46 results about "Spherical harmonics" patented technology

Some embodiments of a method may include: obtaining information for a three-dimensional (3D) Gaussian model corresponding to a 3D scene, wherein the information comprises a set of attributes of the 3D Gaussian model; parsing the information for a first attribute of the set of attributes, wherein the first attribute corresponds to a position of the 3D Gaussian model; parsing the information for a second attribute of the set of attributes, wherein the second attribute corresponds to a covariance of the 3D Gaussian model; parsing the information for third, fourth, and fifth attributes, wherein the third, fourth, and fifth attributes correspond to first, second, and third sets of spherical harmonics coefficients associated with the 3D Gaussian model; parsing the information for a sixth attribute of the set of attributes, wherein the sixth attribute is an alpha coefficient for the 3D Gaussian model; and rendering the 3D scene using the parsed attributes.

The invention relates to the technical field of three-dimensional reconstruction, in particular to a lightweight three-dimensional reconstruction method and system based on a three-dimensional Gaussian model, and the method comprises the steps: constructing the three-dimensional Gaussian of a target scene based on a multi-view original image of the target scene through employing a 3DGS algorithm; identifying the minimum resolution of each Gaussian primitive in the three-dimensional Gaussian, setting a spherical region according to the minimum resolution, taking the intersection result of the spherical region and the Gaussian primitive as a region evaluation score, and trimming the redundancy region geometry in the three-dimensional Gaussian in combination with the opacity; and taking the maximum zoom scale of the Gaussian primitive as a spatial density proxy variable, and dynamically distributing spherical harmonic coefficient orders according to a local spatial density proxy variable so as to meet the rendering requirements of different three-dimensional Gaussian geometric regions. On the premise that the image synthesis quality is not lost, the model scale and the transmission overhead can be remarkably compressed, the resource constraint condition of the edge computing equipment can be effectively adapted, and the higher training speed and the better rendering effect are achieved.

The invention discloses a double-layer ionosphere modeling method fusing low-orbit satellite data, which comprises the following steps of: preprocessing ground-based GNSS (Global Navigation Satellite System) data to obtain an STEC expression of a ground-based GNSS; preprocessing the precise orbit determination data of the low-orbit satellite to obtain a VTEC expression of the precise orbit determination data; obtaining an electron density profile product of the radio occultation of the low-orbit satellite, and obtaining VTEC of the radio occultation through profile integration; using two groups of spherical harmonic coefficients to express global VTEC distribution, and constructing an observation equation; and determining weights of different types of data by using Helmert variance component estimation, and finally solving to obtain two groups of spherical harmonic coefficients to generate an ionized layer grid product. Projection errors caused by vertical layering in a traditional single-layer model are weakened, meanwhile, precise orbit determination data and radio occultation data of a low-orbit satellite are combined, the problem that ionosphere TEC cannot be correctly layered in a double-layer model is solved, data of areas where GNSS tracking stations are sparsely distributed are supplemented, and the reliability of the GNSS tracking stations is improved. Therefore, a global ionosphere model with higher precision is obtained.

The invention discloses a GRACE and Swarm time-varying gravity field fusion filtering method based on a state space model, and the method comprises the steps: taking a spherical harmonic coefficient as a state quantity, constructing a random walk process equation, introducing three types of observations, employing a quantization parameter for observation noise and process noise covariance, constructing according to an order / power law, and carrying out the self-adaptive updating along with the monthly; a Nelder-Mead method is adopted to search for spectral index parameters, and an EM algorithm and a statistical method are utilized to update other parameters in a closed / quasi-closed mode; obtaining the state and posterior covariance of a full time sequence by using Kalman filtering and RTS smoothing; in the GRACE and GRACE-FO window period, continuous reconstruction is carried out by means of a process model and Swarm; and outputting quality evaluation information including monthly gravity field coefficients, posterior covariance, innovative variance ratio, residual whitening test, space power spectrum, uncertainty band and the like. According to the method, while physical rationality and calculation feasibility are ensured, a continuous and stable monthly time-varying gravitational field sequence with quantifiable uncertainty is realized.

