A multi-modal image analysis system for a czochralski silicon single crystal growth interface

Abstract

The application discloses a kind of multi-mode image analysis systems of straight pull silicon single crystal growth interface, belong to image analysis technical field, specifically include: manifold mapping module obtains solid-liquid interface visible light sequence and infrared sequence, visible light sequence and infrared sequence are mapped to continuous manifold space;Characteristic extraction module extracts the reflection profile vector of visible light sequence and the temperature gradient vector of infrared sequence;Offset solving module solves the relative time offset between modal;Matrix generation module constructs cross-modal graph neural network according to relative time offset, generates deformation compensation matrix;Boundary reconstruction module applies deformation compensation matrix to reflection profile vector and temperature gradient vector, reconstructs the cross-modal alignment boundary feature under oscillation environment;Tensor fusion module carries out tensor fusion calculation to cross-modal alignment boundary feature, outputs micro boundary coordinate set, and the application greatly improves the accuracy of crystal diameter microcosmic change machine vision identification.

Description

Technical Field

[0001] This invention relates to the field of image analysis technology, and specifically to a multimodal image analysis system for the Czochralski silicon single crystal growth interface. Background Technology

[0002] The Czochralski method is the mainstream process for preparing high-quality silicon single crystals. During the single crystal growth stage, high-precision monitoring of the microstructure of the solid-liquid interface is crucial for achieving constant crystal diameter control and defect suppression. To comprehensively acquire interface state information, the industry has widely adopted multimodal image sensing schemes, deploying visible light cameras and infrared thermal imagers to collaboratively observe the crystal growth state. The visible light band can directly capture the reflective features of the melt surface and the physical boundaries of the crystal, while infrared thermal imaging excels at penetrating complex optical interference and quantitatively measuring the local thermal radiation distribution in the solid-liquid interface region. The data from these two heterogeneous modes are highly complementary in terms of feature dimensions, providing a rich data foundation for machine vision to comprehensively evaluate the topological geometry and thermodynamic evolution of the growth interface.

[0003] The current problem is that the Czochralski silicon single crystal growth process is accompanied by intense melt thermal convection and argon shear stress, causing the meniscus at the solid-liquid interface to exhibit nonlinear high-frequency oscillations. The physical contours of the interface reflected by visible light images and the local temperature gradient boundaries characterized by infrared thermal imaging have intrinsic differences in physical properties. Due to the heterogeneity of exposure mechanisms and sampling frequencies of multi-source sensors, the edge features of these two modes will undergo asynchronous geometric deformation over time. Traditional static pixel-level image registration or conventional feature fusion algorithms cannot adaptively compensate for this sub-millimeter-level dynamic topological deformation, resulting in ghosting and blurred boundaries in the extracted solid-liquid interface contours, severely reducing the accuracy of machine vision recognition of microscopic changes in crystal diameter. Summary of the Invention

[0004] The purpose of this invention is to provide a multimodal image analysis system for the Czochralski silicon single crystal growth interface, thereby solving the problems in the background art.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] A multimodal image analysis system for the Czochralski silicon single crystal growth interface includes:

[0007] The manifold mapping module is used to acquire the visible light and infrared sequences of the solid-liquid interface and map the visible light and infrared sequences to a continuous manifold space.

[0008] The feature extraction module is used to construct the ordinary differential equation tensor field in the continuous manifold space and extract the reflective contour vector of the visible light sequence and the temperature gradient vector of the infrared sequence.

[0009] The offset calculation module is used to input the reflective profile vector and temperature gradient vector into the hypernet model to generate alignment weights and calculate the relative time offset between modes.

[0010] The matrix generation module is used to construct a cross-modal graph neural network based on the relative time offset, calculate the topological deformation field of the solid-liquid interface, and generate a deformation compensation matrix.

[0011] The boundary reconstruction module is used to apply the deformation compensation matrix to the reflective profile vector and the temperature gradient vector to reconstruct the cross-modal aligned boundary features under oscillating conditions.

[0012] The tensor fusion module is used to perform tensor fusion calculations on cross-modal aligned boundary features, extract the physical contour curves of the solid-liquid interface, and output the microscopic boundary coordinate set.

[0013] As a further aspect of the present invention: in the manifold mapping module, the process of acquiring the visible light sequence and infrared sequence of the solid-liquid interface and mapping the visible light sequence and infrared sequence to the continuous manifold space is as follows:

[0014] The original sensor image of the solid-liquid interface is acquired, the optical reflection matrix and thermal radiation matrix inside the original sensor image are separated, the optical reflection matrix is ​​arranged according to the timestamp to obtain the visible light sequence, and the thermal radiation matrix is ​​arranged to obtain the infrared sequence.

[0015] The visible light sequence and the infrared sequence are input into the feature network to analyze the visual boundary tensor of the visible light sequence and the thermal gradient tensor of the infrared sequence. The visual boundary tensor and the thermal gradient tensor are then input into the encoding network to perform a nonlinear transformation.

[0016] A Riemann geometric metric model is constructed based on the implicit eigenvectors output by the nonlinear transformation. The local homeomorphic projection coordinates of the implicit eigenvectors are solved, and the visible light sequence and infrared sequence are mapped to the continuous manifold space based on the local homeomorphic projection coordinates.

[0017] As a further aspect of the present invention: in the feature extraction module, the content of constructing an ordinary differential equation tensor field in the continuous manifold space and extracting the reflected contour vector of the visible light sequence and the temperature gradient vector of the infrared sequence is as follows:

[0018] Receive visible light and infrared sequences mapped to a continuous manifold space, define hidden state features along the time dimension, and fit the derivative function of the hidden state features using a feedforward neural network;

[0019] Based on the derivative function, a fundamental vector field representing the sequence evolution is constructed. The fundamental vector field is projected onto the tangent space of the manifold to generate an ordinary differential equation tensor field. The continuous-time integral trajectory is calculated in the ordinary differential equation tensor field.

[0020] Obtain the visual tensor output by the continuous-time integral trajectory of the visible light sequence, apply the differential operator to the visual tensor to perform matrix convolution operation, and extract the physical boundary pixels to generate the reflective contour vector;

[0021] Obtain the thermal radiation tensor output by the continuous-time integral trajectory of the infrared sequence, calculate the partial derivatives of the thermal radiation tensor in the spatial orthogonal directions, and generate a temperature gradient vector by analyzing the difference in local thermal radiation distribution.

