A method and system for CBCT tooth segmentation and tooth numbering based on cross-scale spectral routing

Abstract

The present application relates to a kind of CBCT tooth segmentation and tooth number based on cross-scale spectrum routing method and system, belong to medical image processing field.The method uses U-shaped encoder-decoder network, including hybrid CNN-Mamba encoder, cross-scale spectrum router CSSR, frequency context aggregator FCA, five-level decoder, five deep supervision segmentation head and auxiliary boundary head.Encoder extracts six-level feature pyramid, inserts three-direction Mamba block from the 2nd level;CSSR is cross-scale self-adaptive reorganization to shallow and deep layer skip connection with double set of hybrid expert mode, and its residual weight starts from zero learning;FCA extracts Fourier, DB2 wavelet and multi-scale Mexican hat frequency domain descriptor in parallel, and modulates deep layer fusion feature by FiLM mechanism;Decoder is progressively up-sampled and spliced with CSSR modulation feature, and five deep supervision heads respectively output 33 class voxel prediction, directly obtain per-tooth instance and its tooth number.The present application can improve the accuracy of three-dimensional tooth segmentation and tooth number.

Description

Technical Field

[0001] This invention belongs to the field of medical image processing, specifically relating to a CBCT tooth segmentation and tooth position numbering method and system based on cross-scale spectral routing. Background Technology

[0002] CBCT can provide high-resolution three-dimensional images of the oral and maxillofacial structures with a relatively low radiation dose. Accurate segmentation and proper tooth numbering of each tooth are fundamental to orthodontic treatment planning, implant planning, surgical simulation, and digital dental CAD systems. This task requires simultaneously identifying the tooth structure, depicting the crown and root boundaries, and distinguishing the left and right sides of the dental arch and corresponding teeth in the upper and lower jaws.

[0003] Early approaches typically extended the 2D detection framework to 3D dental data. For example, ToothNet uses Mask R-CNN to detect tooth edges; the coarse-to-fine V-Net approach refines boundaries through progressively higher resolution; multi-task fully convolutional networks simultaneously predict tooth regions and surface probability maps, then use label-controlled watersheds to separate adjacent teeth; centroid-based and Gaussian decoupling methods separate contacting teeth using geometric centers; and hierarchical morphology approaches also introduce candidate regions and shape priors.

[0004] Clinical systems similar to this application often employ a cascaded process: first, teeth or dental arch regions are detected; second, semantic or instance segmentation is performed; and finally, tooth position numbers are assigned using independent labeling modules or heuristic rules. ToothSeg combines semantic segmentation heads and instance segmentation heads, and handles tooth merging, splitting, and label rearrangement through a self-correction mechanism; OralSeg combines the Swing Transformer and spatial Mamba modules in the UNetR backbone to obtain local and global dependencies of volume data. For networks that originally only performed semantic segmentation, it is also necessary to split contact instances through connected component analysis and assign tooth position number labels within predicted instances using majority voting.

[0005] In terms of encoders, schemes such as U-Mamba and SegMamba use state-space models to replace or supplement self-attention, modeling long-range dependencies with linear complexity. In terms of skip connections, UNet++ uses dense nested connections, Attention U-Net uses gating to suppress irrelevant features, and hybrid expert schemes resample multiple coding scales and then process them by different experts. In terms of frequency domain, Fourier and wavelet decomposition can provide multi-resolution spectral information, but there is still a lack of a unified tooth segmentation scheme that jointly optimizes multiple types of spectral descriptors with cross-scale skip connection routes.

[0006] The existing technology has the following drawbacks:

[0007] 1. Multi-stage error propagation. When region detection, segmentation, and tooth position numbering are completed sequentially by independent modules, missed detections, adhesions, or boundary deviations in the previous stage will be propagated to the next stage, and each module needs to be trained, tuned, and deployed separately.

[0008] 2. Fine-grained boundaries are easily lost. The gap between adjacent teeth may only have one voxel, and the grayscale of the tooth root and alveolar bone is very similar; fixed one-to-one skip connections make it difficult to utilize both shallow boundary details and deep semantics simultaneously according to the needs of different decoding layers.

[0009] 3. Insufficient long-range spatial relationships. Missing teeth, edentulous teeth, restorations, and individual anatomical differences weaken local appearance cues, making it difficult to reliably infer the global positional relationship of the dental arch required for tooth position numbering solely from local convolution.

[0010] 4. Cross-scale fusion lacks adaptability. Simple splicing, addition, or attention gating usually use similar scale combinations for all samples, and repeated resampling at multiple scales can lead to information redundancy and computational burden.

[0011] 5. Sparse experts may degenerate. When using Top-K expert routing, the gating system tends to concentrate on a small number of experts in the long term, resulting in insufficient training of the remaining experts and making it difficult to form complementary spatial feature processing capabilities.

[0012] Therefore, the technical problems to be solved by this application are: to complete 3D tooth instance segmentation and tooth position numbering within a single end-to-end network; to enable different decoding layers to adaptively acquire cross-scale information according to the input; to use global frequency context to assist expert selection; to maintain the boundaries of adjacent teeth and roots; and to improve training reliability through stable initialization and load balancing. Summary of the Invention

[0013] The purpose of this invention is to solve the aforementioned technical problems and provide a CBCT tooth segmentation and tooth position numbering method and system based on cross-scale spectrum routing.

