Gaussian splatting based anti-aliasing filtering method and apparatus, storage medium and device

Abstract

This invention proposes an anti-aliasing filtering method, apparatus, storage medium, and device based on Gaussian splashing. The method includes: acquiring the camera pose, original Gaussian primitive parameters, and filter kernel size of the scene; back-projecting an ideal low-pass filter defined in the two-dimensional image space onto the three-dimensional spatial coordinate system according to the camera pose and filter kernel size, generating a back-projection filter in the corresponding viewpoint coordinate system to limit the size expansion and transparency attenuation of the Gaussian primitives in the depth direction; calculating the expansion coefficient based on the volume change of the primitives after the back-projection filter is applied, and performing scale modulation on the Gaussian primitives; rendering based on the modulated Gaussian primitives to output an anti-aliasing target image. This invention is not constrained by the rendering process and avoids the incompatibility caused by embedding the anti-aliasing strategy into the rendering strategy through explicit filtering in three-dimensional space, achieving a general anti-aliasing processing task for the reconstruction strategy based on Gaussian primitives.

Description

Technical Field

[0001] This invention belongs to the field of explicit visual signal representation, and specifically relates to an anti-aliasing filtering method, apparatus, storage medium and device based on Gaussian splashing. Background Technology

[0002] Explicit visual signal representation refers to the method of parametrically representing signals using explicitly defined mathematical functions or geometric structures. This representation method has extremely high rendering efficiency and real-time performance, as well as excellent high-frequency detail capture capabilities, and has been widely used in new viewpoint synthesis tasks.

[0003] In recent years, 3D Gaussian Splatting (3DGS), as a typical explicit representation technique, reconstructs 3D scenes using a large number of anisotropic Gaussian spheres with properties of position, covariance, color, and opacity. Due to its primitive-based rasterization rendering, this method can achieve real-time interactive frame rates while maintaining extremely high rendering quality.

[0004] When faced with varying rendering scales, 3D Gaussian splashing often produces aliasing rendering results, such as jagged edges, abnormal brightness, and bloat of detailed components. Existing solutions use isotropic 3D filtering kernels to process scene primitives, thereby limiting the scene's frequency to match the sampling rate. However, this method not only excessively reduces the opacity of Gaussian primitives, causing background bleeding in the rendering results, but also alters the original shape of the Gaussian primitives, weakening their ability to represent scene edges and details. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes an anti-aliasing filtering method, apparatus, storage medium, and device based on Gaussian splashing, achieving multi-scale universal anti-aliasing for different rendering strategies. The technical solution provided by this invention is as follows:

[0006] Firstly, an anti-aliasing filtering method based on Gaussian splashing includes the following steps:

[0007] Obtain the camera pose of the scene, the original Gaussian elements, and the preset filter kernel size;

[0008] Back projection filtering step: Based on the camera pose and filter kernel size, the ideal low-pass filter defined in the two-dimensional image space is explicitly back-projected and mapped to the three-dimensional spatial coordinate system to generate a back projection filter in the corresponding viewpoint coordinate system. This back projection filter is used to limit the size expansion and transparency attenuation of the Gaussian unit in the depth direction.

[0009] Scale-consistent expansion step: Calculate the expansion coefficient based on the volume change of the Gaussian element after the back-projection filter is applied, and use the expansion coefficient to scale the Gaussian element to guide it to maintain its shape while expanding, so as to conform to the anisotropic characteristics of the scene.

[0010] Rendering steps: Based on scale-modulated Gaussian primitives, rasterization, ray-Gaussian intersection, or ray tracing rendering are performed to output an anti-aliasing target image.

[0011] Preferably, the back projection filtering step specifically includes:

[0012] Construct a two-dimensional filter matrix in the image space, which is controlled by a preset filter kernel size;

[0013] The two-dimensional filter matrix is ​​back-projected from the image space to the three-dimensional world space using the inverse matrix of the view transformation matrix and the inverse matrix of the affine projection Jacobian matrix to generate the back-projection filter covariance matrix.