The invention discloses a GNSS (Global Navigation Satellite System) nonlinear deformation correction method based on a full-spectrum three-dimensional thermoelastic model. The GNSS nonlinear deformation correction method comprises the following steps: carrying out discrete Fourier decomposition on a temperature time sequence of each grid point; carrying out space spherical harmonic expansion and coefficient projection on each decomposed frequency; based on a space spherical harmonic expansion and coefficient projection result, considering the periodicity of the temperature, and performing sine / cosine representation of a frequency-by-frequency temperature item; performing spherical harmonic representation and time expansion on the deformed displacement field corresponding to the periodic temperature based on the spatial spherical harmonic expansion and coefficient projection result; solving a deformation equation in spherical coordinates in a Love number form to obtain an expression of a complex Love number; based on the complex spherical harmonic coefficient and the complex Love number of the temperature, full-spectrum synthesis of three-component displacement at the spherical surface is carried out; and performing internal consistency and external dispersion verification based on a full-spectrum synthesis result.

The invention relates to the technical field of three-dimensional reconstruction and rendering, and particularly discloses an underwater long-sight-distance adaptive three-dimensional reconstruction and rendering method based on a Gaussian variable-distance field, and the method comprises the steps: carrying out the initialization point cloud generation based on a motion recovery structure algorithm for RGB image data obtained by underwater image collection equipment; points on the initialized point cloud are combined with a three-dimensional Gaussian distribution model, a three-dimensional Gaussian primitive is defined, and parameter initialization about information such as a Gaussian geometric center, a three-dimensional covariance matrix, opacity and color is carried out on the three-dimensional Gaussian primitive; the method comprises the following steps: establishing a Gaussian cross-space transformation model, performing transformation from a Cartesian coordinate space to a homogeneous coordinate space on a three-dimensional Gaussian primitive, establishing a Gaussian full-parameter space mapping model, mapping color information of the three-dimensional Gaussian primitive after cross-space transformation into a spherical harmonic function, and spatial adaptive three-dimensional reconstruction and rendering in an underwater long-sight-distance environment are realized.

The invention relates to the field of array signal processing, and discloses an underwater target azimuth estimation method based on spherical harmonic noise model sparse reconstruction, which comprises the following steps of: calculating array output data to obtain a sample covariance matrix, establishing a spherical harmonic noise model, expressing spatial noise power density by adopting a finite-order spherical harmonic function, determining an initial power spectrum, and estimating the azimuth of an underwater target according to the initial power spectrum. Initializing the spherical harmonic noise model to obtain a noise covariance matrix, determining an expected model covariance matrix according to the noise covariance matrix, performing peak search on the initial power spectrum to obtain an estimated orientation, and refitting based on the estimated orientation to update the noise covariance matrix and the expected model covariance matrix; the initial power spectrum is subjected to sparse reconstruction based on the expectation model covariance matrix and the sample covariance matrix before updating to obtain an updated power spectrum, when the difference between the updated power spectrum and the initial power spectrum meets the convergence condition, the peak value of the updated power spectrum is searched to determine the target orientation, and super-resolution and robust orientation estimation is achieved.

The invention provides a three-dimensional semantic scene completion method and system based on semantic-physical joint representation. The method comprises the following steps: extracting image features according to multi-view image input, and mapping the image features to a three-dimensional voxel space; voxel features containing local semantic information and three-view features containing global semantic information are extracted through a double-branch encoder, key anchor points with identifiable semantic features are screened out according to semantic consistency of the voxel features and the three-view features, and efficient initialization of Gaussian representation in a key area is guided; and then introducing a semantic spherical harmonic function, projecting Gaussian semantic representation to an orthogonal spherical harmonic space, enhancing the modeling capability of local context geometric structure information, and promoting the semantic-geometric representation consistency of the context by using key voxel distribution alignment, thereby realizing three-dimensional semantic scene completion with both precision and efficiency.

A system generates initial Gaussian elements defined by parameter sets that include, for each Gaussian element a spherical harmonics (SH) coefficient array, a learnable parameter vector, and a learnable weight vector. The system performs a training process comprising rasterizing current Gaussian elements to generate a rendered image of the scene as viewable from a current camera position, wherein for each Gaussian element of the current Gaussian elements that intersects the camera ray, the system determines an opacity value for a location based on a view-dependent scaling value that depends on the current camera position, a position vector, and the learnable parameter vector.

