TCFNet: Coarse-to-Fine Face-Bone Point Movement

• The paper presents TCFNet, which leverages a dual-stage coarse-to-fine architecture combining Transformer-based global feature extraction with local geometric refinement for bidirectional face-bone point cloud transformation.
• It overcomes previous limitations by addressing small receptive fields, noisy predictions, and complex registration through an integrated end-to-end framework.
• TCFNet demonstrates superior accuracy on dense point clouds, achieving statistically significant improvements in metrics like Chamfer Distance compared to state-of-the-art methods.

Searching arXiv for TCFNet and closely related coarse-to-fine transformer point-cloud works. Searching arXiv for "TCFNet Transformer-based Coarse-to-Fine Point Movement Network". Transformer-based Coarse-to-Fine Point Movement Network (TCFNet) is an end-to-end, unsupervised deep learning framework for dense, bidirectional transformation between facial and skeletal point clouds in orthognathic surgical planning. It is formulated as a point-to-point transformation problem between skeletal and facial point clouds and is designed to address limited scalability, small receptive fields, noisy predictions, and the complex preprocessing and postprocessing operations based on registration reported for earlier deep learning-based simulation methods. The model adopts a coarse-to-fine architecture in which a Transformer-based network performs a global stage and a local information aggregation network performs a refinement stage, with the two stages reinforcing each other to generate precise point movement paths (Zhang et al., 20 Aug 2025).

1. Problem setting and scope

TCFNet is introduced for bidirectional face-bone transformation, a task described as significant for computer-aided surgical simulation in orthognathic surgical planning. In the reported framing, the objective is dense transformation between facial and skeletal point clouds rather than sparse correspondence estimation or mesh-based deformation. The method is explicitly intended for dense face-bone point cloud transformations and is evaluated on gathered datasets derived from CT data (Zhang et al., 20 Aug 2025).

The paper positions the method against two classes of limitations. Traditional biomechanical simulation methods are described as being limited by computational time consumption levels, labor-intensive data processing strategies, and low accuracy. Recent deep learning-based simulation methods are described as unable to process large-scale points, as having limited receptive fields that lead to noisy points, and as employing complex preprocessing and postprocessing operations based on registration. TCFNet is presented as a response to those constraints by combining global and local stages within a single end-to-end framework (Zhang et al., 20 Aug 2025).

A defining characteristic is bidirectionality. The network predicts both bone-to-face and face-to-bone transformations, rather than only one direction. This is encoded both architecturally and in the loss construction, where bidirectional similarity and regularization terms are optimized jointly. A plausible implication is that the authors treat the two directions as mutually constraining views of the same anatomical transformation problem, rather than as separate tasks.

2. Two-stage coarse-to-fine architecture

The architecture comprises three main modules: data preprocessing, a coarse stage based on a Transformer network, and a fine stage based on a Local Information Aggregation Network (LIA-Net). Dense point clouds are sampled from CT-derived meshes; outlier removal, normalization, and regularization are used to ensure consistent inputs. For network input, the point clouds are set to 20,480 points (Zhang et al., 20 Aug 2025).

The coarse stage uses a Transformer-based backbone built on Point Transformer V3 (PTv3). The fine stage uses LIA-Net to compensate for neighborhood precision loss in the Transformer-based stage by modeling local geometric structures, specifically edges, orientations, and relative position features. The previous global features are used to guide the local displacement through a gated recurrent unit (GRU). The final system therefore operates as a global-to-local pipeline: a coarse displacement field is predicted first, and a fine-grained displacement field then refines it (Zhang et al., 20 Aug 2025).

This coarse-to-fine decomposition is central to the identity of TCFNet. The reported contribution is not merely the use of a Transformer on point clouds, but the explicit coupling of a global stage and a local stage. The paper states that the Transformer-based network and LIA-Net reinforce each other to generate precise point movement paths. TCFNet should therefore be understood as a two-stage movement model rather than as a single-backbone feature extractor.