[0014] To achieve the above objectives, the technical solution of the present invention is: a CBCT tooth segmentation and tooth position numbering method based on cross-scale spectral routing, comprising:

[0015] Acquire cone-beam computed tomography (CBCT) volume data and add three absolute coordinate channels to the CBCT volume data to form a network input;

[0016] The network input is fed into a U-shaped encoder-decoder network, which includes a hybrid CNN-Mamba encoder, a cross-scale spectrum router (CSSR), a frequency context aggregator (FCA), a five-level decoder, five deep supervised segmentation heads, and an auxiliary boundary head.

[0017] A six-level feature pyramid {e0, ..., e5} is extracted using the hybrid CNN-Mamba encoder, wherein three-directional Mamba coding blocks are inserted starting from level 2;

[0018] The modulated skip features are obtained by performing cross-scale adaptive recombination of {e0, ..., e4} using the CSSR.

[0019] The FCA is used to extract Fourier descriptors, DB2 wavelet descriptors and multi-scale Mexican hat descriptors from the bottleneck feature e5 and deep fusion features, and the deep fusion features are modulated in FiLM mode.

[0020] The five-level decoder performs upsampling reconstruction step by step. Each level concatenates the upsampled features with the corresponding CSSR modulation skip features and then feeds them into a convolutional block to obtain the five-level decoding output.

[0021] The five deep supervision segmentation heads are used to predict 33 classes of voxels for the five-level decoding output. The 33 classes include the background class and 32 permanent tooth classes, thereby directly outputting each tooth instance and its tooth position number.

[0022] The auxiliary boundary header is used to perform single-channel boundary map prediction on the finest decoded output.

[0023] Furthermore, the three-directional Mamba coding block for input The processing includes the following sub-steps:

[0024] Performing group normalization and depthwise separable 3×3×3 convolution on x yields the following results: ;

[0025] Along the three directions of depth D, height H and width W respectively The sequence is rearranged, and after layer normalization and Mamba state space processing, the spatial shape is restored, resulting in a state space output in three directions.

[0026] The state space outputs from the three directions are averaged across the channels, projected through a 1×1×1 convolution, and added to the residual of the input x to obtain the intermediate feature x. mid :

[0027]

[0028] x mid The data is fed into a feedforward network consisting of two 1×1 convolutional layers and GELU, and then again connected to x. mid The residuals are summed to obtain the coded block output:

[0029] .

[0030] Furthermore, the CSSR comprises two parallel expert groups, Group A and Group B, wherein:

[0031] Group A faces {e0, e1, e2} and uses e1 as the anchor point. Each feature is first projected, and then spatially refined through group normalization, ReLU, and deep convolution with learnable residual weights. Each feature is resampled to the anchor point resolution and then stitched and fused together, entering 4 spatial experts. Group A sets 3 independent gating networks to generate outputs that return e0, e1, and e2 respectively.

[0032] Group B faces {e2, e3, e4} and uses e3 as the anchor point. It adopts a larger projection dimension than Group A, uses the original unmodulated e2, and sets up two independent gated networks.

[0033] The residuals generated by group A for e2 are calculated in parallel with those of group B, without being propagated in series.

[0034] CSSR for each jump feature e i The modulation formula is:

[0035]

[0036] Among them o i Output for gating experts, Proj i To map back to the original number of channels in the two-layer bottleneck structure, α i Learn from scratch.

[0037] Furthermore, the internal structure of each spatial expert includes: input 1×1 convolution, group normalization, ReLU, 3×3×3 depthwise convolution, output 1×1 convolution, group normalization, ReLU; where the input projection doubles the number of channels, and the output projection restores the number of channels;

[0038] Each gated network concatenates the global mean, global maximum, and spatial standard deviation, and then obtains expert weights via a small multilayer perceptron and Softmax:

[0039]

[0040] Where g(z) represents the expert weight vector generated by the gating network for the input feature z, and its length is equal to the number of experts N; z represents the fused feature fed into the gating network; MLP represents a multilayer perceptron; GAP(z) represents global average pooling of z in the spatial dimension; GMP(z) represents global max pooling of z in the spatial dimension; STD spatial (z) represents the standard deviation of z in the spatial dimension; the semicolon in square brackets indicates feature concatenation; Softmax indicates that the gating score is normalized into expert weights.

[0041] Each gate activates only the K=2 experts with the highest weights, and these two weights are then Softmax normalized again; the 3 gates in group A and the 2 gates in group B total M=5 independent gate networks, with each gate corresponding to N=4 experts;

[0042] The cumulative number of times each gating system selects each expert based on the training batch. m The coefficient of variation of the square of the number of uses is used as the load balancing term.

[0043]

[0044] When the usage of each expert is approximately balanced, the above loss approaches 0; when a single expert dominates, the above loss increases; for experts with 0 selections, random batches of elements are periodically sampled for diagnostic forward propagation, and L2 penalty is applied to their output.