[0014] The covariance matrix of the back projection filter is superimposed on the covariance matrix of the original Gaussian element to limit the scale of the Gaussian element and the frequency range of the reconstructed scene.

[0015] The transparency compensation coefficient is calculated based on the ratio of the determinants of the covariance matrices before and after superposition, and this coefficient is used to attenuate the opacity of the Gaussian elements to ensure energy conservation during the filtering process.

[0016] Preferably, the covariance matrix of the back-projection filter is mathematically expressed as follows:

[0017] ;

[0018] in, Denotes the covariance matrix of the back projection filter. Represents the view transformation matrix. Denotes the Jacobian matrix for the affine projection approximation. This indicates the transpose operation. -1 This indicates the inverse operation. This represents a two-dimensional filter matrix in image space, configured as a filter size control scalar. With diagonal matrix The product of.

[0019] Preferably, the covariance matrix of the back-projection filter is applied to the original Gaussian elements to obtain the filtered Gaussian elements. Its mathematical expression is:

[0020] ;

[0021] in, Indicates the first The covariance matrix of the original Gaussian elements, Indicates the corresponding to the first The covariance matrix of the back projection filter after filtering Gaussian elements Indicates the coordinates of the query point. This indicates the center position of the original Gaussian unit. Represents determinant operations; terms in the formula It is configured as a transparency compensation coefficient to attenuate the peak opacity of Gaussian elements based on the volume ratio of the covariance matrices before and after filtering, so as to maintain the energy conservation of Gaussian elements while expanding the covariance.

[0022] Preferably, the scale uniformity expansion step specifically includes:

[0023] Calculate the volume ratio between the filtered Gausky element covariance matrix and the original Gausky element covariance matrix;

[0024] Based on the volume ratio, an isotropic expansion adjustment factor is derived. This factor characterizes the degree of total volume expansion introduced by filtering;

[0025] Using the expansion regulation factor The scaling of the original Gaussian element along its three axes is uniformly modulated to obtain the modulated scaling.

[0026] Preferably, the expansion regulation factor The calculation formula is as follows:

[0027] ;

[0028] in, Indicates the first The covariance matrix of the original Gaussian elements, Indicates the corresponding to the first The covariance matrix of the back projection filter after filtering Gaussian elements Representing determinant operations, the mathematical expression for the unified modulation is:

[0029] ;

[0030] in, This represents the original Gaussian scaling factor. This represents the new Gaussian scaling factor after uniform modulation.

[0031] Secondly, an anti-aliasing filter based on Gaussian splashing, the device comprising:

[0032] The input module obtains the camera pose of the scene, the original Gaussian elements, and the preset filter kernel size;

[0033] The back-projection filter generation module explicitly back-projects an ideal low-pass filter defined in the two-dimensional image space to the three-dimensional spatial coordinate system. The input of this module is the camera pose and the filter kernel size, and the output is the back-projection filter in the corresponding view coordinate system, which limits the Gaussian element size and transparency attenuation.

[0034] The scale-consistent expansion module designs an expansion coefficient based on the volume change of the Gaussian element after filtering by the back-projection filter, guiding the expansion of the Gaussian element while ensuring that the shape remains unchanged.

[0035] The rendering module performs rasterization, ray-Gaussian intersection, or ray tracing rendering based on scale-modulated Gaussian units, and outputs an anti-aliasing target image.

[0036] Preferably, the back-projection filter generation module is specifically configured as follows: First, a two-dimensional filter matrix in the image space is constructed, which has a filter kernel size in the image plane direction and degenerates to zero along the line of sight direction; using the inverse matrix of the Jacobian matrix of the projection transformation and the inverse matrix of the view transformation matrix, the two-dimensional filter matrix is ​​back-projected from the image space to the three-dimensional world space to obtain the back-projection filter covariance matrix; the back-projection filter covariance matrix performs low-pass filtering through covariance expansion in the direction parallel to the image plane, while maintaining the variance unchanged in the depth direction perpendicular to the image plane.

