the process.
[0066] (3) Backsampling generation process: ① Initialization: The generation phase begins with sampling the initial point cloud using standard Gaussian sampling. ; ②Stepwise denoising sampling: for Execute sequentially a. Input To the network, obtain the predicted noise. ; b. Calculation and ; c. Sampling random variables ,get: ; d. Observation Consistency Backfilling: To ensure that the observed point cloud is not destroyed during the generation process in the repair task, the next state is obtained at each time step. Then, based on the observation mask M, the observed area is backfilled with the corresponding values of the input point cloud to obtain the final result. :
[0067] in, This indicates element-wise multiplication. This backfill operation ensures that the generated point cloud is strictly consistent across the observation area, thus achieving strongly constrained completion for restoration purposes. ③ Output: The generated point cloud is finally obtained through iterative denoising. .
[0068] The output of the third step is a point cloud generated from noise. .
[0069] Example 5 Based on Example 3, step 4 is used to train the denoising network, enabling it to learn and predict noise under the three-way independent three-dimensional Gaussian forward diffusion defined in step 2. This ensures that the point cloud generated by the back diffusion in step 3 can gradually approximate the true complete point cloud distribution. Consistent with the standard training method of traditional diffusion models, this invention uses a noise prediction target for training, that is, allowing the network to directly learn the noise components injected during the forward diffusion process. Considering that this invention uses independent diffusion intensity parameters in the three coordinate axes, the noise prediction target is based on the construction of noisy samples independently along each axis. Specifically, as follows: (1) Training samples and random step sampling: Complete point cloud for each training sample The random sampling diffusion time step t, where .
[0070] (2) Constructing noisy samples that are independent on each axis: Based on the cumulative retention coefficients in the three directions obtained in step 2, construct a diagonal matrix. And sample standard Gaussian noise The noise is independent along the three coordinate axes. Therefore, the noisy point cloud sample at time step t is represented as:
[0071] in, This indicates the percentage of the original point cloud retained along each axis in the three directions. This represents the noise injection ratio in the three directions. Since the parameters in the three directions are independent of each other, the noisy sample exhibits anisotropic diffusion characteristics consistent with those in step 2 in the three coordinate axes.
[0072] (3) Input and output of the denoising network: Define a neural network (denoiser) as The input to the denoising network, excluding the current state In addition to time step t and conditional features c, it also includes part of the point cloud. and its observation mask M; the network with The splicing or equivalent fusion form is used as input to explicitly distinguish between the observed region and the region to be repaired; the output is the predicted noise.
[0073] in, and Same shape.
[0074] Example 6 Based on Example 5, a diffusion standard loss function based on noise prediction is adopted: The training objective uses the standard simplified loss function from the diffusion model to minimize the mean square error between the actual noise and the predicted noise, i.e.:
[0075] Where t is sampled uniformly throughout all diffusion steps. To construct The injected real Gaussian noise. Because... The formation process employs an axis-by-axis independent cumulative retention coefficient matrix. Therefore, although the above loss function adopts the standard noise prediction form, its training objects implicitly contain different diffusion intensities and noise distribution characteristics in the three coordinate axes, thus maintaining consistency with the aforementioned three-direction independent control mechanism of this invention.
[0076] Equivalent expression for axis expansion: To clearly reflect the three-directional independent modeling feature of this invention, the above loss function can also be equivalently written as:
[0077] in, ; represent the network's prediction results for noise components in the three coordinate axes, respectively. This expression indicates that although the present invention uses the standard noise prediction training objective of the diffusion model, the network learns noise formed under the independent diffusion mechanism in three directions, thus still maintaining the ability to adaptively model the structural differences of each axis.
[0078] (5) Training objectives and parameter updates: During training, the Adam or AdamW generator is used to minimize the above loss function, and the parameters of the denoising network are iteratively updated until the model converges on the validation set.
[0079] The output of the fourth step is the parameters of the trained denoising network. And a complete backdiffusion process that can be used to generate point clouds from random noise (based on step 3).
[0080] Example of parameter range: a. Diffusion steps T : ; b. Trim the bottom bounds : ; c. Clip the top bound : ; d. Sensitivity : ; g. Points : (Commonly used numbers are 1024 / 2048 / 4096).
Claims
1. A method for repairing point clouds in a 3D Gaussian diffusion model for indoor applications, characterized in that, The missing point cloud is represented as a 3D point set. The centroid of the point cloud is introduced as the spatial reference center. The axial distance components of each point relative to the centroid are constructed, and the second-order statistics of each axis direction are calculated as the orientation scale signal. The noise intensity is recalibrated axially based on the deviation between the orientation scale signal and the reference scale, forming a directional adaptive 3D Gaussian forward diffusion model in the form of diagonal covariance. The noise component is predicted in each diffusion step using a denoising network and updated according to the axial diffusion intensity. At the same time, the observation consistency constraint is introduced. Finally, the error between the injected real noise and the predicted noise in the forward diffusion model is trained using the diffusion standard loss function to obtain the optimized diffusion model.