[0022] As a further aspect of the present invention: in the offset calculation module, the step of inputting the reflective contour vector and temperature gradient vector into the hypernetwork model to generate alignment weights, and calculating the relative time offset between modes, is as follows:

[0023] State features are constructed by splicing reflective contour vectors and temperature gradient vectors. These state features are then input into the hypernetwork model to perform perceptual hidden layer mapping, and the dynamic parameters of the target network are output.

[0024] The dynamic parameters are loaded into the target network, and the reflective contour vector and temperature gradient vector are input into the target network to perform attention tensor multiplication, generating alignment weights between modes.

[0025] The time cross-correlation sequence of the reflective profile vector and the temperature gradient vector is calculated based on the alignment weight, and the extreme coordinates of the time cross-correlation sequence are extracted to calculate the relative time offset.

[0026] As a further aspect of the present invention: in the matrix generation module, the content of the deformation compensation matrix generated by constructing a cross-modal graph neural network based on the relative time offset, calculating the topological deformation field of the solid-liquid interface, and generating the matrix is ​​as follows:

[0027] Feature elements of reflective contour vector and temperature gradient vector are extracted as graph nodes. Directed edges are established by connecting graph nodes of heterogeneous modes based on relative time offset to construct a cross-modal graph neural network.

[0028] In a cross-modal graph neural network, a message passing mechanism is activated to aggregate the spatial states of heterogeneous modal neighbor nodes along directed edges, update the hidden state vectors of graph nodes, and output a cross-modal spatiotemporal feature matrix.

[0029] The cross-modal spatiotemporal feature matrix is ​​input into the spatial relative displacement between nodes of the multilayer perceptron computation graph. The spatial relative displacement is combined to generate a discrete velocity field. Interpolation calculation is performed on the discrete velocity field to fit the topological deformation field of the solid-liquid interface.

[0030] Extract the deformation gradient components at each coordinate position within the topological deformation field, arrange the deformation gradient components into a two-dimensional mesh feature structure, and perform tensor decomposition on the two-dimensional mesh feature structure to generate a deformation compensation matrix.

[0031] As a further aspect of the present invention: in the boundary reconstruction module, the content of reconstructing the cross-modal aligned boundary features under oscillating conditions by applying the deformation compensation matrix to the reflective contour vector and the temperature gradient vector is as follows:

[0032] Calculate the dot product between the deformation compensation matrix and the reflective profile vector, update the coordinate position of the reflective profile vector through affine transformation, and extract the deformation-corrected reflective features.

[0033] Calculate the tensor product of the deformation compensation matrix and the temperature gradient vector, reconstruct the numerical distribution of the temperature gradient vector based on the tensor product, and analyze the deformation correction temperature characteristics.

[0034] A joint tensor is constructed by fusing deformation-corrected reflective features and deformation-corrected temperature features. Feature mapping is then performed on the joint tensor to reconstruct cross-modal aligned boundary features under oscillating conditions.

[0035] As a further aspect of the present invention: the specific content of constructing a joint tensor by fusing deformation-corrected reflective features and deformation-corrected temperature features, and performing feature mapping on the joint tensor to reconstruct the cross-modal aligned boundary features under oscillating conditions is as follows:

[0036] Deformation-corrected reflective features and deformation-corrected temperature features are spliced ​​along the channel dimension, and a joint tensor is constructed by combining the feature distribution channels at the splicing positions.

[0037] The joint tensor is input into the multilayer perceptron to perform feature mapping, and the nonlinear function inside the multilayer perceptron is activated to analyze and fuse the hidden layer parameters.

[0038] Spatial attention weights are assigned to each channel based on the fused hidden layer parameters, and the cross-modal alignment boundary features under oscillating conditions are reconstructed by combining the spatial attention weights.

[0039] As a further aspect of the present invention: in the tensor fusion module, the tensor fusion calculation of the cross-modal aligned boundary features, the extraction of the physical contour curve of the solid-liquid interface, and the output of the microscopic boundary coordinate set are as follows:

[0040] Tensor cross-product operation is performed on each modal component of the cross-modal aligned boundary feature to generate a high-dimensional feature matrix. Pooling operator is applied along the spatial channel dimension of the high-dimensional feature matrix to reduce the dimension of the dense boundary fusion feature.

[0041] Calculate the pixel gradient magnitude of dense boundary fusion features, search for the maximum connected region based on the pixel gradient magnitude, fit the spatial pixel distribution topology inside the maximum connected region, and extract the physical contour curve of the solid-liquid interface.

[0042] Discretization sampling is performed along the extension path of the physical contour curve. The absolute spatial position of the discretized sampling node in the reference frame is analyzed. The absolute spatial positions are arranged in the sampling order to form a data column, and the microscopic boundary coordinate set is output.

[0043] The beneficial effects of this invention are:

[0044] The technical solution of this invention effectively overcomes the time series discretization defect caused by the sampling frequency difference of multi-source sensors by uniformly mapping heterogeneous visible light sequences and infrared sequences to a continuous manifold space and constructing an ordinary differential equation tensor field representing continuous physical evolution within this continuous manifold space. The extracted reflective contour vector and temperature gradient vector are input into the hypernetwork model to generate dynamic alignment weights, accurately calculating the relative time offset between the two physical modes, and completely eliminating the temporal misalignment of edge features caused by heterogeneous exposure mechanisms. This processing mechanism directly corrects the asynchronous geometric deformation of high-frequency oscillating interfaces in the time series at the bottom layer, abandoning the traditional static pixel registration path, and providing a data benchmark with strict physical time consistency for the deep alignment of cross-modal features.

[0045] The technical solution of this invention constructs a cross-modal graph neural network based on the calculated relative time offset, deeply mines the spatial relative displacement relationship between heterogeneous modal feature elements, accurately calculates the topological deformation field of the solid-liquid interface and generates a targeted deformation compensation matrix; the deformation compensation matrix is ​​directly applied to the reflective contour vector and temperature gradient vector to achieve boundary feature reconstruction, and high-fidelity physical contour curves are extracted by tensor fusion calculation, adaptively compensating for sub-millimeter-level dynamic topological distortion caused by strong melt thermal convection and argon shear stress; this deep fusion reconstruction method successfully eliminates the ghosting and boundary blurring defects of the solid-liquid interface fusion contour in dynamic environments, so that the final output microscopic boundary coordinate set has extremely high geometric sharpness, greatly improving the accuracy of machine vision recognition of microscopic changes in crystal diameter. Attached Figure Description

[0046] The invention will now be further described with reference to the accompanying drawings.

[0047] Figure 1 This is a schematic diagram of a multimodal image analysis system for the Czochralski silicon single crystal growth interface according to the present invention. Detailed Implementation

[0048] 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.