[0037] Compared with the prior art, the beneficial effects achieved by the present invention are:

[0038] (1) This invention is not constrained by the rendering process. By explicitly filtering in three-dimensional space, it avoids the incompatibility caused by embedding the anti-aliasing strategy into the rendering strategy. The anti-aliasing strategy proposed in this invention is extended to different variants of the three-dimensional reconstruction method based on Gaussian splashing, thereby improving the quality of the results of the new viewpoint synthesis task.

[0039] (2) The present invention proposes a back projection filter generation module that maintains the opacity property of high-level primitives while anti-aliasing filtering, effectively improving the quality of 3D scene reconstruction.

[0040] (3) This invention proposes a scale consistency expansion module, which solves the problem of changing the aspect ratio of the Gaussian element by equal-proportional modulation, thereby effectively preserving scene details and improving edge quality while eliminating jagged edges. Attached Figure Description

[0041] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0042] Figure 1 The following is a flowchart of the method of the present invention, wherein (a) is a projection diagram of the original three-dimensional Gaussian splash, (b) is a projection diagram of the multi-scale splash expansion, (c) is a projection diagram of the back projection filtering expansion (back projection filtering step of the present invention), and (d) is a projection diagram of the general anti-aliasing Gaussian splash (back projection filtering + scale consistency expansion step of the present invention).

[0043] Figure 2 This is a comparison chart of the results of the synthesis task from a new perspective using the method of the present invention;

[0044] Figure 3 This is a comparison chart of the results of the method of the present invention in the cumulative opacity rendering task;

[0045] Figure 4 This is a comparison chart showing the results of the method of the present invention for a migration task of a 3D Gaussian reconstruction variant. Detailed Implementation

[0046] 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 some embodiments of the present invention, and not all embodiments. 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.

[0047] To make the above-mentioned objectives, features and effects of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0048] Example 1: This invention provides an anti-aliasing filtering method based on Gaussian splashing, such as... Figure 1 As shown, the method includes the following steps:

[0049] Obtain the camera pose, original 3D Gaussian primitive parameters, and preset filter kernel size for the scene;

[0050] Back projection filtering step: Based on the camera pose and filter kernel size, the ideal low-pass filter defined in the two-dimensional image space is explicitly back-projected and mapped to the three-dimensional spatial coordinate system to generate a back projection filter in the corresponding viewpoint coordinate system. This back projection filter is used to limit the size expansion and transparency attenuation of the three-dimensional Gaussian primitives.

[0051] Scale-consistent expansion step: Calculate the expansion coefficient based on the volume change of the primitive after the back projection filter is applied, and use the expansion coefficient to scale the three-dimensional Gaussian primitive to guide it to maintain its shape while expanding, so as to conform to the anisotropic characteristics of the scene.

[0052] Rendering steps: Based on the scaled 3D Gaussian primitives, rasterization, ray-Gaussian intersection or ray tracing rendering are performed to output an anti-aliasing target image.

[0053] The back-projection filtering step specifically includes: first, constructing a two-dimensional filter matrix in image space, which is controlled by a preset filter kernel size parameter; using the inverse of the view transformation matrix and the inverse of the affine projection Jacobian matrix, back-projecting the two-dimensional filter matrix from image space to three-dimensional world space to generate a back-projection filter covariance matrix; superimposing the back-projection filter covariance matrix onto the covariance matrix of the original Gaussian elements to limit the scale of the elements and the frequency range of the reconstructed scene; calculating the transparency compensation coefficient based on the ratio of the determinants of the covariance matrices before and after superposition, and using this coefficient to attenuate the opacity of the Gaussian elements to ensure energy conservation during the filtering process.

[0054] The ideal low-pass filter defined in the two-dimensional image space is a type of filter composed of a two-dimensional identity matrix. With the preset scale factor The matrix obtained by multiplication (i.e., Figure 1 The 2D Mip filter shown in (a) → (b) introduces a minimum scale constraint in the image space by superimposing it onto the projected Gaussian element covariance matrix, thereby effectively smoothing the spatial frequency components of the primitives to match the screen sampling resolution, thus reducing aliasing artifacts caused by undersampling and suppressing aliasing.

