Doctoral Thesis: Geometric Deep Learning For Camera Pose Prediction, Registration, Depth Estimation, and 3D Reconstruction

Xueyang Kang

REVIEW 5 major objections 4 minor 288 references

Doctoral Thesis: Geometric Deep Learning For Camera Pose Prediction, Registration, Depth Estimation, and 3D Reconstruction

T0 review · 5 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This thesis claims that injecting geometric priors—skyline and ground-plane cues, SE(3)-equivariant surfels, focal-stack attention, and wavelet depth features—lets deep models consistently outperform prior state-of-the-art on camera pose es

desk verdict Four methods, three already published, wrapped in a thesis whose abstract overpromises and whose integration claim is never tested. read the letter →

arxiv 2509.01873 v1 pith:QBPOGJN3 submitted 2025-09-02 cs.CV cs.AI

Xueyang Kang This is my paper

classification cs.CVcs.AI

keywords geometricdeeplearningcameraposeestimationpointcloudregistrationfocalstackdepthimplicitsigneddistancefieldswavelettransformSE(3)equivariance3Dreconstruction

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The thesis tries to show that deep learning models for core 3D vision tasks become more accurate and robust when traditional geometric constraints are built into the architecture or the training signal. It proposes four hybrid methods: drone camera orientation tracking anchored by skyline and ground-plane cues fused with IMU data by an adaptive particle filter; point cloud registration via SE(3)-equivariant features on 2D surfels; depth estimation from focal stacks of arbitrary length using a Transformer with a latent LSTM; and implicit SDF reconstruction conditioned on wavelet-transformed depth features. The author claims each method outperforms state-of-the-art baselines on public benchmarks in its task, with particular gains in low-overlap registration, arbitrary-length focal stacks, and fine geometric detail. A sympathetic reader would care because the thesis positions the four methods as interchangeable modules of a larger reconstruction pipeline rather than isolated results.

What carries the argument

Four mechanisms carry the argument: (1) natural geometric primitives—the skyline and ground plane—used as reference cues for roll and pitch tracking, fused by an adaptive particle filter sampling on a multi-resolution spherical manifold; (2) SE(3)-equivariant 2D Gaussian surfel features, encoded by an E2PN-style symmetric convolutional kernel, to make registration robust to rigid transformations and input uncertainty; (3) a Transformer self-attention encoder coupled with an LSTM that sequentially fuses tokens along the focal stack dimension, enabling arbitrary stack lengths and monocular pre-training; and (4) wavelet-transformed depth features, projected onto triplanes and fused via a 2D U-N

What would settle it

Collect a flight sequence in terrain with a curved skyline and uneven ground below 300 meters, using servo-motor ground truth for roll and pitch; if the fusion's RMSE stops beating the IMU-only Madgwick filter, the central drift-resistance claim fails.

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Extended reading notes

Core claim

On the paper's own terms, geometric deep learning bridges the gap between traditional geometry-based methods and data-driven approaches: each of the four proposed methods consistently outperforms state-of-the-art techniques on its individual 3D vision task. The camera pose system uses natural skyline and ground-plane primitives, fused with IMU data through an adaptive particle filter on a spherical manifold, to achieve real-time orientation tracking that is more stable than IMU-only solutions. The registration method introduces a surfel-based SE(3)-equivariant framework that learns position and orientation representations from 2D Gaussian surfels, achieving superior accuracy in indoor and ou

Load-bearing premise

The pose-tracking system assumes the skyline can be approximated by a straight line and that, above 300 meters, the ground is flat and perpendicular to gravity; the thesis itself notes that curved mountain skylines challenge this assumption.