[0049] Please see Figure 1 As shown, this invention is a multimodal image analysis system for the Czochralski silicon single crystal growth interface, comprising:

[0050] The manifold mapping module is used to acquire the visible light and infrared sequences of the solid-liquid interface and map the visible light and infrared sequences to a continuous manifold space.

[0051] The feature extraction module is used to construct the ordinary differential equation tensor field in the continuous manifold space and extract the reflective contour vector of the visible light sequence and the temperature gradient vector of the infrared sequence.

[0052] The offset calculation module is used to input the reflective profile vector and temperature gradient vector into the hypernet model to generate alignment weights and calculate the relative time offset between modes.

[0053] The matrix generation module is used to construct a cross-modal graph neural network based on the relative time offset, calculate the topological deformation field of the solid-liquid interface, and generate a deformation compensation matrix.

[0054] The boundary reconstruction module is used to apply the deformation compensation matrix to the reflective profile vector and the temperature gradient vector to reconstruct the cross-modal aligned boundary features under oscillating conditions.

[0055] The tensor fusion module is used to perform tensor fusion calculations on cross-modal aligned boundary features, extract the physical contour curves of the solid-liquid interface, and output the microscopic boundary coordinate set.

[0056] In one embodiment of the present invention, the process of acquiring the visible light sequence and infrared sequence of the solid-liquid interface and mapping the visible light sequence and infrared sequence to the continuous manifold space in the manifold mapping module is as follows:

[0057] The acquisition of the original sensing image of the solid-liquid interface is accomplished using a multispectral imaging device. This device simultaneously records visible light band reflection information and mid-infrared band radiation information under the same field of view, forming an original sensing image containing dual-modal data. A matrix decomposition operation is then performed on this original sensing image. Based on the spectral response characteristic curve, the intensity value of each pixel is decomposed into optical reflection and thermal radiation components. The optical reflection components form an optical reflection matrix of the same size as the image, where each element represents the light intensity reflectance at that coordinate location in the visible light band. The thermal radiation components form a thermal radiation matrix of the same size as the image, where each element represents the thermal radiation intensity at that coordinate location in the mid-infrared band. According to the acquisition time recorded by the built-in clock chip of the imaging device, each frame of the original sensing image is assigned a timestamp with millisecond precision. The optical reflection matrices corresponding to 1000 consecutive frames of images are arranged in ascending order of timestamps to form a visible light sequence with dimensions of channel number multiplied by frame number multiplied by height multiplied by width. Similarly, the thermal radiation matrix is ​​arranged in ascending order of timestamps to form an infrared sequence with the same dimensions. The two sequences maintain a strict correspondence on the time axis, and each pair of timestamps identifies a set of dual-modal data at the same moment.

[0058] Visible light and infrared sequences are input into two independent branches of the feature network. The visible light branch contains three 3x3 convolutional layers. The first layer outputs a 64-channel feature map, the second layer outputs a 128-channel feature map, and the third layer outputs a 256-channel feature map. By progressively expanding the receptive field, it captures multi-scale visual information from local edges to global contours, ultimately outputting a 256-channel visual boundary tensor. This tensor encodes the position of the light-dark contrast boundary between the silicon crystal and the melt at the solid-liquid interface at the pixel level. The infrared branch contains the same number of convolutional layers but shares some parameters. It extracts a thermal gradient tensor based on the spatial distribution characteristics of the temperature field in the thermal radiation matrix. Each channel of this tensor represents the rate of temperature change in different directions. Channels 1 to 64 represent the horizontal gradient, channels 65 to 128 represent the vertical gradient, channels 129 to 192 represent the diagonal gradient, and channels 193 to 256 represent higher-order spatial derivative responses. The visual boundary tensor and the thermal gradient tensor are concatenated along the channel dimension and then fed into the encoding network. The encoding network adopts a four-layer fully connected structure with 512, 256, 128 and 64 neurons respectively. Each layer is followed by a hyperbolic tangent activation function. The 64-dimensional vector output by the last layer is the implicit feature vector after nonlinear transformation. This vector compresses the information of the visible light and infrared modes into a unified low-dimensional representation.

[0059] Based on the implicit eigenvectors output by the nonlinear transformation, a Riemann geometric metric model is constructed. First, the neighborhood relationship of each sample point in the 64-dimensional implicit feature space is regarded as a discrete sampling of a smooth manifold. The 15 nearest neighbors of each sample point are selected as local neighborhoods. The Euclidean distance matrix between each point in the neighborhood is calculated. The distance matrix is ​​transformed into a set of basis vectors of the local tangent space through a multidimensional scaling method. These basis vectors define the Riemann metric tensor of the implicit manifold at the sample point. The metric tensor is stored in the form of a 6x6 matrix. The diagonal elements of the matrix represent the scaling factor of each manifold coordinate direction, and the off-diagonal elements represent the coupling strength between coordinate directions. After obtaining the Riemann metric for each sample point, the local homeomorphic projection coordinates of the implicit eigenvectors are calculated. Specifically, a reference sample point is selected as the origin of the manifold coordinates. For each target sample point, the inverse operation of the exponential mapping is performed along the geodesic path connecting the two points on the manifold, mapping each point on the manifold to a flat coordinate system in the tangent space at the origin. This mapping constitutes a homeomorphic transformation locally, and the result is the local homeomorphic projection coordinate, with each coordinate represented by a six-dimensional vector. Finally, based on these local homeomorphic projection coordinates, all visible light and infrared sequence frames are uniformly embedded into a six-dimensional continuous manifold space. Each point in this space represents the position of a set of bimodal data on the manifold, and the manifold distance between adjacent points reflects the similarity of the corresponding frames in terms of geometric structure and temperature distribution.

[0060] In one embodiment of the present invention, the feature extraction module, wherein the step of constructing an ordinary differential equation tensor field in a continuous manifold space and extracting the reflected contour vector of the visible light sequence and the temperature gradient vector of the infrared sequence is as follows:

[0061] The system receives visible light and infrared sequences mapped to a continuous manifold space as the initial input data set for feature extraction. To accurately capture the high-frequency oscillation dynamics of the solid-liquid interface under high-temperature melt thermal convection, a hidden state feature h(t) representing the physical evolution of crystal growth is defined along the time dimension, where t represents the time variable. A feedforward neural network with three hidden layers is used to fit the nonlinear derivative function of this hidden state feature over time; the input to the feedforward neural network includes the current hidden state feature h(t) and the mapped multimodal image features. Through iterative optimization of the network weights, the approximation result output by the feedforward neural network can be accurately expressed as a differential equation: In the formula, θ represents the learnable parameter matrix of the neural network containing 1024 nodes. This neural network fitting mechanism effectively overcomes the shortcomings of traditional discrete-time modeling methods in capturing continuous physical deformation trajectories. It enables the extracted hidden state derivative function to smoothly and continuously reflect the micro-state mutation rate of visible light and infrared modal data at any time point, laying a precise mathematical foundation for dynamic time alignment and high-dimensional feature compensation.