[0055] The aforementioned back projection utilizes the linear approximation logic of perspective projection to inversely propagate the low-pass filtering constraints of the image plane to three-dimensional space (i.e., Figure 1 (b) → (c)). Specifically, for each three-dimensional Gaussian element, first at its center point position... Perform a first-order Taylor expansion at the given point to obtain the Jacobian matrix of the affine projection transformation. and the current view transformation matrix .

[0056] By solving the inverse process of the above transformation matrix, this embodiment constructs the covariance matrix of the back projection filter in three-dimensional space. Its mathematical expression is as follows:

[0057] ;

[0058] in, This represents a two-dimensional filter matrix in image space, configured as a filter size control scalar. With diagonal matrix The product of these factors degenerates to zero along the line of sight. Through this explicit back-projection, the covariance matrix of the back-projection filter performs low-pass filtering only in the direction parallel to the image plane through covariance expansion, while maintaining the variance unchanged in the depth direction perpendicular to the image plane, thereby avoiding the erroneous energy diffusion in the depth direction caused by traditional 3D filters.

[0059] The inverse process of the Jacobian matrix of the affine projection transformation Its mathematical expression is as follows:

[0060] ;

[0061] in Represents the coordinates in the two-dimensional image plane space. Represents the coordinates in the 3D camera space. and These represent the camera's focal length in the horizontal and vertical directions, respectively.

[0062] The covariance matrix of the back projection filter Applied to the original Gaussian elements, the filtered imaging plane-dilated Gaussian elements are obtained (i.e. Figure 1 The mathematical expression for (c) → (d) is:

[0063] ;

[0064] in, Indicates the first The covariance matrix of the original Gaussian elements, Indicates the corresponding to the first The covariance matrix of the back projection filter with Gaussian elements. Indicates the coordinates of the query point. Indicates the center position of the Gaussian unit. Represents determinant operations; terms in the formula It is configured as a transparency compensation coefficient. This coefficient is used to attenuate the peak opacity of the Gaussian elements based on the volume ratio of the covariance matrices before and after filtering, so as to maintain the energy conservation of the Gaussian elements while expanding the covariance, effectively preventing background bleeding or transparency distortion caused by filtering.

[0065] The scale consistency expansion step specifically includes:

[0066] The volume ratio between the filtered Gausky element covariance matrix and the original Gausky element covariance matrix is ​​calculated. This ratio reflects the degree of total volume expansion introduced by the filtering operation.

[0067] Based on the volume ratio, an isotropic expansion adjustment factor is derived. The calculation formula is as follows:

[0068] ;

[0069] in, This represents the original Gaussian scaling factor. This represents the scaling factor of the Gaussian elements after filtering, which characterizes the degree of overall volume expansion introduced by the filtering.

[0070] Using the expansion regulation factor The scaling of the original Gaussian element along its three axes is uniformly modulated to obtain the modulated scaling. This process involves modifying the original scaling... Directly multiply by the aforementioned expansion adjustment factor To achieve this, its mathematical expression is:

[0071] ;

[0072] in This indicates the new Gaussian scaling factor after modulation.

[0073] Through the unified modulation operation described above, aliasing can be eliminated through filtering while maintaining the original aspect ratio of the Gaussian elements. This ensures that the filtering only serves as a scale guide signal, rather than directly adding the isotropic components generated by the filtering to the original scaling, thereby achieving decoupled control of shape and frequency and effectively preserving the edge quality and details of the scene.

[0074] The method described in this invention can be applied to various new viewpoint compositing tasks based on 3D Gaussian implementations and is transferable. The above embodiments are described as general anti-aliasing Gaussian splatting. The benchmark methods for comparison in new viewpoint compositing tasks are: 3D Gaussian Splatting (3DGS), Mip-Splatting, and Analytic Splatting; the benchmark methods for comparison in cumulative opacity rendering tasks are Mip-Splatting and Analytic Splatting; the benchmark methods for transfer tasks targeting 3D Gaussian reconstruction variants are: Gaussian Opacity Fields (GOF) and 3D Gaussian Ray Tracing (3DGRT). Specific implementation details vary depending on the task; therefore, the following will describe different tasks and their specific implementations, including new viewpoint compositing tasks, cumulative opacity rendering tasks, and transfer tasks targeting 3D Gaussian reconstruction variants using this method.