The invention belongs to the technical field of underwater sound channels and physical fields, and relates to a numerical mixing calculation method for a forward scattering sound field of an underwater regular-shape object. The method comprises the following steps: acquiring an initial projection contour of a three-dimensional geometric model of a regular shape object in a specified projection plane and an incident direction; discrete points of the initial projection contour are divided into upper boundary points and lower boundary points; performing interpolation completion on the upper boundary points and the lower boundary points, so that the upper boundary points and the lower boundary points are the same in number and share abscissas; discretizing the supplemented projection contour by using a trapezoidal plane element; calculating a forward scattering far field morphological function based on a discretization result; and calculating the forward scattering target intensity of the object. The method provided by the invention can cover the shape range of the scattering object suitable for the analysis method, does not need to calculate special functions such as Bessel and spherical harmonic and a complex series expression formed by combining the special functions, and obviously improves the calculation efficiency.

The invention discloses a gradient coil design method and system for a rotary surface. The method comprises the following steps: providing a wiring surface required by a gradient coil to be designed and the structure and size of a target area; representing a bus on the wiring surface in a parameter equation form; representing a flow function of the current as series expansion located on the wiring surface; setting a to-be-solved target field and an allowable error, wherein the target field of the linear region is set based on the coefficient of the magnetic field spherical harmonic wave; establishing a spherical harmonic magnetic field sensitivity matrix and a power consumption matrix based on the stream function and the target area; establishing an optimization problem by taking coil power consumption as an optimization objective function and target field deviation as a constraint, and solving the optimization problem to obtain stream function distribution; and discretization is carried out based on stream function distribution to obtain coil wiring characteristics. The method can be suitable for the design of the gradient coil on the complex curved surface only by using a small number of variables, greatly improves the calculation and parameter optimization efficiency of the coil, and facilitates the reduction of the discomfort of a matrix.

This invention discloses an artificial intelligence-based method, system, and storage medium for generating panoramic sound audio. The method includes the following steps: S1. Inputting the original audio signal and scene parameters, obtaining the time-domain-frequency domain features and spatial scene features of the original audio signal through a multimodal feature extraction algorithm, and weighted fusing the time-domain-frequency domain features and spatial scene features to obtain fused features; S2. Constructing the mathematical expression basis of the 3D spatial sound field model based on the spherical harmonic function, mapping the fused features to three-dimensional spatial coordinates through a sound field modeling algorithm to obtain the 3D spatial sound field model; S3. Using an adaptive rendering algorithm, converting the 3D spatial sound field model into multi-channel panoramic sound audio output according to the parameters of the target playback device. This invention achieves automated panoramic sound audio generation by inputting the original audio signal and scene parameters for feature extraction, fusion, and sound field modeling, and converting the output based on adaptive rendering. It has the advantages of automation, high efficiency, and high precision.

The invention discloses a panoramic sound audio generation method and system based on artificial intelligence, and a storage medium, and the method comprises the following steps: S1, inputting an original audio signal and scene parameters, obtaining the time domain-frequency domain features and space scene features of the original audio signal through a multi-modal feature extraction algorithm, carrying out weighted fusion on the time domain-frequency domain features and the space scene features to obtain fusion features; s2, constructing a mathematical expression basis of a 3D space sound field model based on a spherical harmonic function, and mapping fusion features to three-dimensional space coordinates and the 3D space sound field model through a sound field modeling algorithm; and S3, converting the 3D space sound field model into multi-channel panoramic sound audio output according to the parameters of the target playing equipment by using an adaptive rendering algorithm. According to the method, feature extraction, fusion and sound field modeling are carried out by inputting the original audio signals and scene parameters, automatic panoramic sound audio generation is realized based on adaptive rendering conversion output, and the method has the advantages of automation, high efficiency, high precision and the like.