[0062] Based on the derivative function obtained from the previous step, a fundamental vector field characterizing the dynamic evolution of the multimodal feature sequence is constructed. Since the physical properties of the high-frequency oscillation interface are constrained by specific geometric conditions, this fundamental vector field is projected onto the local tangent space of the continuous manifold using an orthogonal projection operator, thereby generating an ordinary differential equation tensor field that conforms to the physical topological conservation laws. In the generated ordinary differential equation tensor field, the Runge-Kutta numerical integration algorithm is used to calculate the continuous-time integral trajectory; the integration step size is set to 0.01 seconds to ensure a balance between capturing high-frequency oscillation details and maintaining computational efficiency. The process of calculating the continuous-time integral trajectory is expressed by the integral expression: To provide a quantitative description, the integral has a lower limit of t0 and an upper limit of T, where t0 represents the set integration start time, corresponding to the 120th second of the initial stage of constant-diameter growth of silicon single crystals, and T represents the target prediction time point. Through this continuous-time tensor field integration within the manifold tangent space, the smooth evolution path of heterogeneous data on arbitrary sub-millimeter time slices can be effectively reconstructed, greatly improving the spatiotemporal resolution of dynamic matching between heterogeneous sensing sequences.

[0063] A smooth visual tensor is obtained from the continuous-time integral trajectory of the visible light sequence based on the aforementioned ordinary differential equation. This visual tensor eliminates inter-frame jump errors from the camera due to continuous compensation in the time dimension. A two-dimensional matrix convolution operation is performed on this visual tensor using the Laplacian differential operator. The core convolution kernel size is configured as a 3x3 matrix, and the center weight coefficient is set to 8 to enhance the contrast between the center pixel and its surrounding neighborhood. Through matrix convolution, the abrupt changes in the physical morphology of reflective material at the solid-liquid interface caused by the surface tension of the melt can be accurately captured, precisely extracting the set of physical boundary pixels exhibiting high-frequency oscillations. These extracted physical boundary pixels are then curve-fitted and vectorized according to their connectivity in two-dimensional space, ultimately generating a continuous reflective contour vector with a dimension of 256. The reflective profile vector directly reflects the degree of geometric distortion of the meniscus in the visible light mode. The above matrix convolution operation effectively filters out the optical diffraction interference caused by the argon gas flow inside the growth furnace, so that the output reflective profile vector has extremely high physical fidelity and noise resistance.

[0064] A smoothed thermal radiation tensor is obtained from the infrared sequence based on the same continuous-time integral trajectory. This tensor also possesses the continuous-time resolution property to eliminate the influence of heterogeneous sampling frequencies. The partial derivative matrices of this thermal radiation tensor are calculated along the two orthogonal directions: the horizontal spatial axis and the vertical spatial axis. Let the energy function of the thermal radiation tensor distribution in two-dimensional space be E(x,y). Then, the corresponding formulas for calculating the partial derivatives in the orthogonal spatial directions are the gradient vectors: The transpose of the matrix is ​​given, where x and y represent the horizontal and vertical coordinates in the spatial plane coordinate system, respectively. By jointly solving the partial derivative information in the orthogonal directions, the energy difference of the local thermal radiation distribution at the solid-liquid interface at the microscale can be accurately analyzed. These local thermal radiation distribution differences, which characterize the thermal energy jump, are normalized and spliced ​​according to a specific spatial scanning order to generate a temperature gradient vector with dimension 256. The generated temperature gradient vector accurately characterizes the local temperature boundary drift characteristics caused by thermal convection at the solid-liquid interface from the infrared perspective, completing a high-quality cross-modal vector extraction process that includes visible light geometric features and infrared thermodynamic features.

[0065] In one embodiment of the present invention, the step of inputting the reflective contour vector and temperature gradient vector into the hypernetwork model to generate alignment weights, and calculating the relative time offset between modes, is as follows:

[0066] The previously extracted reflective contour vector (256 dimension) and temperature gradient vector (256 dimension) are obtained. An element-wise concatenation operation is performed on these two heterogeneous feature sequences along the feature channel dimension to construct a global state feature of dimension 512. This global state feature fully preserves the physical deformation information of the solid-liquid interface captured by visible light images and the local temperature gradient drift information characterized by infrared thermal imaging. The constructed state feature is input into a pre-defined hypernetwork model to perform perceptual hidden layer mapping. This hypernetwork model acts as a dynamic weight generator, containing three fully connected hidden layers and a nonlinear activation function. When the high-dimensional state feature flows through the hypernetwork model, the neurons within the model perform deep spatial analysis of the potential coupling relationship between the visible light and infrared modal features, thereby dynamically calculating and outputting a set of dynamic parameters for controlling the target network structure's operating mechanism. Mathematically, assuming the state feature is represented by variable S and the hypernetwork mapping function by variable H, the generated dynamic parameters are represented by variable W, where the value of variable W is equal to the matrix operation result of the nonlinear spatial transformation of variable S by function H. This set of dynamic parameters contains all the feature weight matrices and bias vectors required by the target network, realizing the purpose of real-time adaptive generation of matching parameters based on the actual oscillation physical state of the solid-liquid interface at the current moment. It effectively avoids the problem of insufficient generalization ability of fixed network parameters when dealing with high-frequency nonlinear physical dynamics, and provides a customized network computing power foundation for accurate time alignment of cross-modal image features.

[0067] The dynamic parameters output in real time from the hypernetwork model are fully loaded into the pre-defined target network, enabling the connection weights and bias nodes of each hidden layer within the target network to complete the parameter structure update and initialization. After the dynamic parameter loading operation is completed, the original extracted reflective contour vector and temperature gradient vector are fed into the target network as parallel input data, respectively. The updated network operators are used to perform attention tensor multiplication operations on cross-modalities. Inside the target network, the input reflective contour vector and temperature gradient vector are linearly transformed into query feature matrix, key feature matrix, and value feature matrix, respectively. The network uses the transpose of the query feature matrix and the key feature matrix to perform a spatial dot product operation, calculating the correlation score matrix of the two modal features at different time steps. To prevent the gradient propagation from vanishing due to excessively large inner product values, the correlation score matrix is ​​numerically scaled by dividing by the square root of the feature space dimension, and an exponential normalization function is applied to process the scaled score matrix, that is, to calculate the probability distribution result of the exponential operation of the scaled matrix, ultimately generating alignment weights representing the correlation between modalities. The generated alignment weights are presented in the form of a normalized probability distribution matrix. Each element in the matrix precisely quantifies the degree of correlation between the physical contour changes of the visible light mode and the temperature gradient changes of the infrared mode on the time evolution axis, providing a reliable quantitative evaluation index for solving the asynchronous time distortion caused by heterogeneous sampling of multi-source image sensors.