[0075] For the above tasks, all benchmark methods use default settings. For general anti-aliasing Gaussian splashing, the filter size control scalar is set. The hyperparameters are set to 0.1, and the remaining hyperparameters are consistent with the 3D Gaussian splashing method, using the same loss function, a hybrid loss of L1-Loss and SSIM, for supervision. The training and testing datasets include synthetic and real datasets: a multi-scale synthetic dataset (downsampled from the Blender dataset) and a Mip-NeRF 360 dataset, totaling 17 different scenes (8 synthetic and 9 real scenes). Both training and testing data are set to multi-scale to meet the contrast requirements of anti-aliasing rendering. Random initialization is used for training the synthetic dataset, with an initial Gaussian primitive number of 100k. For the real dataset, sparse point clouds are first obtained using the Structure from Motion (SfM) algorithm, and then Gaussian primitives are initialized based on these sparse point clouds. Furthermore, the number of training iterations for all methods is set to 30K.

[0076] For new viewpoint synthesis tasks Figure 2 This demonstrates the advantages of our method in representing foreground and background occlusion relationships and scene detail structure. For example, in the synthetic dataset, at the top of the knob and the intersection of the microphone transmission lines in the microphone scene, baseline methods exhibit background penetration artifacts, while only our method correctly preserves the foreground's occlusion relationship with the background. In the real dataset, at the vine location of the vase decoration in the garden scene, baseline methods show varying degrees of missing vine structure, while our method can reconstruct the vine structure details more completely. Figure 2The results provided include RGB rendering views, error maps against the ground truth, and cumulative opacity rendering maps for all methods and ground truth values. It is important to note that since the ground truth value for the cumulative opacity rendering map cannot be directly obtained, a proxy mask obtained through monocular depth estimation of the RGB image is used as a reference value, and this reference value is only for qualitative comparison.

[0077] For cumulative opacity rendering tasks Figure 3 The rendering results of the method of this invention are compared with those of two baseline methods (multi-scale Gaussian sputtering method and analytical Gaussian sputtering method). Figure 3 In the comparison, the baseline method clearly shows different degrees of abnormal opacity attenuation in the following scenarios: the edge of the cymbals and the drum wall in the first row of the drums scene; the edge of the outermost round basin in the second row of the ship scene; the tabletop in the third row of the bonsai scene; and the ground and the chairs around the trees in the fourth row of the treehill scene. In contrast, this method produces rendering results that are more consistent with the real opaque objects.

[0078] For migration tasks targeting variants of 3D Gaussian reconstruction, Figure 4 This demonstrates the improved scene multi-scale representation capabilities achieved by combining this method with different baselines. Each method renders images at different resolutions from the same viewpoint within a chair scene. Figure 4 In the first row of the initial resolution rendering image, the edge pattern of the backrest; the third row of the four-fold downsampling rendering image, the cushion pattern; and the fourth row of the eight-fold downsampling rendering image, the embossed area, all showed aliasing artifacts and abnormal brightness increases compared to the baseline method. However, this method effectively limited the sampling frequency and produced anti-aliasing rendering results that are closer to the true values.

[0079] Example 2: An anti-aliasing filter device based on Gaussian splashing, comprising: an input module for acquiring the camera pose, original 3D Gaussian primitive parameters, and a preset filter kernel size; a back-projection filter generation module for explicitly back-projecting an ideal low-pass filter defined in a 2D image space to a 3D spatial coordinate system, the input of which is the camera pose and the filter kernel size, and the output is a back-projection filter in the corresponding viewpoint coordinate system, limiting the size and transparency attenuation of the 3D Gaussian primitives; a scale-consistent expansion module for designing expansion coefficients based on the volume change of the primitives after filtering by the back-projection filter, guiding the expansion of the 3D Gaussian primitives while ensuring that the shape remains unchanged; and a rendering module for performing rasterization, ray-Gaussian intersection, or ray tracing rendering based on the scale-modulated 3D Gaussian primitives, and outputting an anti-aliasing target image.