3. Coarse stage: PTv3-based global point movement

The coarse stage is built on PTv3, which replaces KNN with point cloud serialization and groups points into local windows or patches via serialized order using space-filling curves such as Z-order or Hilbert. This design is used to allow attention mechanisms to cover wider spatial context efficiently, with a receptive field of up to 1024. Queries, keys, and values are computed via MLPs, and scalar attention is defined as follows (Zhang et al., 20 Aug 2025):

$$w_{ij} = \langle \mathbf{q}_i, \mathbf{k}_j \rangle / \sqrt{c_a}, \qquad \mathbf{f}^{\text{attn}}_i = \sum_{\mathbf{x}_j} \mathrm{Softmax}(w_i)_j \mathbf{v}_j$$

The stage also includes patch pooling and upsampling through Max/Mean pooling, and the description notes that noise augmentation improves transformation flexibility. Its output is a coarse displacement field, denoted $\phi_{B\rightarrow\widehat{F}}$ and $\phi_{F\rightarrow\widehat{B}}$, producing preliminary coarse outputs $\widehat{H}_F$ and $\widehat{H}_B$ (Zhang et al., 20 Aug 2025).

The role of this stage is global correspondence learning at the patch level. In the terminology of the paper, TCFNet learns unique, complicated correspondences at the patch and point levels. The coarse stage addresses the patch level, using serialized point grouping and attention to expose large receptive fields. This suggests that the model treats long-range structural relations as necessary for anatomically plausible displacement estimation.

4. Fine stage: LIA-Net and guided local refinement

LIA-Net is introduced specifically to address the weaker local structure modeling of PTv3 after discarding KNN. The fine stage takes the coarse output as input and reconstructs local geometric evidence using neighborhood computation, with the summary reporting KNN with, for example, $K=8$ (Zhang et al., 20 Aug 2025).

Its local feature extraction has two branches. One branch is a Static EdgeConv branch that captures local neighborhood feature differences. The other branch is a Global-Relative Position branch that explicitly models relative orientation and distance to the farthest regions through learnable weights, including

$$\mathbf{W}_d = \frac{(r - |\vec{\mathbf{pq}}|)^2} {\sum_{\mathbf{q} \in \Omega_{\text{far}}}(r - |\vec{\mathbf{pq}}|)^2}$$

The summary further notes angle/orientation encoding via trigonometric weighting on axes. Global features from the previous stage are injected through a GRU, and the fine stage outputs fine-grained displacement fields $\phi_{\widehat{F}\rightarrow F}$ and $\phi_{\widehat{B}\rightarrow B}$. Final predictions $H_F$ and $\phi_{B\rightarrow\widehat{F}}$0 are obtained by composing the coarse and fine displacements (Zhang et al., 20 Aug 2025).

The structural logic of the fine stage is therefore not generic refinement. It is local refinement guided by global context. The paper states that LIA-Net can effectively compensate for the neighborhood precision loss of the Transformer-based network. In that sense, the model’s “fine” stage is corrective rather than merely decorative: it restores local anatomical precision that the global stage alone does not fully preserve.

5. Objective function and supervision

TCFNet is trained with a composite objective that combines coarse similarity, fine similarity, cross-regularization, a local density/distribution loss, and an optional auxiliary loss for critical structures. The main bidirectional optimization is reported as (Zhang et al., 20 Aug 2025)

$\phi_{B\rightarrow\widehat{F}}$1

At the similarity level, the paper distinguishes coarse and fine terms:

$\phi_{B\rightarrow\widehat{F}}$2

$\phi_{B\rightarrow\widehat{F}}$3

The Chamfer Distance and Earth Mover’s Distance are given as

$\phi_{B\rightarrow\widehat{F}}$4

$\phi_{B\rightarrow\widehat{F}}$5

The local density/distribution loss is reported as

$\phi_{B\rightarrow\widehat{F}}$6

The auxiliary loss is explicitly motivated by deformable medical image registration and uses expert knowledge for reconstructing critical organs. For $\phi_{B\rightarrow\widehat{F}}$7 labeled local structures, it is defined as (Zhang et al., 20 Aug 2025)

$\phi_{B\rightarrow\widehat{F}}$8

The total loss is

$\phi_{B\rightarrow\widehat{F}}$9

This objective construction makes the training signal multi-level and optionally anatomy-aware. A plausible implication is that the method is designed to stabilize both global anatomical consistency and local clinically sensitive regions within the same optimization program.