2. The method for repairing point clouds of a three-dimensional Gaussian diffusion model for indoor use according to claim 1, characterized in that, Specifically as follows: Step 1: Represent the missing point cloud data and model its orientation, and construct the axial distance components and their second-order axial distance statistics under the centroid reference. Step 2: Based on the second-order statistics obtained in Step 1, construct a three-dimensional Gaussian forward diffusion model with directional adaptive noise control, form independent noise intensity parameters for each axis, and construct a diagonal covariance matrix. Step 3: Construct a direction-adaptive reverse denoising sampling process that matches Step 2. Initialize from standard Gaussian noise and gradually reverse sample to obtain the repaired point cloud. In the reverse sampling process, introduce observation consistency constraints to ensure that the generated result is consistent with the missing point cloud in the observed area. Step 4: Train the diffusion model using the diffusion standard loss function based on noise prediction, so that it can learn to predict the noise injected during the forward diffusion process under the axial diffusion schedule in Step 2, thereby achieving the stable reverse denoising repair in Step 3.
3. The method for repairing point clouds of a three-dimensional Gaussian diffusion model for indoor use according to claim 2, characterized in that, Step 1 specifically includes: The missing point cloud in the indoor space is represented as a point set. , For the first i Point cloud coordinates; calculate the centroid of the point cloud. And construct the axis-wise distance component relative to the centroid for each point: （1） Then, for each point, define its distance components relative to the centroid in three directions: （2） Finally, construct the second-order distance statistics in the three directions: （3） in, Points; Representing point clouds in The spatial unfolding scale and dispersion degree in the direction are used as the direction scale signal for step 2, which is controlled by noise on each axis.
4. The method for repairing point clouds of a three-dimensional Gaussian diffusion model for indoor use according to claim 3, characterized in that, Step 2 specifically involves: first constructing a reference scale using second-order statistics along each axis. Or axis-by-axis reference scale And define the relative deviation: ,in (4) in, It is a directional scale constructed based on second-order statistics of axis-by-axis distance. , It represents the distance components of each point relative to the centroid in three directions; For reference scale; Then, based on the relative deviation, the parameters for controlling the noise intensity at time step t are... Perform axis-by-axis recalibration to obtain axis-by-axis noise intensity: （5） in, This is the sensitivity coefficient. The range of values is ; For the clipping function to make ; The range of values for is , The range of values for is ; t For time steps, , This represents the total time step; structure A three-dimensional diagonal matrix: （6）。 5. The method for repairing point clouds of a three-dimensional Gaussian diffusion model for indoor use according to claim 4, characterized in that, The reference scale The determination method includes any of the following: Method 1: Set as a fixed hyperparameter constant before training. ,and Take 0.5 to 2 times the mean of the second-order statistics for the corresponding direction in the training set; Method 2: Obtain the reference scale for each axis separately through statistical analysis. ; in, This indicates that the average value is being calculated.
6. The method for repairing point clouds of a three-dimensional Gaussian diffusion model for indoor use according to claim 5, characterized in that, The three-dimensional Gaussian forward diffusion process in step 2 adopts a diagonal covariance form, and its one-step transition distribution is as follows: （7） in, This is the current state. This indicates scaling the previous state along the axis. The diagonal covariance matrix injected for axis-by-axis noise, thereby... The noise intensity in the three directions is independent of each other and is matched with the directional scale signal.
7. The method for repairing point clouds of a three-dimensional Gaussian diffusion model for indoor use according to claim 6, characterized in that, In step 3, the denoising network is at least in the current diffusion state. The time step t and conditional information are used as inputs and outputs as prediction noise, wherein the conditional information includes any one or a combination of the following: (1) Conditional features c extracted from the missing point cloud by the point cloud feature encoder; (2) Missing point cloud And its observation mask M.
8. The method for repairing point clouds of a three-dimensional Gaussian diffusion model for indoor use according to claim 6, characterized in that, Step 3 is as follows: Backdiffusion is used to progressively generate point clouds from random noise. Let the backdiffusion distribution be a diagonal Gaussian independent of each axis: （8） in, c These are partial point cloud conditional features extracted in step 1. These are the parameters for the denoising network. reverse mean for: （9） Inverse covariance : （10） Among them, the noise intensity of each axis The centroid-axis distance statistics from step 2 are given. , , ; The specific process of backsampling is as follows: ① Initialization: The generation phase begins with sampling the initial point cloud using standard Gaussian sampling. ; ②Stepwise denoising sampling: for Execute sequentially; a. Input The noise is then fed into a denoising network to obtain the predicted noise. ; b. Calculation and ; c. Sampling random variables ,get: ; d. Observation Consistency Backfilling: Obtaining the next state at each time step. Then, based on the observation mask M, the observed area is backfilled with the corresponding values of the input point cloud to obtain the final result. : （11） Here, ⊙ represents element-wise multiplication to ensure that the generated point cloud is consistent with the input missing point cloud in the observed area.
9. The method for repairing point clouds of a three-dimensional Gaussian diffusion model for indoor use according to claim 8, characterized in that, Step 4 employs a diffusion standard loss function based on noise prediction. The specific method for defining the loss function is as follows: Let time step t The noisy point cloud sample is: （12） in, This indicates the initial step with a noisy cloud. Standard Gaussian noise, ; , , ; It is a unit diagonal matrix; the denoising network outputs predicted noise. And define the standard noise prediction loss for the diffusion model: （13） in, It expresses expectation.
10. The method for repairing point clouds of a three-dimensional Gaussian diffusion model for indoor use according to claim 1, characterized in that, Step 1 also includes conditional encoding of the missing point cloud: using a point cloud feature encoder to extract global shape features and local context features from the missing point cloud, which are then used as conditional features c and input into the denoising network in step 3 to constrain the repair result to be consistent with the missing point cloud in terms of geometric shape and local structure.