Editorial extensions

If this is right

Camera orientation tracking runs in real time on an embedded Jetson Nano and beats IMU-only filtering against drift in natural scenes, making it deployable for drone-based imaging.
Surfel-based equivariant registration retains high recall on low-inlier point clouds and degrades gracefully even with only 256 sampled points, supporting robotics and mobile scanning use cases.
FocDepthFormer accepts any number of focal-stack frames, so one trained model can serve different stack sizes and can be pre-trained on monocular RGB-D data to reduce reliance on scarce focal-stack datasets.
Wavelet-conditioned implicit SDF reconstruction yields more complete and detailed meshes across object-scale and architectural-scale scenes, and is described as a plug-and-play module for existing implicit SDF frameworks.
The modular design suggests that improvements in pose, registration, depth, and reconstruction each strengthen the corresponding stage of a full 3D reconstruction pipeline.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: the pose estimator's reliance on a single straight skyline and a flat ground plane means the claimed robustness likely holds only in open terrain; the thesis itself acknowledges curved mountain skylines as a failure mode.
Editorial inference: because the four modules are evaluated separately, the thesis does not prove that chaining them into one end-to-end reconstruction pipeline preserves the individual gains; a system-level integration test would be a natural next step.
Editorial inference: the wavelet-conditioning idea could plausibly transfer to other implicit representations, such as radiance-field or Gaussian-splatting reconstructions, where high-frequency detail is also a bottleneck.
Editorial inference: the latent LSTM fusion for focal stacks suggests a general recipe for any ordered image set with per-frame focus cues, including smartphone refocus stacks or light-field captures.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

Quick read on arXiv:2509.01873. It's a PhD thesis gathering four method chapters; three are already published (ICRA, CVPR workshop, AJCAI), one is under review. The per-chapter work is mostly solid, but the abstract's claim that the 'four proposed methods consistently outperform state-of-the-art' is broader than the evidence supports. And the thesis's own integration story—claiming a modular 3D reconstruction pipeline—is never actually evaluated end-to-end.

What's genuinely new and worth keeping: Chapter 4's surfel-based SE(3)-equivariant registration is a real engineering contribution, with a thorough ablation suite, robustness analysis, and a small, fast model. Chapter 5's Transformer+LSTM design for focal stacks is a sensible answer to fixed-length CNN methods, and the cross-dataset results on Mobile Depth and LightField4D are convincing. Chapter 6's wavelet-conditioned SDF is a plausible plug-in module with good ablation coverage on DTU and Tanks and Temples. Chapter 3's skyline/ground-plane cues fused with IMU through an adaptive particle filter is a clever low-power design, and it runs in real time on a Jetson Nano.

Soft spots, in proportion. First, Table 4.1 shows Ours at 1.57° RE on KITTI, worse than SpinNet's 1.08°, yet the text claims superiority—an inconsistency that must be fixed. Second, the Chapter 3 comparison against ORB-SLAM3, R-VIO, and DM-VIO is selective, with missing entries, and those are full 6-DoF systems evaluated only on roll/pitch. The load-bearing assumption there—straight-line skyline and flat ground above 300 m—is acknowledged in Section 3.5 as challenged by curved mountains, but the experiments never include such terrain. So the stress-test concern is on target: the central pose-tracking claim is untested exactly where it should hold. Also, most tables have no error bars, and there's no code/data release, which limits verification.

Who is this for? Anyone working in visual-inertial orientation tracking, point cloud registration, focal-stack depth, or implicit reconstruction will find the chapters readable and the ablations informative. But cite the published papers, not the thesis.

If this crossed my desk as a journal submission, I'd send it to peer review—the published chapters give it real weight—but I'd expect revision on the overclaims, the table inconsistency, and the missing end-to-end evaluation. As an arXiv thesis, it's a fine record of the work; just don't quote the abstract verbatim.

Referee Report

5 major / 4 minor

Summary. The thesis combines geometric priors with deep learning across four 3D vision tasks. Chapter 3 proposes a camera-orientation tracker that fuses IMU data with skyline and ground-plane cues through an adaptive particle filter on a spherical manifold, targeting UAV/natural-environment operation. Chapter 4 introduces a surfel-based registration network with an SE(3)-equivariant encoder, cross-attention, and Huber loss, evaluated on 3DMatch and KITTI. Chapter 5 presents FocDepthFormer, a Transformer-LSTM architecture for depth-from-focal-stack with arbitrary stack length, evaluated on DDFF, FOD500, Mobile Depth, and LightField4D. Chapter 6 proposes a wavelet-conditioned implicit SDF reconstruction method that fuses multi-scale wavelet-transformed depth features with triplane features, evaluated on DTU, Tanks and Temples, and a cultural heritage dataset. The abstract claims that the four methods 'consistently outperform state-of-the-art techniques across individual 3D vision tasks.'