6. Dataset design and experimental evaluation

The reported dataset contains 120 paired samples of face and bone point clouds from healthy volunteers’ CT data. Each point cloud has up to 25,000 points, with 20,480 used for TCFNet input and 4,096 used for state-of-the-art baselines because of GPU constraints. Surgeons labeled local regions of interest such as nose and lip for auxiliary loss and evaluation. The split is 95 samples for training and 25 for testing, with augmentations used (Zhang et al., 20 Aug 2025).

The paper evaluates CD (mm), EMD (mm), MPED, JSD, HD (mm), and inference time and memory usage for dense prediction. The main quantitative comparison reported in the summary is as follows (Zhang et al., 20 Aug 2025):

Method	Points and key metrics	Time / memory
TCFNet	20480; CD 4.11 ± 0.96; EMD 3.6 ± 1.59; MPED 77.65 ± 25.68; HD 33.3 ± 9.03	0.3 s; 22,436 MB
PTv3	4096; CD 4.26; EMD 2.94; MPED 80.64; HD 35.95	0.19 s; 3,912 MB
P2P-Conv	4096; CD 4.27; EMD 4.58; MPED 82.68; HD 180.8	1.13 s; 14,158 MB
P2P-Net	4096; CD 4.56; EMD 3.62; MPED 90.24; HD 35.49	0.22 s; 15,232 MB

The quantitative interpretation given in the summary is that TCFNet robustly outperforms others in CD, MPED, and HD and matches or beats most methods on EMD, while keeping time and memory competitive for large point clouds. The paper also reports that local error on ROIs such as nose and lip is best or nearly best, especially after including the auxiliary loss. Statistical validation uses a Wilcoxon rank-sum test, with $\phi_{F\rightarrow\widehat{B}}$0 for TCFNet versus state-of-the-art methods on CD, indicating statistically significant improvements. Ablation experiments show that removing LIA-Net or global-to-local positional features causes significant drops in both global and local accuracy, and that adding auxiliary loss yields further improvements in critical regions. Qualitative visualizations are described as showing more accurate and outlier-free reconstructions globally and locally, including lips, nose, and coronoid process (Zhang et al., 20 Aug 2025).

A notable reported distinction is dense prediction at full resolution. The comparison emphasizes that TCFNet handles dense datasets of approximately 20k points, whereas the cited state-of-the-art methods are limited to fewer than 5k points. The paper also states that TCFNet requires no complex registration steps and no template alignment (Zhang et al., 20 Aug 2025).

7. Position within coarse-to-fine transformer research

TCFNet belongs to a broader family of coarse-to-fine architectures on arXiv, but its target problem and implementation are distinct. In scene flow, PointPWC-Net estimates point cloud motion through a pyramid in which coarse flow is upsampled and warped to finer levels (Wu et al., 2019). In point cloud registration, CoFiNet extracts hierarchical correspondences from coarse to fine without keypoint detection (Yu et al., 2021). In 3D single-object tracking, PTTR predicts tracking results in a coarse-to-fine manner using Relation-Aware Sampling, a Point Relation Transformer, and a Prediction Refinement Module (Zhou et al., 2021), while the 3D Siamese Transformer Network uses an iterative coarse-to-fine correlation network for template–search matching (Hui et al., 2022).

TCFNet differs from those systems in at least three explicit ways. First, its task is bidirectional face-bone transformation rather than tracking, registration, or scene flow. Second, its coarse stage is implemented with PTv3-style serialized patch attention rather than the cost-volume hierarchy of PointPWC-Net or the tracking-oriented attention structures of PTTR and STNet. Third, its refinement stage is not a generic decoder but LIA-Net, which is designed to compensate for local precision loss by modeling local geometric structures and by using global features through a GRU (Zhang et al., 20 Aug 2025).

This positioning also clarifies what TCFNet is not. It is not only a Transformer over point tokens, because the paper explicitly argues that Transformer-only modeling loses neighborhood precision and must be supplemented by local aggregation. It is not only a local geometric network, because the reported motivation for PTv3 is the need for wider spatial context and dense processing. The architecture is therefore best understood as a coarse-to-fine point movement network in the literal sense of its title: a model that first establishes global displacement structure and then refines point movement paths at local anatomical resolution (Zhang et al., 20 Aug 2025).