[0068] Based on the output alignment weights, local sliding feature data blocks of the reflective contour vector and temperature gradient vector are extracted within a set observation time window, and the temporal cross-correlation sequence of these two modal sequences is calculated at different time delay steps. Specifically, a time sliding calculation window with a length of 50 sampling points is set, keeping the feature data sequence of the infrared mode fixed, while the feature data sequence of the visible light mode is translated frame by frame along the physical time axis. In each translation transformation, the sum of the weighted inner products of the two feature sequences and the alignment weight matrix within the overlapping interval is calculated. By traversing all preset translation steps, for example, translating successively from -30 steps to +30 steps, a temporal cross-correlation sequence containing 61 discrete cross-correlation values ​​can be obtained. Each discrete calculated value in this temporal cross-correlation sequence truly reflects the degree of matching and fit of the dynamic evolution trajectories between the two heterogeneous feature modes at a specific time delay node. After completing the weighted inner product traversal calculation, the extreme coordinates of the time cross-correlation sequence are extracted. This involves using an optimization algorithm to find the index of the point with the maximum value in the time cross-correlation sequence. Assuming the found maximum point corresponds to the 15th step in the translation sequence, and given that the base time sampling interval of the multi-source image sensors is 10 milliseconds, the relative time offset between the two modes can be calculated as 150 milliseconds by multiplying the translation steps by the sampling interval. This calculated relative time offset accurately reflects the objective time difference caused by different sensor exposure mechanisms, thus providing an absolutely quantitative physical calibration parameter for temporal feature alignment compensation of high-frequency oscillating interface images.

[0069] In one embodiment of the present invention, a cross-modal graph neural network is constructed based on the relative time offset to calculate the topological deformation field of the solid-liquid interface, and the deformation compensation matrix is ​​generated as follows:

[0070] The reflective contour vector and temperature gradient vector, both with a dimension of 256, are obtained from the preprocessing stage. Each feature data value in these two heterogeneous sequences is extracted as an independent data computation node, thus initializing a total of 512 graph nodes in the topological space. To accurately reflect the causal relationship between the two physical modes in the dynamic evolution process, directed edges representing the information flow are established between the graph nodes of the heterogeneous modes based on the calculated 150-millisecond relative time offset. In specific implementation, a time difference threshold interval is set, where the sampling time of the visible light mode graph node is increased by 150 milliseconds. After a millisecond relative time offset, if the timestamp falls within the time difference threshold range of a specific graph node in the infrared modality, a directed edge is generated between the two graph nodes, and the weight of the edge is set to be proportional to the time fit. By traversing all graph nodes and calculating the time matching degree, a complete network topology connection structure is connected, and a cross-modal graph neural network containing a node feature matrix and an adjacency matrix is ​​established. This network model transforms isolated one-dimensional vector data into a complex non-Euclidean geometric data structure with spatiotemporal coupling, providing a basic network framework for cross-modal high-dimensional feature interaction.

[0071] In the constructed cross-modal graph neural network, the message passing mechanism for information interaction is activated, and the network is controlled to perform multiple rounds of graph convolution aggregation operations, enabling each individual graph node to perceive the state changes of its surrounding associated nodes. Spatial state information of heterogeneous modal neighbor nodes is aggregated along the established directed edges, and the feature values ​​of adjacent feature elements pointing to the current center node are merged using a weighted summation method. The specific operational model can be represented as the state evolution equation H2=A*H1*W1, where H2 represents the updated secondary hidden state matrix, A is the adjacency matrix representing the directed connection relationships between graph nodes, and H1 is the current primary node hidden state. The matrix W1 is the learnable weight parameter matrix of the network layer. After message passing and spatial state aggregation calculation at three network depths, the optical geometric features carried by the central graph node itself are deeply fused with the temperature gradient features contained in its adjacent infrared graph nodes. The hidden layer state vector of each graph node is updated using the fused mixed information. After completing the state update calculation process of all network graph nodes, the 512 high-dimensional state vectors containing rich cross-modal fusion information are integrated and rearranged to output a cross-modal spatiotemporal feature matrix with a dimension of 256 by 256. This matrix fully characterizes the micro-spatiotemporal coupling characteristics of the solid-liquid interface meniscus under physical nonlinear oscillation conditions.

[0072] The generated cross-modal spatiotemporal feature matrices are batch-input into a multilayer perceptron with four hidden layers for nonlinear coordinate transformation calculations. The neurons within the multilayer perceptron are used to reduce the dimensionality of the high-dimensional matrix information and perform spatial mapping, accurately calculating the spatial relative displacement vectors of each heterogeneous graph node in the physical coordinate system. These spatial relative displacement vectors, possessing direction and magnitude attributes, are combined to generate a discrete velocity field covering the entire monitoring area. Each discrete data point in this velocity field corresponds to the absolute deformation rate of a local region at the solid-liquid interface within the current observation period. To fill the geometric gaps between the discrete data points, a bilinear interpolation algorithm is used to process the generated discrete velocity field. Continuous interpolation calculations are performed with a spatial grid resolution of 0.1 mm for the target plane. Assuming the velocity variables of four adjacent known nodes in the discrete velocity field are V1, V2, V3, and V4, the unknown velocity distribution value V at any specific coordinate position in the plane is calculated using the bilinear interpolation formula V = a*x*y + b*x + c*y + d. The coefficients a, b, c, and d in the formula are uniquely determined by the velocity variables of these four known adjacent nodes. Through high-density continuous numerical interpolation calculations, a continuous topological deformation field that can completely describe the dynamic evolution of the entire solid-liquid interface is smoothly fitted, transforming the originally discrete point changes into a globally visible physical mapping of fluid distortion.