[0080] The back-projection filter generation module is specifically configured as follows: First, a two-dimensional filter matrix in the image space is constructed. This matrix has a filter kernel size in the image plane direction, but degenerates to zero along the line of sight. Using the inverse of the Jacobian matrix of the projection transformation and the inverse of the view transformation matrix, the two-dimensional filter matrix is ​​back-projected from the image space to the three-dimensional world space to obtain the back-projection filter covariance matrix. The back-projection filter covariance matrix performs low-pass filtering through covariance expansion in the direction parallel to the image plane, while maintaining the variance unchanged in the depth direction perpendicular to the image plane.

[0081] The back projection filter generation module and scale consistency expansion module of the present invention are not constrained by the rendering process. Through explicit filtering in three-dimensional space, they achieve a general anti-aliasing processing task for reconstruction strategies based on three-dimensional Gaussian primitives.

[0082] Example 3: The non-transitory computer-readable storage medium of this example stores a computer program that, when executed by a processor, implements the steps of the anti-aliasing filtering method based on Gaussian splashing in Example 1.

[0083] The computer-readable storage medium in this embodiment can be an internal storage unit of the terminal, such as the terminal's hard disk or memory; the computer-readable storage medium in this embodiment can also be an external storage device of the terminal, such as a plug-in hard disk, smart memory card, secure digital card, flash memory card, etc. equipped on the terminal; furthermore, the computer-readable storage medium can include both the terminal's internal storage unit and external storage devices.

[0084] The computer-readable storage medium of this embodiment is used to store computer programs and other programs and data required by the terminal. The computer-readable storage medium can also be used to temporarily store data that has been output or will be output.

[0085] Example 4: The electronic device of this example includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps of the anti-aliasing filtering method based on Gaussian splashing in Example 1.

[0086] In this embodiment, the processor can be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits, off-the-shelf programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc. The memory can include read-only memory and random access memory, and provides instructions and data to the processor. A portion of the memory can also include non-volatile random access memory. For example, the memory can also store device type information.

[0087] Those skilled in the art will clearly understand that each implementation can be achieved using software plus the necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0088] This invention provides an anti-aliasing filtering method and apparatus based on Gaussian splashing. Many methods and approaches exist for implementing this technical solution, and the above descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the protection scope of this invention.

Claims

1. An anti-aliasing filtering method based on Gaussian splashing, characterized in that, Includes the following steps: Obtain the camera pose of the scene, the original Gaussian elements, and the preset filter kernel size; Back projection filtering step: Based on the camera pose and filter kernel size, the ideal low-pass filter defined in the two-dimensional image space is explicitly back-projected and mapped to the three-dimensional spatial coordinate system to generate a back projection filter in the corresponding viewpoint coordinate system. This back projection filter is used to limit the size expansion and transparency attenuation of the Gaussian unit in the depth direction. Scale-consistent expansion step: Calculate the expansion coefficient based on the volume change of the Gaussian element after the back-projection filter is applied, and use the expansion coefficient to scale the Gaussian element to guide it to maintain its shape while expanding, so as to conform to the anisotropic characteristics of the reconstructed scene. Rendering steps: Based on scale-modulated Gaussian primitives, rasterization, ray-Gaussian intersection, or ray tracing rendering are performed to output an anti-aliasing target image.

2. The anti-aliasing filtering method based on Gaussian splashing according to claim 1, characterized in that, The back projection filtering step specifically includes: Construct a two-dimensional filter matrix in the image space, which is controlled by a preset filter kernel size; The two-dimensional filter matrix is ​​back-projected from the image space to the three-dimensional world space using the inverse matrix of the view transformation matrix and the inverse matrix of the affine projection Jacobian matrix to generate the back-projection filter covariance matrix. The covariance matrix of the back projection filter is superimposed on the covariance matrix of the original Gaussian element to limit the scale of the Gaussian element and the frequency range of the reconstructed scene. The transparency compensation coefficient is calculated based on the ratio of the determinants of the covariance matrices before and after superposition, and this coefficient is used to attenuate the opacity of the Gaussian elements to ensure energy conservation during the filtering process.