Significance. If fully supported, the thesis would contribute practical geometry-aware modules for pose tracking, registration, depth estimation, and reconstruction. Notable strengths are the real-time embedded deployment of the pose tracker, the use of explicit surface orientation and uncertainty in registration, the LSTM-based variable-length focal-stack processing, and the wavelet-conditioned implicit surface prior. However, the broad SOTA claim is not consistently supported by the reported tables, and one chapter's assumptions are untested in the environments the chapter targets. The correctable nature of these issues makes the manuscript worth revising.

major comments (5)

[Abstract and §4, Table 4.1] The abstract states that the four methods 'consistently outperform state-of-the-art techniques across individual 3D vision tasks.' Table 4.1 directly contradicts this for Chapter 4 on KITTI: Ours has RE=1.57°, while SpinNet achieves RE=1.08°. The text in §4.4.1 claims a 'smaller rotation error (around 8-11% reduction)' compared to the second-best model, but on KITTI the rotation error is about 45% larger than SpinNet's. This is load-bearing for the central claim and must be corrected, either by reporting the comparable/competitive status on that metric or by removing the overclaim.
[§3.4, Tables 3.1 and 3.2] The mixed-test duration is reported as 960 s in Table 3.1 and 9200 s in Table 3.2. Several entries in Table 3.2 are missing (notably R-VIO and DM-VIO in several rows), yet the prose states that the proposed method 'performs consistently across different sequences' and compares favorably. In addition, the text first says ORB-SLAM3, R-VIO, and DM-VIO were selected for comparison, then says these algorithms were found unsuitable and the comparison is against IMU-only Madgwick filtering. The experimental protocol and table completeness must be clarified before the robustness and superiority claims of Chapter 3 can be accepted.
[§3.3.2, §3.3.3, §3.5] The skyline tracking assumes a straight-line skyline (Eqs. 3.1–3.4) and the ground-plane cue assumes a flat ground orthogonal to gravity above 300 m (Eqs. 3.8–3.12). Section 3.5 explicitly acknowledges that 'complex terrains with curved mountains challenge the straight-line assumption.' Yet all experiments in §3.4 are rooftop or drone sequences with largely linear horizons and planar ground. There is no evaluation on curved mountain skylines, partially occluded horizons, or non-planar terrain, which are precisely the 'natural environments' claimed in the abstract. If these geometric cues fail, the particle filter is left with only IMU, and the claimed advantage over IMU-only solutions vanishes. This is a correctness-risk concern: the central pose-tracking claim for unstructured natural scenes is not yet demonstrated.
[§5.3.1, Table 5.3] In the FOD500 results, AiFNet is reported with absRel=0.400, sqrRel=4.32e-1, yet δ1=85.12. These values are mutually implausible: an absRel of 0.400 typically corresponds to much lower δ1 accuracy. This suggests a data entry or metric-calculation error. Because the table is used to show that the proposed method outperforms baselines, the correctness of the baseline numbers is essential. Please verify all entries in Table 5.3 and report corrected values.
[§4.4.2, Table 4.4] The robustness analysis states that 'the registration error remains within 4-5% of the input translation, and the rotation error within 3-4%.' For the largest perturbation (100°, 200 cm), Table 4.4 reports TE=12.59 cm, which is 6.3% of the input translation, not within 5%. The textual summary is therefore inconsistent with the table. Either the claim or the table should be corrected.

minor comments (4)

[§3.3] The equation numbering is inconsistent: the text refers to 'Equation 1' while equations are numbered (3.1)–(3.20). Algorithm 1 has garbled line references and undefined symbols (ε, δt, b, Ω1, Ω2, Ω3). Please polish the pseudocode and define all variables.
[§5.2.1 and §5.2.4] The Circle-of-Confusion definition appears both as Eq. (5.1) and Eq. (5.9), with slightly different notation. The symbol δ is used both for the accuracy threshold in Eq. (5.15) and for the variance in Eq. (5.8), causing ambiguity.
[§4, Tables] In Table 4.1, the RoReg row contains a stray arrow '↓' and the column alignment is inconsistent. In Table 4.2, the 'Average' column is formatted differently from the other columns. Please unify table formatting.
[Overall] There are several typos and formatting artifacts, e.g., 'AutoV AE' in §6.10, '3D Unet' without hyphenation, and inconsistent use of 'SOTA' vs. 'state-of-the-art.' A careful proofreading pass is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the thesis validates four independent methods against external benchmarks without reducing any derivation to its own inputs.