[0045] Furthermore, the FCA includes three parallel frequency domain branches:

[0046] Fourier branch: After dimensionality reduction from the bottleneck e5, perform a three-dimensional real fast Fourier transform. Let A = log(1 + |RFFT(e5)|). Extract the mean, maximum, low-frequency mean, and high-frequency mean of the full-frequency grid channels from A. Take the first quarter of the frequency grid for each axis in the low-frequency region and the complement for the high-frequency region. Concatenate the values ​​to obtain the Fourier descriptor v. fft ;

[0047] RFFT(·) represents the three-dimensional real-valued Fast Fourier Transform; |·| represents the magnitude of the complex spectrum;

[0048] DB2 wavelet branch: A fixed Daubechies-2 three-dimensional outer product filter is used to decompose the group B fusion features into 8 sub-bands by group convolution with frozen weights. The mean absolute value and root mean square of each sub-band are calculated and then concatenated.

[0049] Mexican Hat Branch: Employing an Improved Ricker Wavelet Kernel with Three Incremental Scales

[0050] The fusion features of group B are subjected to a fixed-weight deep 3D convolution, with each kernel being zero-mean and L2 normalized, and the mean absolute value, root mean square and maximum absolute value are extracted by scale.

[0051] The three descriptors are projected onto a common dimension using LayerNorm-Linear-ReLU-Linear-ReLU and then concatenated. Finally, channel-wise parameters are generated using LayerNorm-Linear-ReLU-Linear. and Modulate the fusion feature f of group B in FiLM mode B :

[0052]

[0053] The final layer of the FCA fusion network uses zero initialization, so that at the start of training... = =0, FCA was originally constant modulation.

[0054] Furthermore, the decoding process of the five-level decoder is as follows:

[0055] Use d5=e5 as the starting decoding feature;

[0056] The output of the l-th level decoding is:

[0057]

[0058] Each of the five decoded outputs is connected to a deep supervised segmentation head to generate 33 types of voxel predictions;

[0059] The finest decoded output d0 is also connected to a lightweight boundary header to predict single-channel boundary maps;

[0060] The true boundary B is determined by whether the adjacent voxels are of different classes, and at least one of the two adjacent voxels belongs to the foreground tooth; therefore, no dilation is performed on the boundary.

[0061] Furthermore, the total loss function is:

[0062]

[0063] Where β(t) adopts a preheating followed by cosine decay scheduling;

[0064] Segmentation loss Simultaneously calculate the TopK cross-entropy of the five deep-supervised outputs. With Tversky's loss Equal weight combination:

[0065]

[0066] This represents the segmentation loss over the five deep supervision outputs; This represents the hard voxel cross-entropy calculated only for a predetermined proportion of voxels with the highest loss; This represents the Tversky loss calculated only for the actual tooth categories that appear in the current batch; and These represent the weights of the two losses mentioned above, and they are equally weighted.

[0067] The TopK cross-entropy of difficult voxels only calculates the predetermined proportion of voxels with the highest loss; the Tversky loss only counts the actual tooth categories that occurred in the current batch.

[0068]

[0069] Where β > α, to increase the penalty for false negatives;

[0070] Boundary loss The sum of the binary cross-entropy between the predicted boundary and the true boundary, and the Dice loss:

[0071]

[0072] L boundary B̂ represents the boundary supervision loss; B̂ represents the predicted boundary probability map output by the auxiliary boundary head; B represents the ground truth boundary map generated from the ground truth segmentation labels; L represents the boundary supervision loss. BCE(·,·) L represents the binary cross-entropy loss; Dice(·,·) This indicates Dice's loss.

[0073] Furthermore, the training phase uses the following configuration:

[0074] All CBCT scans were resampled to an isotropic spacing of 0.3 mm, and the training block size was 128×160×160.

[0075] Using 4 32GB GPUs, a total batch size of 12, and training for 1000 epochs;

[0076] The optimizer is SGD with Nesterov acceleration, momentum 0.99, and weight decay of 3×10⁻⁶. -5 The initial learning rate is 0.01 and polynomial decay is used;

[0077] Enable FP16 automatic mixed precision and torch.compile;

[0078] During inference, a 0.5 overlap sliding window and Gaussian fusion are used, but no enhancements are used during testing.

[0079] Furthermore, the network input is preprocessed based on the self-configuration stage design of nnU-Net before being fed into the hybrid CNN-Mamba encoder; all six levels of convolution in the hybrid CNN-Mamba encoder use 3×3×3 convolution kernels, and instance normalization and LeakyReLU are applied after convolution.

[0080] This invention also provides a CBCT tooth segmentation and tooth position numbering system based on cross-scale spectral routing, which performs the method described above, including:

[0081] The image acquisition module is configured to acquire CBCT volume data and add three absolute coordinate channels to the CBCT volume data to form a network input.

[0082] The hybrid coding module is configured to extract a six-level feature pyramid {e0, ..., e5} through a hybrid CNN-Mamba encoder, wherein three-directional Mamba coding blocks are inserted starting from level 2;

[0083] The cross-scale spectrum routing module is configured to perform cross-scale adaptive recombination of {e0, ..., e4} through CSSR to obtain the modulated hopping features;

[0084] The frequency context aggregation module is configured to extract Fourier descriptors, DB2 wavelet descriptors and multi-scale Mexican hat descriptors from bottleneck feature e5 and deep fusion features via FCA, and modulate the deep fusion features in a FiLM manner.