3. The anti-aliasing filtering method based on Gaussian splashing according to claim 2, characterized in that, The mathematical expression of the covariance matrix of the back-projection filter is as follows: ； in, Denotes the covariance matrix of the back projection filter. Represents the view transformation matrix. Denotes the Jacobian matrix for the affine projection approximation. This indicates the transpose operation. -1 This indicates the inverse operation. This represents a two-dimensional filter matrix in image space, configured as a filter size control scalar. With diagonal matrix The product of.

4. The anti-aliasing filtering method based on Gaussian splashing according to claim 3, characterized in that, The covariance matrix of the back projection filter is applied to the original Gaussian elements to obtain the filtered Gaussian elements. Its mathematical expression is: ； in, Indicates the first The covariance matrix of the original Gaussian elements, Indicates the corresponding to the first The covariance matrix of the back projection filter after filtering Gaussian elements Indicates the coordinates of the query point. This indicates the center position of the original Gaussian unit. Represents determinant operations; terms in the formula It is configured as a transparency compensation coefficient to attenuate the peak opacity of Gaussian elements based on the volume ratio of the covariance matrices before and after filtering, so as to maintain the energy conservation of Gaussian elements while expanding the covariance.

5. The anti-aliasing filtering method based on Gaussian splashing according to claim 1, characterized in that, The scale consistency expansion step specifically includes: Calculate the volume ratio between the filtered Gausky element covariance matrix and the original Gausky element covariance matrix; Based on the volume ratio, an isotropic expansion adjustment factor is derived. This factor characterizes the degree of total volume expansion introduced by filtering; Using the expansion regulation factor The scaling of the original Gaussian element along its three axes is uniformly modulated to obtain the modulated scaling.

6. The anti-aliasing filtering method based on Gaussian splashing according to claim 5, characterized in that, The expansion regulation factor The calculation formula is as follows: ； in, Indicates the first The covariance matrix of the original Gaussian elements, Indicates the corresponding to the first The covariance matrix of the back projection filter after filtering Gaussian elements Representing determinant operations, the mathematical expression for the unified modulation is: ； in, This represents the original Gaussian scaling factor. This represents the new Gaussian scaling factor after uniform modulation.

7. An anti-aliasing filter device based on Gaussian splashing, characterized in that, The device includes: The input module obtains the camera pose of the scene, the original Gaussian elements, and the preset filter kernel size; The back-projection filter generation module explicitly back-projects an ideal low-pass filter defined in the two-dimensional image space to the three-dimensional spatial coordinate system. The input of this module is the camera pose and the filter kernel size, and the output is the back-projection filter in the corresponding view coordinate system, which limits the Gaussian element size and transparency attenuation. The scale-consistent expansion module designs an expansion coefficient based on the volume change of the Gaussian element after filtering by the back-projection filter, guiding the expansion of the Gaussian element while ensuring that the shape remains unchanged. The rendering module performs rasterization, ray-Gaussian intersection, or ray tracing rendering based on scale-modulated Gaussian units, and outputs an anti-aliasing target image.

8. The anti-aliasing filter device based on Gaussian splashing according to claim 7, characterized in that, The back-projection filter generation module is specifically configured as follows: First, a two-dimensional filter matrix in the image space is constructed. This matrix has a filter kernel size in the image plane direction, but degenerates to zero along the line of sight. Using the inverse of the Jacobian matrix of the projection transformation and the inverse of the view transformation matrix, the two-dimensional filter matrix is ​​back-projected from the image space to the three-dimensional world space to obtain the back-projection filter covariance matrix. The back-projection filter covariance matrix performs low-pass filtering through covariance expansion in the direction parallel to the image plane, while maintaining the variance unchanged in the depth direction perpendicular to the image plane.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the anti-aliasing filtering method based on Gaussian splashing as described in any one of claims 1-6.

10. A computer device comprising a processor, a memory, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the anti-aliasing filtering method based on Gaussian splashing as described in any one of claims 1-6.

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