full rationale

The thesis is an empirical compilation. Each content chapter proposes a method and evaluates it on public benchmarks (3DMatch/KITTI, DDFF/FOD500, DTU/Tanks-and-Temples). The geometric relationships used in Chapter 3 (skyline slope/intercept to roll/pitch, ground-plane normal via Rodrigues' formula) are analytical cues, not fitted quantities renamed as predictions. The particle filter variances are tuned constants, not the claimed output. Chapter 4's equivariant encoder is an architectural choice adapted from prior work and tested by ablations; no prediction is defined in terms of the fitted parameters. Chapter 5 uses the Circle-of-Confusion formula only as motivation, while depth is learned from data with external supervision. Chapter 6 conditions an implicit SDF on wavelet-transformed depth features from a monocular depth prior; although this raises a possible domain-overlap concern, the text does not assert that the prior was trained on the evaluation targets, and conditioning a reconstruction on an independent depth cue is not definitionally circular. The self-citations in Chapters 3–5 refer to the author's own peer-reviewed papers, which are independent prior publications and are not invoked as the sole justification for the present claims. The acknowledged limitations (curved skylines, view-dependent appearance, textureless scenes, memory footprint) are honest caveats that affect generalization but do not make any derivation equivalent to its inputs. No load-bearing step reduces by construction to a fitted value or to a self-citation chain.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The thesis introduces no new physical entities. Its central claims rest on standard computer vision and geometry assumptions (perspective projection, Rodrigues formula, CoC model, SDF representation), plus several domain-specific assumptions about natural scenes and depth priors, which are acknowledged in the text. The main fitted components are network weights and hand-set hyperparameters, several of which are not fully specified.

free parameters (6)

Particle filter variances and thresholds (Chapter 3) = Not fully specified; 'set as a constant according to practical tests'
The fusion quality in Algorithm 1 depends on variances delta_C1, delta_C2, distance threshold epsilon, and sampling resolutions Omega_1,2,3, which are chosen by hand and by practical tuning.
Surfel uncertainty normalization C and inverse-depth range (Chapter 4, Eq. 4.5-4.7) = Not specified numerically
The surfel radius formula uses a normalization factor C and truncated inverse-depth range (rho_min, rho_max) that are set by the sensor model and affect registration robustness.
Huber loss threshold delta (Chapter 4, Eq. 4.10) = 0.6 m
The threshold balances L1 and L2 loss behavior and is chosen for the 3DMatch/KITTI experiments.
LSTM token activation threshold and loss weight (Chapter 5) = activation threshold 0.4, alpha = 0.2
The token L2-norm threshold controls how many tokens enter the LSTM, and alpha weights the sharpness regularizer in Eq. 5.8; both are tuned on validation data.
Wavelet decomposition levels and pretrained wavelet autoencoder weights (Chapter 6) = Three resolutions; autoencoder pretrained on sharp depth maps
The model conditions on wavelet features from a pretrained autoencoder, whose weights are fitted on depth map data and directly influence reconstruction fidelity.
Pretrained monocular depth model used in Chapter 6 = Not named in the available text
The reconstruction pipeline processes images through a monocular depth model before wavelet transform; the quality of that external prior affects the final SDF reconstruction.

assumptions (7)

domain assumption The skyline in natural scenes can be approximated as a straight line for roll and pitch estimation (Chapter 3, Eq. 3.1-3.4)
Used to fit slope and intercept via least squares; the thesis acknowledges in Section 3.5 that curved mountains challenge this assumption.
domain assumption The ground plane is flat and orthogonal to the gravity vector when the camera is above 300 m (Chapter 3, Section 3.3.3)
The trigonometic back-projection in Eq. 3.8-3.11 requires a flat ground plane at known height to estimate the plane normal; this is an environmental assumption.
domain assumption The camera is never upside down during operation (Chapter 3, Section 3.3.2)
Used to search for the skyline along a predicted vertical direction; inverted camera states would break the search.
domain assumption Surface normals derived from depth gradients are accurate enough to serve as equivariant input signals (Chapter 4, Section 4.3.1)
The surfel representation uses normal vectors computed via a Sobel operator on depth; noisy depth maps lead to noisy normals, which the model must tolerate.
standard math The Circle-of-Confusion model correctly describes defocus blur as a function of depth and focus distance (Chapter 5, Eq. 5.1)
The CoC equation is a standard optics model; the thesis uses it to motivate depth-from-defocus and to design the sharpness regularizer.
standard math The zero-crossing of an implicit SDF corresponds to the reconstructed surface and can be optimized via ray sampling (Chapter 6, Section 6.1)
This is the standard formulation of implicit SDF reconstruction; the thesis relies on it for training and marching-cubes extraction.
domain assumption A pretrained monocular depth model provides a reliable geometric prior for wavelet feature conditioning (Chapter 6, Figure 6.7)
The pipeline conditions on depth maps from an external monocular depth estimator; if this prior is inaccurate, the wavelet features inject wrong geometry into the SDF.