[0085] The decoding and prediction module is configured to perform progressive upsampling reconstruction through a five-level decoder. At each level, the upsampled features are concatenated with the corresponding CSSR modulation jump features and then fed into a convolutional block to obtain the five-level decoding output. Five deep-supervised segmentation heads are used to predict 33 types of voxels on the five-level decoding output respectively, and an auxiliary boundary head is used to predict the single-channel boundary map of the finest decoding output.

[0086] The 33 categories include background categories and 32 permanent tooth categories. The network output directly provides each tooth instance and its position number.

[0087] Compared with the prior art, the present invention has the following beneficial effects:

[0088] 1. Reduce cascading errors. Since segmentation and tooth position numbering categories are jointly output in the same network, detection omissions or post-processing rules will not continue to amplify errors as independent stages, and the deployment chain is also simpler.

[0089] 2. Improve the synergistic utilization of boundaries and semantics. The dual-set CSSR enables each decoding scale to select information from multiple encoding scales based on the sample, and shallow details and deep semantics are no longer limited by fixed skip connections.

[0090] 3. Enhanced global position discrimination. FCA injects Fourier global spectrum, wavelet subband energy, and multi-scale local frequency response into the gating, providing additional context for tooth position numbering when local anatomical references are lacking.

[0091] 4. Maintain training stability. Zero initialization ensures that CSSR and FCA do not disrupt the backbone network representation during the initial training phase, and load balancing loss reduces long-term idleness of experts.

[0092] 5. Improve difficult voxels and tooth boundaries. TopK cross-entropy focuses on optimizing difficult voxels, Tversky increases the penalty for missed teeth, and boundary heads directly constrain the intersection of adjacent classes.

[0093] 6. The experimental results are clear. On the ToothFairy 3 test set, the F1 score of the method in this application is 0.9783 and the panoramic Dice score is 0.9280; for objects requiring correct tooth position numbering labels, the F1 score is 0.9650 and the panoramic quality Dice score is 0.9160, all of which are higher than the six comparative methods listed. Attached Figure Description

[0094] Figure 1 This is the overall architecture of the end-to-end CBCT tooth segmentation network of the present invention.

[0095] Figure 2 This section details the structure of cross-scale spectrum routers and frequency context aggregators.

[0096] Figure 3 The results of frontal projection segmentation and numbering comparison for representative test cases.

[0097] Figure 4 The results of three-dimensional tooth segmentation qualitative comparison for cases of missing teeth. Detailed Implementation

[0098] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0099] This invention provides a CBCT tooth segmentation and tooth position numbering method based on cross-scale spectral routing, comprising:

[0100] Acquire cone-beam computed tomography (CBCT) volume data and add three absolute coordinate channels to the CBCT volume data to form a network input;

[0101] The network input is fed into a U-shaped encoder-decoder network, which includes a hybrid CNN-Mamba encoder, a cross-scale spectrum router (CSSR), a frequency context aggregator (FCA), a five-level decoder, five deep supervised segmentation heads, and an auxiliary boundary head.

[0102] A six-level feature pyramid {e0, ..., e5} is extracted using the hybrid CNN-Mamba encoder, wherein three-directional Mamba coding blocks are inserted starting from level 2;

[0103] The modulated skip features are obtained by performing cross-scale adaptive recombination of {e0, ..., e4} using the CSSR.

[0104] The FCA is used to extract Fourier descriptors, DB2 wavelet descriptors and multi-scale Mexican hat descriptors from the bottleneck feature e5 and deep fusion features, and the deep fusion features are modulated in FiLM mode.

[0105] The five-level decoder performs upsampling reconstruction step by step. Each level concatenates the upsampled features with the corresponding CSSR modulation skip features and then feeds them into a convolutional block to obtain the five-level decoding output.

[0106] The five deep supervision segmentation heads are used to predict 33 classes of voxels for the five-level decoding output. The 33 classes include the background class and 32 permanent tooth classes, thereby directly outputting each tooth instance and its tooth position number.

[0107] The auxiliary boundary header is used to perform single-channel boundary map prediction on the finest decoded output.

[0108] This invention also provides a CBCT tooth segmentation and tooth position numbering system based on cross-scale spectral routing, which performs the method described above, including:

[0109] The image acquisition module is configured to acquire CBCT volume data and add three absolute coordinate channels to the CBCT volume data to form a network input.

[0110] The hybrid coding module is configured to extract a six-level feature pyramid {e0, ..., e5} through a hybrid CNN-Mamba encoder, wherein three-directional Mamba coding blocks are inserted starting from level 2;

[0111] The cross-scale spectrum routing module is configured to perform cross-scale adaptive recombination of {e0, ..., e4} through CSSR to obtain the modulated hopping features;

[0112] The frequency context aggregation module is configured to extract Fourier descriptors, DB2 wavelet descriptors and multi-scale Mexican hat descriptors from bottleneck feature e5 and deep fusion features via FCA, and modulate the deep fusion features in a FiLM manner.