The invention relates to the technical field of neutron transport numerical calculation, in particular to a cross section generation method and device based on flux moment homogenization and transport correction coupling and a storage medium, and the method comprises the steps: S1, building a geometric model of a reactor assembly or lattice cell, carrying out the energy Monte Carlo calculation, and generating a conventional cross section based on statistical data; s2, extracting a spherical harmonic function flux moment and a total reaction rate moment, calculating a total cross section spherical harmonic function correction term, and introducing a conventional scattering cross section to complete flux moment homogenization correction; and S3, exporting a first-order scattering matrix, carrying out transport correction to obtain a transport correction term, and correcting the conventional cross section according to the transport correction term and the total cross section spherical harmonic function correction term to generate a final multi-group cross section. According to the method, the anisotropies of the total cross section and the scattering cross section are synergistically corrected, the calculation precision of the method in the strong anisotropy problem is improved on the premise of keeping the standard cross section data structure, and the compatibility with a widely applied reactor core calculation program is ensured.

Techniques to handle the Spherical Harmonic (SH) coefficients associated with 3DGS towards effective compression are described herein. SH coefficients are used to represent view dependent RGB color values, which takes a significant amount of memory—48 out of 59 parameters per Gaussian. By applying suitable transformation to SH coefficients, the inter-channel redundancies are exploited, thereby effectively reducing the memory requirements by 50%.

A preparation method of a metamaterial with continuously distributed physical attributes comprises the following steps: firstly, introducing a spherical harmonic function to realize unique representation and optimization of a physical attribute field, realizing spatial continuous transition of the physical attribute field, generating a metamaterial structure meeting functional requirements, and then preparing the metamaterial by adopting an additive manufacturing method. According to the method, physical attribute fields (such as rigidity and heat conductivity) and corresponding geometric structures of the structure can be represented and optimized according to functional requirements of the structure under actual service conditions, automatic design of the metamaterial with continuously distributed physical attributes can be realized, and the method has higher flexibility and universality in design of bearing and heat-conducting structures.

The application relates to a satellite collision probability estimation method, device and readable storage medium. The satellite collision probability estimation method comprises the following steps: forward propagation of a non-Gaussian relative velocity probability density function to obtain a reference velocity histogram, so as to determine an initial parameter set of a Gaussian mixture model; every first preset time interval, a plurality of sets of distance residuals and angle residuals of a first satellite and a second satellite in a running state are updated, so as to update the parameter set of the Gaussian mixture model; every second preset time interval, the relative positions of the first satellite and the second satellite are updated, and the instantaneous collision volume of the first satellite and the second satellite is determined by using the separation axis theorem; the mean values of Gaussian components in the updated parameter set are substituted into a static spherical harmonic coefficient table for query, so as to obtain the relative position probability density of the first satellite and the second satellite; and the collision probability is obtained based on the instantaneous collision volume and the relative position probability density, so that fast and accurate estimation is realized.

The invention discloses a complex particle three-dimensional morphology digital twinning method based on a spherical harmonic function and principal component analysis, and the method comprises the steps: (1) employing a three-dimensional scanner to scan a real particle morphology so as to obtain a triangular mesh data file of a particle surface morphology, and employing a self-adaptive curved surface optimization algorithm to optimize a scanned particle triangular mesh; (2) performing shape scaling on the particles to obtain spheroids by using triangular surface grid data after particle scanning optimization, and performing 30-order spherical harmonic function expansion on the spheroids to realize parameterization and digital reconstruction on the particles with complex morphology; and (3) performing principal component analysis on the shape parameters and the spherical harmonic function parameters of all the scanned particles to obtain characteristic values and characteristic vectors of a parameter matrix, constructing random morphology parameters based on the characteristic values and the characteristic vectors, and constructing a brand-new random particle surface morphology through the reverse process of the step (2). According to the method, basic guarantee is provided for quantitative analysis of the three-dimensional morphology of the surface of the complex granular material and performance analysis of the granular composite material.

The invention relates to the technical field of geophysical exploration methods, in particular to a magnetic model construction method based on geomagnetic data constraint inversion and width learning. The method comprises the following steps: S1, processing and fusing multi-source data to obtain processed and fused data; s2, performing physical constraint embedding according to the processed and fused data to obtain data after physical constraint embedding; s3, step-by-step inversion is carried out according to the data after physical constraint embedding, and a spherical harmonic coefficient dynamic correction term is obtained. According to the magnetic model construction method based on geomagnetic data constraint inversion and width learning, incremental updating is conducted, by dynamically adjusting feature nodes and enhancing nodes, only local weight re-calculation is needed, online model updating is achieved, the calculation efficiency is improved by more than 50%, node expansion is automatically triggered according to new data errors, and over-fitting / under-fitting is avoided.