[0073] Deformation gradient components at various coordinate positions within the continuously fitted topological deformation field are extracted along the spatial physical coordinate axes. By calculating the partial derivatives of the topological deformation field along the X-axis and Y-axis, a microscopic partial derivative information matrix characterizing the intensity of local deformation is obtained. These extracted discrete deformation gradient components are arranged according to their true coordinate positions on the physical observation surface, constructing a two-dimensional grid structure of 128 rows by 128 columns. Each cell of this grid structure stores the deformation tensor information of the corresponding small spatial region. To eliminate high-frequency noise interference from local strong convection and extract the core deformation principal components, an odd-numbered... The heterogeneous value decomposition algorithm performs tensor decomposition calculations on the two-dimensional mesh feature structure. The tensor decomposition process can be expressed as the matrix equation M = U * S1 * Vk, where M is the original two-dimensional mesh feature matrix, U is the left singular vector matrix, Vk is the right singular vector matrix, and S1 is a diagonal matrix containing singular values. In the diagonal matrix S1 generated by decomposition, small singular values ​​with values ​​less than a set threshold of 0.05 are removed to filter out high-frequency noise components of environmental disturbances. The top 50 largest singular values ​​are retained to reconstruct the main deformation features. The reconstructed and denoised feature parameters are used to generate the final deformation compensation matrix, thus providing a reliable mathematical model after denoising for accurate alignment and dynamic correction of cross-modal heterogeneous features.

[0074] In one embodiment of the present invention, the process of applying the deformation compensation matrix to the reflective profile vector and the temperature gradient vector to reconstruct the cross-modal aligned boundary features under oscillating conditions is as follows:

[0075] Obtain the 128x128 deformation compensation matrix and the 256-dimensional reflective contour vector generated in the previous steps. First, perform a dot product operation between these two mathematical data structures to achieve spatial feature mapping interaction. Specifically, multiply each row element of the deformation compensation matrix with the corresponding column element of the reflective contour vector and sum them to calculate the basic mapping vector containing dynamic deformation correction weights. Based on this basic mapping vector, perform an affine transformation operation on the original reflective contour vector in a 2D Cartesian physical coordinate plane. The mathematical expression of this affine transformation is... The process involves multiplying the original 2D spatial coordinate set of the reflective profile vector by the rotation and scaling parameter matrix derived from the deformation compensation matrix, and adding a translation vector to compensate for the overall physical profile drift caused by argon shear stress, thereby generating a new coordinate set after position update calculation. By performing the above affine transformation calculation, the absolute coordinate position of the reflective profile vector on each time slice is accurately updated, so that the physical geometric deformation distortion caused by camera heterogeneous sampling is completely smoothed out, and finally the deformation-corrected reflective features that eliminate the influence of nonlinear high-frequency oscillations are extracted in the spatial domain.

[0076] The same 128x128 deformation compensation matrix is ​​obtained and then tensor-producted with the 256-dimensional temperature gradient vector extracted from the preprocessing. Since the temperature gradient represents the thermal energy distribution in the infrared mode, ordinary dot product operations usually cannot capture its diffusion deformation characteristics in multiple physical directions. Therefore, tensor product is used to expand the spatial representation dimension of thermodynamic features. Performing tensor product calculation generates a joint topology matrix with a higher-order data structure. Each element in this joint topology matrix accurately reflects the local temperature gradient generated when subjected to strong thermal convection impact from the high-temperature melt. Complex offset direction and offset magnitude; based on the multidimensional nonlinear drift weights contained in the calculated joint topology matrix, spatial reshaping and bilinear interpolation are performed on the local energy value distribution of the original temperature gradient vector, and the energy values ​​of local high-temperature pixels that have undergone spatial drift are redistributed and returned to their true physical coordinates; through large-scale numerical reconstruction and energy distribution calibration of the temperature gradient vector, the problem of thermal trailing blur in infrared images caused by exposure time difference of heterogeneous sensors is completely repaired, thereby accurately resolving the deformation correction temperature characteristics that can perfectly match the visible light image in spatial physical location.

[0077] A joint tensor is constructed by fusing deformation-corrected reflective features and deformation-corrected temperature features. Feature mapping is then performed on the joint tensor to reconstruct cross-modal aligned boundary features under oscillating conditions. The specific content is as follows:

[0078] Deformation-corrected reflective features processed by spatial affine transformation and deformation-corrected temperature features processed by numerical reconstruction are obtained. The data structures for both features are set to contain 256 depth feature channels. The feature matrices of these two heterogeneous modes are aligned in memory space, and a direct stitching operation is performed strictly along the depth channel dimension of the feature data. For example, the spatial resolution of the deformation-corrected reflective features is 128 x 128 with 256 channels, and the spatial resolution of the deformation-corrected temperature features is also 128 x 128 with 256 channels. By directly stitching and merging the feature distribution channels at the stitching position in the depth direction, the object... By superimposing these two data matrices representing different modal attributes, a high-dimensional joint tensor with 512 feature channels is constructed. This joint tensor simultaneously encompasses optical reflection physical information characterizing the geometric undulations of the meniscus at the solid-liquid interface and infrared temperature distribution information characterizing the thermal convection energy gradient of the melt surface within a single data structure. This tight stitching method along the channel dimension establishes an initial cross-correspondence between visual and thermodynamic modalities on the underlying data plane, forcibly constraining the originally independent heterogeneous sensing features within the same high-dimensional spatial coordinate system, providing a unified topological data foundation for deep micro-feature fusion and dynamic boundary alignment.

[0079] The constructed high-dimensional joint tensor with 512 feature channels is fed into a pre-configured multilayer perceptron (MLP) to perform deep-dimensional feature mapping calculations. This MLP typically has three fully connected hidden layers. When the data stream of the joint tensor passes through the MLP nodes, the data within the original spliced ​​channels is first linearly weighted and summed using the network connection weight matrix. Then, a pre-defined nonlinear function within the MLP's hidden layers is forcibly activated to process the linear summation result. The nonlinear function used here is a modified linear unit function (MRU), which utilizes its one-sided suppression characteristic to filter out invalid environmental background noise caused by physical oscillations within the joint tensor. Furthermore, during the progressive propagation through multiple hidden layers, the deep nonlinear coupling relationship between the visible light physical contour and the infrared thermal gradient is continuously abstracted and extracted. Through this high-intensity network operator forward propagation and mapping calculation, the network output accurately resolves a set of fused hidden layer parameters containing high-level semantic information. This set of fused hidden layer parameters not only carries the core physical boundary shape features after dimensionality reduction but also fully expresses the dynamic mutual mapping and correlation of the two modal features under high-frequency thermal oscillation interference.