[0113] The decoding and prediction module is configured to perform progressive upsampling reconstruction through a five-level decoder. At each level, the upsampled features are concatenated with the corresponding CSSR modulation jump features and then fed into a convolutional block to obtain the five-level decoding output. Five deep-supervised segmentation heads are used to predict 33 types of voxels on the five-level decoding output respectively, and an auxiliary boundary head is used to predict the single-channel boundary map of the finest decoding output.

[0114] The 33 categories include background categories and 32 permanent tooth categories. The network output directly provides each tooth instance and its position number.

[0115] The following is a detailed implementation process of the present invention.

[0116] like Figure 1 , 2As shown, the overall network of this invention adopts a U-shaped encoder-decoder structure, based on the self-configuration stage design of nnU-Net. The network consists of a hybrid CNN-Mamba encoder, a cross-scale spectrum router (CSSR), a frequency context aggregator (FCA), a five-level decoder, five deep-supervised segmentation heads, and an auxiliary boundary head. The input is CBCT volume data and three absolute coordinate channels, and the output is the background plus 33 voxel predictions for 32 permanent tooth categories, thus directly obtaining the tooth-by-tooth instance and its tooth position number.

[0117] 1. Encoding, routing, and decoding process

[0118] The hybrid encoder extracts a feature pyramid {e0, ..., e5} through six levels of 3×3×3 convolutions, followed by instance normalization and LeakyReLU. Three-directional Mamba blocks are added starting from level 2. A CSSR (CSSR Matrix) is located between the encoder and decoder, refining e0 to e4 with two parallel hybrid expert groups. FCA (Frequency-based Acoustic Coding) extracts Fourier, DB2 wavelet, and multi-scale Mexican cap descriptors from bottleneck and deep fusion features, influencing the routing decisions of the deep groups with frequency context. The decoder reconstructs the segmentation results through five levels of upsampling, concatenating the upsampled features with the corresponding CSSR modulated skip features at each level, and setting a deep supervision head; the finest decoded output is also concatenated with a boundary head.

[0119] 2. Three-way Mamba encoding block

[0120] For input First, group normalization and depthwise separable 3×3×3 convolutions are performed to obtain... Along depth respectively ,high and width Direction The sequence is rearranged, normalized by layers, and processed by a Mamba state space layer to restore its spatial shape. The outputs in the three directions are averaged by channels, projected by a 1×1×1 convolution, and then added to the input residuals.

[0121]

[0122] The intermediate features are then passed through a feedforward network consisting of two 1×1 convolutional layers and GELU, and residual connections are used again:

[0123]

[0124] 3. Cross-scale spectrum router (CSSR)

[0125] CSSR refines each jump feature through learnable residual correction, where o i Output for gating experts, Proj i To map back to the original number of channels in the two-layer bottleneck, αi Learning starts from scratch. Therefore, initially, CSSR is equivalent to the original skip connections, and then cross-scale corrections are learned progressively:

[0126]

[0127] Group A is oriented towards {e0, e1, e2} with e1 as the anchor point. Each feature is first projected, then spatially refined through group normalization, ReLU, and deep convolution with learnable residual weights; these residual weights can be initialized to 0.1. After each feature is resampled to the anchor point resolution, stitched together, and fused, it enters four spatial experts. Group A uses three independent gating networks to produce outputs returning e0, e1, and e2, respectively.

[0128] Group B is oriented towards {e2, e3, e4} and uses e3 as the anchor point. It employs a larger projection dimension and two independent gating networks. Group B uses the raw, unmodulated e2; the residuals generated by Group A on e2 are computed in parallel with those of Group B and are not propagated in series, thus avoiding interference between shallow routing results and deep routing. FCA is only inserted into Group B.

[0129] Each spatial expert consists of an input 1×1 convolution-group normalized ReLU, a 3×3×3 depthwise convolution, and an output 1×1 convolution-group normalized ReLU; the input projection doubles the number of channels, and the output projection restores the number of channels. Gating simultaneously pools the global mean, global maximum, and spatial standard deviation, and then passes them through a small multilayer perceptron and Softmax to obtain the expert weights.

[0130]

[0131] Each gate only activates the one with the highest weight. Several experts were selected, and the two weights were then Softmax normalized again. The total of the three gating controls in group A and the two gating controls in group B is... Each gated network corresponds to an independent gating network. One expert.

[0132] To avoid expert collapse, the number of times each gating system selects each expert is accumulated according to the training batch. m The coefficient of variation of the square of the number of uses is used as the load balancing term.

[0133]

[0134] The loss approaches zero when the usage of each expert is approximately balanced; the loss increases when a single expert dominates. For experts with zero selections, random batches of elements can be periodically sampled for diagnostic forward propagation, and a small L2 penalty can be applied to their outputs to promote the generation of non-zero routing weights.

[0135] 4. Frequency Context Aggregator (FCA)

[0136] FCA consists of three parallel frequency domain branches. Each branch outputs a compact descriptor, which is then projected onto a common dimension via LayerNorm-Linear-ReLU-Linear-ReLU.