This application relates to the field of water storage analysis technology, and provides a method and related equipment for jointly inverting changes in terrestrial water storage. The method includes: acquiring a hydrological model and surface deformation data of a target area, and constructing basis functions for the target area; performing spherical harmonic analysis on the hydrological model to convert it into spherical harmonic coefficients; establishing a first observation equation between the spherical harmonic coefficients and the basis function coefficients, and establishing a second observation equation between the surface deformation data and the basis function coefficients; solving for the basis function coefficients based on the first and second observation equations to obtain the final coefficient vector of the basis functions; and calculating the change in terrestrial water storage in the target area based on the final coefficient vector and the basis functions. The method of this application can simultaneously improve the spatiotemporal resolution and accuracy of jointly inverting changes in terrestrial water storage.

The application discloses a kind of earth magnetic field horizontal component representation methods of removing pole singularity, comprising: based on adolf schmidt semi-normalized spherical harmonic theory, the spherical harmonic representation of geomagnetic field magnetic potential function is obtained by spherical harmonic polynomial expansion calculation method;With south pole or north pole as center, mirror center symmetry extension is carried out to great circle on sphere, so that each point on sphere has a mirror point, so that the mirror extension function of geomagnetic field magnetic potential function is obtained;Two-dimensional Fourier expansion is carried out to mirror extension function using double Fourier series, and double coverage function expansion is obtained;Based on double coverage function expansion, the horizontal component of geomagnetic field is calculated, i.e. the spherical gradient of spherical magnetic potential function is calculated.The realization is based on the existing IGRF model magnetic potential expansion coefficient, the magnetic field tangent vector representation is obtained without being polluted by pole problem, and a new modeling idea and calculation method of spherical tangent vector field are provided.

The small sample point cloud target classification method based on LSHW-Mamba network relates to the technical field of 3D point cloud processing and deep learning, and solves the problems that the existing technology focuses on feature mining in the Euclidean space domain, and under the condition of insufficient target samples, the feature representation ability of the target geometric structure is insufficient, and it is difficult to capture the key information for distinguishing similar objects. The present application explicitly analyzes the spectral response of the local geometric structure of the point cloud through the spherical harmonic function, combines the local spherical harmonic wavelet transform to realize the geometric feature extraction of the point cloud, simultaneously introduces the geometric gating mechanism to optimize the feature propagation efficiency of the Mamba model, models the target features in parallel with the Transformer attention branch, considers the relevance of the local and global features of the target, and improves the discrimination ability of the network model for the target under the small sample scene. The present application effectively solves the core problems of insufficient feature discrimination and decreased classification accuracy under the small sample condition.

The application discloses a kind of three-dimensional special-shaped particle general contact detection method, system, platform and storage medium based on spherical harmonics and machine learning, by introducing spherical harmonics as unified shape descriptor, and constructs a general machine learning model that can accept the descriptor as input, the paradigm breakthrough of special-shaped particle contact detection in discrete element simulation is realized.I.e.the scheme realizes the generalization processing of single model to multiple or even unknown special-shaped particle shape, solves the fixed limit of existing machine learning method one shape one model;In terms of computing performance, forward inference is replaced by complex geometry intersection, so that the contact detection efficiency is improved by several times to several tens of times compared with traditional algorithm, and the more complex the particle shape is, the more significant the advantage is;At the same time, spherical harmonics modeling reduces the memory occupation of shape data, so that large-scale, multi-shape particle system high-fidelity efficient simulation becomes possible, and promotes the application of particle mechanics numerical simulation technology in engineering practice.