[0080] Based on the analytically derived fusion hidden layer parameters, spatial attention weights are assigned to each feature channel in a 2D spatial plane. During this process, an exponential normalization function is used to perform probability distribution mapping calculations on the fusion hidden layer parameters, ensuring that each output weight value is strictly limited to the effective range of 0 to 1. For example, for a 128x128 spatial pixel grid, the generated spatial attention weight matrix is ​​used to perform point-to-point weighted multiplication operations on each pixel coordinate point within the grid. Pixels located in the core region of high-frequency oscillation at the solid-liquid interface and possessing significant modal complementarity are assigned high weight values ​​close to 1, while pixels in the peripheral region far from the interface or with extremely low signal-to-noise ratio are assigned low weight values ​​close to 0. Combining this dynamically assigned spatial attention weights, pixel-level energy enhancement and noise suppression are applied to the original joint features, greatly amplifying the feature channels that truly characterize the physical properties of the interface. This eliminates the sampling time difference of multi-source sensors and the physical distortion of melt convection, thereby reconstructing cross-modal aligned boundary features that accurately conform to the real physical form under high-frequency oscillation conditions with high fidelity, completely solving the technical problem of ghosting at the edge contours of the original image.

[0081] In one embodiment of the present invention, the tensor fusion module performs tensor fusion calculation on cross-modal aligned boundary features to extract the physical contour curve of the solid-liquid interface and outputs the content of the microscopic boundary coordinate set as follows:

[0082] The cross-modal alignment boundary features reconstructed by spatial attention weights are obtained, and the visible light deformation correction component and infrared temperature deformation correction component contained within them are extracted. Assuming that these two modal components are both represented as 256-dimensional feature vectors in the current processing stage, a tensor outer product operation is performed on these two feature vectors. Through cross-multiplication of vector elements, a high-dimensional feature matrix with a spatial dimension of 256 by 256 is generated. Each matrix node within this high-dimensional feature matrix contains deeply coupled information between geometric deformation and thermodynamic state, resulting in a strong non-linear relationship between the originally parallel data sets. Linear cross-mapping; to eliminate the curse of dimensionality and interference from local redundant features caused by high-dimensional data during the calculation process, a global max pooling operator is applied along the spatial channel dimension of the high-dimensional feature matrix for dimensionality reduction calculation; within the effective region of the pooling operator, by comparing and retaining the maximum response value within each fixed step size receptive field, the original massive 256x256 matrix is ​​compressed and mapped into a feature distribution map with significantly reduced dimensionality but highly condensed core features; after this pooling dimensionality reduction process, the dense boundary fusion features that have been filtered out of high-frequency oscillation artifacts are successfully resolved, providing high signal-to-noise ratio data support for accurate physical contour extraction.

[0083] The dense boundary fusion features obtained from the dimensionality reduction analysis are extracted. In the two-dimensional image coordinate space, the spatial derivative of this feature map is calculated using a difference operator. The gray-level change rate of each pixel along the horizontal and vertical axes is calculated respectively. The square roots of the sum of the squares of these two orthogonal derivatives are then used to accurately calculate the pixel gradient magnitude of each pixel within the dense boundary fusion features. This pixel gradient magnitude accurately reflects the degree of signal intensity jump caused by abrupt changes in the physical properties of the solid-liquid interface in the local image region. Based on the calculated pixel gradient magnitude distribution map, a non-maximum suppression algorithm is applied within the global search range. Optimization is performed by setting a gradient threshold of 120 to filter background noise in smooth areas, thereby accurately searching for maxima connected regions with gradient values ​​exceeding the threshold of 120 and exhibiting continuous spatial arrangement. For these marked and extracted maxima connected regions, the least squares method or spline curve algorithm is used to fit the spatial pixel distribution topology within the region. High-order polynomial equations are used to smooth the connection transition of discrete high-gradient pixel points, perfectly restoring the real nonlinear meniscus geometry at the solid-liquid interface, and finally accurately extracting a smooth and continuous solid-liquid interface physical contour curve.

[0084] After obtaining a smooth and continuous solid-liquid interface physical profile curve, in order to convert this geometric topological representation into digital signal parameters that can be directly read by the industrial control unit, a fixed-interval discretization sampling operation is performed along the geometric extension path of the physical profile curve. Specifically, the spatial interval of the discretization sampling is set to 1 mm, and feature points are sequentially intercepted along the tangent direction of the curve starting from the physical starting point of the curve. For example, 150 key discretization sampling nodes are uniformly collected on a profile curve with a total length of 150 mm. Combining the pre-calibrated industrial camera parameter matrix and the physical coordinate transformation relationship inside the growth furnace, these 150... The relative image pixel coordinates of the sampling nodes are mapped to absolute physical coordinates, thereby accurately resolving the absolute spatial position of each discretized sampling node in the real three-dimensional physical reference frame. After completing the spatial position resolution operation, the horizontal and vertical coordinate values ​​of these 150 absolute spatial positions are arranged linearly according to their spatial sampling order on the contour curve, and combined to generate a compact one-dimensional data column containing complete interface geometric information. Based on this, a set of micro-boundary coordinates is output that can be directly called by the micro-diameter change machine vision recognition module, thus completely completing the topological feature extraction and coordinate quantization output process of cross-modal aligned boundaries.

[0085] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the claims of this invention should still fall within the patent coverage of this invention.

Claims

1. A multi-modal image analysis system for a Czochralski silicon single crystal growth interface, comprising: include: The manifold mapping module is used to acquire the visible light and infrared sequences of the solid-liquid interface and map the visible light and infrared sequences to a continuous manifold space. The feature extraction module is used to construct the ordinary differential equation tensor field in the continuous manifold space and extract the reflective contour vector of the visible light sequence and the temperature gradient vector of the infrared sequence. The offset calculation module is used to input the reflective profile vector and temperature gradient vector into the hypernet model to generate alignment weights and calculate the relative time offset between modes. The matrix generation module is used to construct a cross-modal graph neural network based on the relative time offset, calculate the topological deformation field of the solid-liquid interface, and generate a deformation compensation matrix. The boundary reconstruction module is used to apply the deformation compensation matrix to the reflective profile vector and the temperature gradient vector to reconstruct the cross-modal aligned boundary features under oscillating conditions. The tensor fusion module is used to perform tensor fusion calculations on cross-modal aligned boundary features, extract the physical contour curves of the solid-liquid interface, and output the microscopic boundary coordinate set.