[0137] (1) Fourier branch. After dimensionality reduction from the bottleneck e5, perform a three-dimensional real fast Fourier transform, let A = log(1 +|RFFT(e5)|). Extract the mean, maximum, low-frequency mean and high-frequency mean of the full-frequency grid channels from A; take the first quarter of the frequency grid of each axis in the low-frequency region, and take the complement of the high-frequency region.

[0138]

[0139] (2) DB2 wavelet branch. A fixed Daubechies-2 three-dimensional outer product filter is used to decompose the group B fusion features into 8 sub-bands by group convolution with frozen weights, and the mean absolute value and root mean square value of each sub-band are calculated and then concatenated.

[0140] (3) Mexican Hat Branch. An improved Ricker wavelet kernel with three scale increments is used to perform a fixed-weight deep 3D convolution on the group B fusion features. Each kernel is zero-mean and L2 normalized, and the mean absolute value, root mean square, and maximum absolute value are extracted according to the scale.

[0141]

[0142] The three projection descriptors are concatenated and then processed by LayerNorm-Linear-ReLU-Linear to generate channel-by-channel parameters. and Modulate the fusion feature f of group B in FiLM mode B :

[0143]

[0144] in Limit the modulation amplitude. The last layer of the fusion network is initialized with zero, so that at the start of training... FCA initially uses identity modulation; the network first establishes a reliable spatial representation, and then gradually injects frequency information to reduce early training instability.

[0145] 5. Decoder, Supervision Head, and Loss Function

[0146] The decoder starts at d5=e5. In the five-level upsampling, the decoded features from the previous level are concatenated with the corresponding CSSR modulation features and then input into the convolutional block.

[0147]

[0148] All five decoder outputs generate segmentation predictions and are jointly trained with deep supervision. The finest decoder output is concatenated with a lightweight boundary head to predict a single-channel boundary map. The true boundary B is determined by whether adjacent voxels are of different classes, and at least one of the two adjacent voxels belongs to a foreground tooth; no dilation is performed on the boundary.

[0149]

[0150] in A preheating followed by cosine decay scheduling is employed. The segmentation loss is calculated simultaneously for all five outputs, using a weighted combination of hard voxel cross-entropy and Tversky loss. The hard voxel cross-entropy only calculates a certain percentage of voxels with the highest loss, while the Tversky loss only considers the actual tooth categories appearing in the current batch.

[0151]

[0152]

[0153] set up This can improve the penalty for false negatives, thus emphasizing recall. The boundary loss is the sum of the binary cross-entropy between the predicted boundary and the true boundary, and the Dice loss.

[0154]

[0155] 6. Specific Implementation Examples and Verification Results

[0156] The publicly available ToothFairy 3 dataset is used as an example. This dataset provides voxel-level annotations for 77 maxillofacial structures. In this example, only 32 permanent teeth labels are retained, and other structures are discarded, resulting in a 33-class segmentation task with 32 tooth categories plus background. The official partitioning is used: 479 cases for training, 53 cases for validation, and 53 cases for testing. The training data mainly consists of incomplete dentitions, including cases with only the maxillary or mandibular dental arch and cases with only 3 to 5 isolated teeth remaining.

[0157] All scans were resampled to a 0.3 mm isotropic spacing. The training block size was 128×160×160. Four 32 GB NVIDIA GPUs were used, with a total batch size of 12, and training lasted for 1000 epochs. The optimizer was SGD with Nesterov acceleration, momentum 0.99, and weight decay of 3×10⁻⁶. -5 The initial learning rate was 0.01 with polynomial decay; FP16 automatic mixed precision and torch.compile were enabled. Inference used a 0.5 overlap sliding window with Gaussian fusion, and no test-time enhancement was used. The above values ​​are for the verification examples in the paper and should not be construed as limiting the only implementation parameters.

[0158] Instance metrics do not consider tooth position numbering and include instance F1, average Dice of matched instances, average Dice of all instances, and panoramic Dice. Multi-class instance metrics require correct tooth position labeling and include per-tooth-position object F1, average Dice of correctly labeled true positive instances, and panoramic quality Dice. Comparisons with ReluNet, SwinUNet, U-Mamba, CuiNet, and OralSeg under the same partitioning and preprocessing conditions are shown in Tables 1 and 2.

[0159] Table 1. Instance splitting metrics for the ToothFairy 3 test set

[0160]

[0161] Table 2. Multi-class instance metrics for the ToothFairy 3 test set.

[0162]

[0163] like Figure 3 , 4 The validation results show that the method in this application achieves the highest values ​​across all instances and multiple categories. It produces clearer interdental boundaries, more intact root apexes, less overflow into the alveolar bone, and maintains correct tooth position numbering in edentulous cases. These results are consistent with the design of CSSR, which simultaneously provides shallow boundary details and deep discriminative features, and FCA, which provides global frequency context to the gating network.