The application discloses a three-dimensional modeling and data assimilation method for ionospheric electron density, belongs to the field of space environment monitoring and information technology, and comprises the following steps: constructing a hybrid basis function system based on spherical harmonics and empirical orthogonal functions and establishing a state space model, independently perturbing through key geophysical driving parameters, combining a physical empirical model to construct a physical-statistical dynamic model, fusing multi-source heterogeneous observation data, obtaining an analysis state vector set through a set Kalman filtering algorithm and an asynchronous assimilation window, and reconstructing a three-dimensional electron density field and uncertainty products through the hybrid basis function system based on the analysis state vector set.

A system generates initial Gaussian elements defined by parameter sets that include, for each Gaussian element a spherical harmonics (SH) coefficient array, a learnable parameter vector, and a learnable weight vector. The system performs a training process comprising rasterizing current Gaussian elements to generate a rendered image of the scene as viewable from a current camera position, wherein for each Gaussian element of the current Gaussian elements that intersects the camera ray, the system determines an opacity value for a location based on a view-dependent scaling value that depends on the current camera position, a position vector, and the learnable parameter vector.

The invention provides a GRACE atmospheric de-mixing model modeling method and system based on least square, and belongs to the technical field of atmospheric de-mixing, and the method comprises the following steps: constructing an observation equation; performing inverse fast Fourier transform on the observation value of each fixed latitude along the longitude direction; carrying out integration on the observation equation in the longitude direction by utilizing orthogonality of a trigonometric function, and separating coupled unknown parameters under a specific order to obtain a simplified equation only containing a single unknown parameter; carrying out discretization approximation on the simplified equation, and carrying out standardization processing on the discretized equation by utilizing orthogonality and properties of a discrete trigonometric function and combining a Kronecker symbol to form a standard observation equation form suitable for indirect adjustment; on the basis of a standard observation equation, a spherical harmonic coefficient of a specific order is obtained through indirect adjustment, and finally a complete spherical harmonic coefficient is formed. The method can improve the calculation efficiency on the basis of ensuring the calculation precision of the atmospheric de-mixing model.

The invention provides a high-order continuity maintenance and error control method in an STL curved surface reconstruction process, and relates to the technical field of three-dimensional modeling, and the method comprises the steps: obtaining the connection information of discrete data, constructing a continuous normal vector field based on spherical harmonic decomposition, carrying out the frequency domain processing of a vertex coordinate and a normal vector, and recognizing high-frequency details, and calculating a main curvature direction to determine an insertion control point, and iteratively optimizing the normal deviation until convergence. According to the method, the high-order continuity of the STL curved surface can be effectively kept, the reconstruction error is accurately controlled, and the geometric accuracy and quality of the reconstructed curved surface are improved.

A system generates initial Gaussian elements defined by parameter sets that include, for each Gaussian element a spherical harmonics (SH) coefficient array, a learnable parameter vector, and a learnable weight vector. The system performs a training process comprising rasterizing current Gaussian elements to generate a rendered image of the scene as viewable from a current camera position, wherein for each Gaussian element of the current Gaussian elements that intersects the camera ray, the system determines an opacity value for a location based on a view-dependent scaling value that depends on the current camera position, a position vector, and the learnable parameter vector.

Techniques to handle the Spherical Harmonic (SH) coefficients associated with 3DGS towards effective compression are described herein. SH coefficients are used to represent view dependent RGB color values, which takes a significant amount of memory - 48 out of 59 parameters per Gaussian. By applying suitable transformation to SH coefficients, the inter-channel redundancies are exploited, thereby effectively reducing the memory requirements by 50%.

Some embodiments of a method may include: obtaining information for a three-dimensional (3D) Gaussian model corresponding to a 3D scene, wherein the information comprises a set of attributes of the 3D Gaussian model; parsing the information for a first attribute of the set of attributes, wherein the first attribute corresponds to a position of the 3D Gaussian model; parsing the information for a second attribute of the set of attributes, wherein the second attribute corresponds to a covariance of the 3D Gaussian model; parsing the information for third, fifth, and sixth attributes, wherein the third, fifth, and sixth attributes correspond to first, second, and third sets of spherical harmonics coefficients associated with the 3D Gaussian model; parsing the information for a fourth attribute of the set of attributes, wherein the fourth attribute is an alpha coefficient for the 3D Gaussian model; and rendering the 3D scene using the parsed attributes.