2. The multi-modal image analysis system of an interface of a Czochralski silicon single crystal growth according to claim 1, characterized in that, In the manifold mapping module, the process of acquiring the visible light and infrared sequences of the solid-liquid interface and mapping these sequences to a continuous manifold space includes: The original sensor image of the solid-liquid interface is acquired, the optical reflection matrix and thermal radiation matrix inside the original sensor image are separated, the optical reflection matrix is ​​arranged according to the timestamp to obtain the visible light sequence, and the thermal radiation matrix is ​​arranged to obtain the infrared sequence. The visible light sequence and the infrared sequence are input into the feature network to analyze the visual boundary tensor of the visible light sequence and the thermal gradient tensor of the infrared sequence. The visual boundary tensor and the thermal gradient tensor are then input into the encoding network to perform a nonlinear transformation. A Riemann geometric metric model is constructed based on the implicit eigenvectors output by the nonlinear transformation. The local homeomorphic projection coordinates of the implicit eigenvectors are solved, and the visible light sequence and infrared sequence are mapped to the continuous manifold space based on the local homeomorphic projection coordinates.

3. The multi-modal image analysis system of an interface of a Czochralski silicon single crystal growth according to claim 1, wherein, In the feature extraction module, the step of constructing an ordinary differential equation tensor field in a continuous manifold space to extract the reflected contour vector of the visible light sequence and the temperature gradient vector of the infrared sequence is as follows: Receive visible light and infrared sequences mapped to a continuous manifold space, define hidden state features along the time dimension, and fit the derivative function of the hidden state features using a feedforward neural network; Based on the derivative function, a fundamental vector field representing the sequence evolution is constructed. The fundamental vector field is projected onto the tangent space of the manifold to generate an ordinary differential equation tensor field. The continuous-time integral trajectory is calculated in the ordinary differential equation tensor field. Obtain the visual tensor output by the continuous-time integral trajectory of the visible light sequence, apply the differential operator to the visual tensor to perform matrix convolution operation, and extract the physical boundary pixels to generate the reflective contour vector; Obtain the thermal radiation tensor output by the continuous-time integral trajectory of the infrared sequence, calculate the partial derivatives of the thermal radiation tensor in the spatial orthogonal directions, and generate a temperature gradient vector by analyzing the difference in local thermal radiation distribution.

4. The multi-modal image analysis system of an interface of a Czochralski silicon single crystal growth according to claim 1, wherein, In the offset calculation module, the process of inputting the reflective contour vector and temperature gradient vector into the hypernetwork model to generate alignment weights and calculating the relative time offset between modes is as follows: State features are constructed by splicing reflective contour vectors and temperature gradient vectors. These state features are then input into the hypernetwork model to perform perceptual hidden layer mapping, and the dynamic parameters of the target network are output. The dynamic parameters are loaded into the target network, and the reflective contour vector and temperature gradient vector are input into the target network to perform attention tensor multiplication, generating alignment weights between modes. The time cross-correlation sequence of the reflective profile vector and the temperature gradient vector is calculated based on the alignment weight, and the extreme coordinates of the time cross-correlation sequence are extracted to calculate the relative time offset.

5. The multi-modal image analysis system of an interface of a silicon single crystal growth according to claim 1, wherein, In the matrix generation module, the content of the deformation compensation matrix generated by constructing a cross-modal graph neural network based on the relative time offset to calculate the topological deformation field of the solid-liquid interface is as follows: Feature elements of reflective contour vector and temperature gradient vector are extracted as graph nodes. Directed edges are established by connecting graph nodes of heterogeneous modes based on relative time offset to construct a cross-modal graph neural network. In a cross-modal graph neural network, a message passing mechanism is activated to aggregate the spatial states of heterogeneous modal neighbor nodes along directed edges, update the hidden state vectors of graph nodes, and output a cross-modal spatiotemporal feature matrix. The cross-modal spatiotemporal feature matrix is ​​input into the spatial relative displacement between nodes of the multilayer perceptron computation graph. The spatial relative displacement is combined to generate a discrete velocity field. Interpolation calculation is performed on the discrete velocity field to fit the topological deformation field of the solid-liquid interface. Extract the deformation gradient components at each coordinate position within the topological deformation field, arrange the deformation gradient components into a two-dimensional mesh feature structure, and perform tensor decomposition on the two-dimensional mesh feature structure to generate a deformation compensation matrix.

6. The multi-modal image analysis system of an interface of a silicon single crystal growth according to claim 1, wherein, In the boundary reconstruction module, the process of applying the deformation compensation matrix to the reflective contour vector and the temperature gradient vector to reconstruct the cross-modal aligned boundary features under oscillating conditions is as follows: Calculate the dot product between the deformation compensation matrix and the reflective profile vector, update the coordinate position of the reflective profile vector through affine transformation, and extract the deformation-corrected reflective features. Calculate the tensor product of the deformation compensation matrix and the temperature gradient vector, reconstruct the numerical distribution of the temperature gradient vector based on the tensor product, and analyze the deformation correction temperature characteristics. A joint tensor is constructed by fusing deformation-corrected reflective features and deformation-corrected temperature features. Feature mapping is then performed on the joint tensor to reconstruct cross-modal aligned boundary features under oscillating conditions.

7. The multi-modal image analysis system of an interface of a silicon single crystal growth according to claim 6, wherein, The fusion of deformation-corrected reflective features and deformation-corrected temperature features to construct a joint tensor, and the subsequent feature mapping of the joint tensor to reconstruct the cross-modal aligned boundary features under oscillating conditions, are as follows: Deformation-corrected reflective features and deformation-corrected temperature features are spliced ​​along the channel dimension, and a joint tensor is constructed by combining the feature distribution channels at the splicing positions. The joint tensor is input into the multilayer perceptron to perform feature mapping, and the nonlinear function inside the multilayer perceptron is activated to analyze and fuse the hidden layer parameters. Spatial attention weights for each channel are assigned based on the fused hidden layer parameters, and the cross-modal alignment boundary features under oscillating conditions are reconstructed by combining the spatial attention weights.

8. The multi-modal image analysis system of an interface of a silicon single crystal growth according to claim 1, wherein, In the tensor fusion module, the tensor fusion calculation of cross-modal aligned boundary features, extraction of the physical contour curve of the solid-liquid interface, and output of the microscopic boundary coordinate set are as follows: Tensor cross-product operation is performed on each modal component of the cross-modal aligned boundary feature to generate a high-dimensional feature matrix. Pooling operator is applied along the spatial channel dimension of the high-dimensional feature matrix to reduce the dimension of the dense boundary fusion feature. Calculate the pixel gradient magnitude of dense boundary fusion features, search for the maximum connected region based on the pixel gradient magnitude, fit the spatial pixel distribution topology inside the maximum connected region, and extract the physical contour curve of the solid-liquid interface. Discretization sampling is performed along the extension path of the physical contour curve. The absolute spatial position of the discretized sampling node in the reference frame is analyzed. The absolute spatial positions are arranged in the sampling order to form a data column, and the microscopic boundary coordinate set is output.

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