[0164] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A CBCT tooth segmentation and tooth position numbering method based on cross-scale spectral routing, characterized in that, include: Acquire cone-beam computed tomography (CBCT) volume data and add three absolute coordinate channels to the CBCT volume data to form a network input; The network input is fed into a U-shaped encoder-decoder network, which includes a hybrid CNN-Mamba encoder, a cross-scale spectrum router (CSSR), a frequency context aggregator (FCA), a five-level decoder, five deep supervised segmentation heads, and an auxiliary boundary head. A six-level feature pyramid {e0, ..., e5} is extracted using the hybrid CNN-Mamba encoder, wherein three-directional Mamba coding blocks are inserted starting from level 3; The modulated skip features are obtained by performing cross-scale adaptive recombination of {e0, ..., e4} using the CSSR. The FCA is used to extract Fourier descriptors, DB2 wavelet descriptors and multi-scale Mexican hat descriptors from the bottleneck feature e5 and deep fusion features, and the deep fusion features are modulated in FiLM mode. The five-level decoder performs upsampling reconstruction step by step. Each level concatenates the upsampled features with the corresponding CSSR modulation skip features and then feeds them into a convolutional block to obtain the five-level decoding output. The five deep supervision segmentation heads are used to predict 33 classes of voxels for the five-level decoding output. The 33 classes include the background class and 32 permanent tooth classes, thereby directly outputting each tooth instance and its tooth position number. The auxiliary boundary header is used to perform single-channel boundary map prediction on the finest decoded output.

2. The CBCT tooth segmentation and tooth position numbering method based on cross-scale spectral routing according to claim 1, characterized in that, The three-directional Mamba coding block for input The processing includes the following sub-steps: Performing group normalization and depthwise separable 3×3×3 convolution on x yields the following results: ; Along the three directions of depth D, height H and width W respectively The sequence is rearranged, and after layer normalization and Mamba state space processing, the spatial shape is restored, resulting in a state space output in three directions. The state space outputs from the three directions are averaged across the channels, projected through a 1×1×1 convolution, and added to the residual of the input x to obtain the intermediate feature x. mid : x mid The data is fed into a feedforward network consisting of two 1×1 convolutional layers and GELU, and then again connected to x. mid The residuals are summed to obtain the coded block output: 。 3. The CBCT tooth segmentation and tooth position numbering method based on cross-scale spectral routing according to claim 1, characterized in that, The CSSR comprises two parallel expert groups, Group A and Group B, wherein: Group A faces {e0, e1, e2} and uses e1 as the anchor point. Each feature is first projected, and then spatially refined through group normalization, ReLU and deep convolution with learnable residual weights. Each feature is resampled to the anchor point resolution and then stitched and fused into 4 spatial experts. Group A sets 3 independent gated networks to generate outputs that return e0, e1 and e2 respectively. Group B faces {e2, e3, e4} and uses e3 as the anchor point. It adopts a larger projection dimension than Group A, uses the original unmodulated e2, and sets up two independent gated networks. The residuals generated by group A for e2 are calculated in parallel with those of group B, without being propagated in series. CSSR for each jump feature e i The modulation formula is: Among them o i Output for gating experts, Proj i To map back to the original number of channels in the two-layer bottleneck structure, α i Learn from scratch.

4. The CBCT tooth segmentation and tooth position numbering method based on cross-scale spectral routing according to claim 3, characterized in that, The internal structure of each spatial expert includes: input 1×1 convolution, group normalization, ReLU, 3×3×3 depthwise convolution, output 1×1 convolution, group normalization, ReLU; where the input projection doubles the number of channels, and the output projection restores the number of channels; Each gated network concatenates the global mean, global maximum, and spatial standard deviation, and then obtains expert weights via a small multilayer perceptron and Softmax: Where g(z) represents the expert weight vector generated by the gating network for the input feature z, and its length is equal to the number of experts N; z represents the fused feature fed into the gating network; MLP represents a multilayer perceptron; GAP(z) represents global average pooling of z in the spatial dimension; GMP(z) represents global max pooling of z in the spatial dimension; STD spatial (z) represents the standard deviation of z in the spatial dimension; the semicolon in square brackets indicates feature concatenation; Softmax indicates that the gating score is normalized to expert weights; Each gate activates only the K=2 experts with the highest weights, and these two weights are then Softmax normalized again; the 3 gates in group A and the 2 gates in group B total M=5 independent gate networks, with each gate corresponding to N=4 experts; The cumulative number of times each gating system selects each expert based on the training batch. m The coefficient of variation of the square of the number of uses is used as the load balancing term. When the usage of each expert is approximately balanced, the above loss approaches 0; when a single expert dominates, the above loss increases; for experts with 0 selections, random batches of elements are periodically sampled for diagnostic forward propagation, and L2 penalties are applied to their outputs.

5. The CBCT tooth segmentation and tooth position numbering method based on cross-scale spectral routing according to claim 3, characterized in that, The FCA includes three parallel frequency domain branches: Fourier branch: After dimensionality reduction from the bottleneck e5, perform a three-dimensional real fast Fourier transform. Let A = log(1 + |RFFT(e5)|). Extract the mean, maximum, low-frequency mean, and high-frequency mean of the full-frequency grid channels from A. Take the first quarter of the frequency grid for each axis in the low-frequency region and the complement for the high-frequency region. Concatenate the values ​​to obtain the Fourier descriptor v. fft ; RFFT(·) represents the three-dimensional real-valued Fast Fourier Transform; |·| represents the magnitude of the complex spectrum; DB2 wavelet branch: A fixed Daubechies-2 three-dimensional outer product filter is used to decompose the group B fusion features into 8 sub-bands by group convolution with frozen weights. The mean absolute value and root mean square of each sub-band are calculated and then concatenated. Mexican Hat Branch: Employing an Improved Ricker Wavelet Kernel with Three Incremental Scales The fusion features of group B are subjected to a fixed-weight deep 3D convolution, with each kernel being zero-mean and L2 normalized, and the mean absolute value, root mean square and maximum absolute value are extracted by scale. The three descriptors are projected onto a common dimension using LayerNorm-Linear-ReLU-Linear-ReLU and then concatenated. Finally, channel-wise parameters are generated using LayerNorm-Linear-ReLU-Linear. and Modulate the fusion feature f of group B in FiLM mode B : The final layer of the FCA fusion network uses zero initialization, so that at the start of training... = =0, FCA was originally constant modulation.

6. The CBCT tooth segmentation and tooth position numbering method based on cross-scale spectral routing according to claim 1, characterized in that, The decoding process of the five-level decoder is as follows: Use d5=e5 as the starting decoding feature; The output of the l-th level decoding is: Each of the five decoded outputs is connected to a deep supervised segmentation head to generate 33 types of voxel predictions; The finest decoded output d0 is also connected to a lightweight boundary header to predict single-channel boundary maps; The true boundary B is determined by whether the adjacent voxels are of different classes, and at least one of the two adjacent voxels belongs to the foreground tooth; therefore, no dilation is performed on the boundary.

7. The CBCT tooth segmentation and tooth position numbering method based on cross-scale spectral routing according to claim 1, characterized in that, The total loss function is: Where β(t) adopts a preheating followed by cosine decay scheduling; Segmentation loss Simultaneously calculate the TopK cross-entropy of the five deep-supervised outputs. With Tversky's loss Equal weight combination: This represents the segmentation loss over the five deep supervision outputs; This represents the hard voxel cross-entropy calculated only for a predetermined proportion of voxels with the highest loss; This represents the Tversky loss calculated only for the actual tooth categories that appear in the current batch; and These represent the weights of the two losses mentioned above, and they are equally weighted. The TopK cross-entropy of difficult voxels only calculates the predetermined proportion of voxels with the highest loss; the Tversky loss only counts the actual tooth categories that appear in the current batch. Where β > α, to increase the penalty for false negatives; Boundary loss The sum of the binary cross-entropy between the predicted boundary and the true boundary, and the Dice loss: L boundary B̂ represents the boundary supervision loss; B̂ represents the predicted boundary probability map output by the auxiliary boundary head; B represents the ground truth boundary map generated from the ground truth segmentation labels; L represents the boundary supervision loss. BCE(·,·) L represents the binary cross-entropy loss; Dice(·,·) This indicates Dice's loss.

8. A CBCT tooth segmentation and tooth position numbering system based on cross-scale spectral routing according to claim 1, characterized in that, The following configuration is used during the training phase: All CBCT scans were resampled to an isotropic spacing of 0.3 mm, and the training block size was 128×160×160. Using 4 32GB GPUs, a total batch size of 12, and training for 1000 epochs; The optimizer is SGD with Nesterov acceleration, momentum 0.99, and weight decay of 3×10⁻⁶. -5 The initial learning rate is 0.01 and polynomial decay is used; Enable FP16 automatic mixed precision and torch.compile; During inference, a 0.5 overlap sliding window and Gaussian fusion are used, but no enhancements are used during testing.

9. A CBCT tooth segmentation and tooth position numbering system based on cross-scale spectral routing according to claim 1, characterized in that, Before being fed into the hybrid CNN-Mamba encoder, the network input is preprocessed based on the self-configuration stage design of nnU-Net; the six levels of convolution in the hybrid CNN-Mamba encoder all use 3×3×3 convolution kernels, and after convolution, instance normalization and LeakyReLU are applied.

10. A CBCT tooth segmentation and tooth position numbering system based on cross-scale spectral routing, performing the method as described in any one of claims 1-9, characterized in that, include: The image acquisition module is configured to acquire CBCT volume data and add three absolute coordinate channels to the CBCT volume data to form a network input. The hybrid coding module is configured to extract a six-level feature pyramid {e0, ..., e5} through a hybrid CNN-Mamba encoder, wherein three-directional Mamba coding blocks are inserted starting from level 2; The cross-scale spectrum routing module is configured to perform cross-scale adaptive recombination of {e0, ..., e4} through CSSR to obtain the modulated hopping features; The frequency context aggregation module is configured to extract Fourier descriptors, DB2 wavelet descriptors and multi-scale Mexican hat descriptors from bottleneck feature e5 and deep fusion features via FCA, and modulate the deep fusion features in a FiLM manner. The decoding and prediction module is configured to perform progressive upsampling reconstruction through a five-level decoder. At each level, the upsampled features are concatenated with the corresponding CSSR modulation jump features and then fed into a convolutional block to obtain the five-level decoding output. Five deep-supervised segmentation heads are used to predict 33 types of voxels on the five-level decoding output respectively, and an auxiliary boundary head is used to predict the single-channel boundary map of the finest decoding output. The 33 categories include background categories and 32 permanent tooth categories. The network output directly provides each tooth instance and its position number.

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