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Cite this review

Pith. "Pith review of Doctoral Thesis: Geometric Deep Learning For Camera Pose Prediction, Registration, Depth Estimation, and 3D Reconstruction." pith.science (2026). https://pith.science/paper/QBPOGJN3

@misc{pith2026250901873,
  author       = {Pith},
  title        = {Pith review of: Doctoral Thesis: Geometric Deep Learning For Camera Pose Prediction, Registration, Depth Estimation, and 3D Reconstruction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QBPOGJN3}},
  note         = {Machine review of arXiv:2509.01873}
}

read the original abstract

Modern deep learning developments create new opportunities for 3D mapping technology, scene reconstruction pipelines, and virtual reality development. Despite advances in 3D deep learning technology, direct training of deep learning models on 3D data faces challenges due to the high dimensionality inherent in 3D data and the scarcity of labeled datasets. Structure-from-motion (SfM) and Simultaneous Localization and Mapping (SLAM) exhibit robust performance when applied to structured indoor environments but often struggle with ambiguous features in unstructured environments. These techniques often struggle to generate detailed geometric representations effective for downstream tasks such as rendering and semantic analysis. Current limitations require the development of 3D representation methods that combine traditional geometric techniques with deep learning capabilities to generate robust geometry-aware deep learning models. The dissertation provides solutions to the fundamental challenges in 3D vision by developing geometric deep learning methods tailored for essential tasks such as camera pose estimation, point cloud registration, depth prediction, and 3D reconstruction. The integration of geometric priors or constraints, such as including depth information, surface normals, and equivariance into deep learning models, enhances both the accuracy and robustness of geometric representations. This study systematically investigates key components of 3D vision, including camera pose estimation, point cloud registration, depth estimation, and high-fidelity 3D reconstruction, demonstrating their effectiveness across real-world applications such as digital cultural heritage preservation and immersive VR/AR environments.

Figures

Figures reproduced from arXiv: 2509.01873 by the authors.

**Figure 1.1.** Chapter relationships and outline structures of dependencies, [PITH_FULL_IMAGE:figures/full_fig_p022_1_1.png] view at source ↗

**Figure 2.1.** Geometric deep learning diagram combines various deep learning [PITH_FULL_IMAGE:figures/full_fig_p027_2_1.png] view at source ↗

**Figure 2.** , deep learning regression models are applied to both object pose [PITH_FULL_IMAGE:figures/full_fig_p027_2.png] view at source ↗

Figures from the paper (75 more)

**Figure 2.2.** Figure 2.2: Deep learning methods for pose regression. (a) PoseNet: a CNN [PITH_FULL_IMAGE:figures/full_fig_p028_2_2.png]

**Figure 2.** Figure 2: , including the traditional ICP-based approach, multi-level feature [PITH_FULL_IMAGE:figures/full_fig_p028_2.png]

**Figure 2.3.** Figure 2.3: Deep learning methods for point cloud registration. (a) [240]: an [PITH_FULL_IMAGE:figures/full_fig_p029_2_3.png]

**Figure 2.4.** Figure 2.4: Deep learning architectures for depth prediction. (a) Deep Vir [PITH_FULL_IMAGE:figures/full_fig_p031_2_4.png]

**Figure 2.** Figure 2: depicts a fundamental Structure from the Motion approach, [PITH_FULL_IMAGE:figures/full_fig_p033_2.png]

**Figure 2.5.** Figure 2.5: Illustration of structure from motion by multi-view images, image [PITH_FULL_IMAGE:figures/full_fig_p034_2_5.png]

**Figure 2.6.** Figure 2.6: Common SLAM framework: (a) visual SLAM, (b) Lidar-based [PITH_FULL_IMAGE:figures/full_fig_p036_2_6.png]

**Figure 2.7.** Figure 2.7: 3D reconstruction by using a 3D recurrent method (a), and [PITH_FULL_IMAGE:figures/full_fig_p037_2_7.png]

**Figure 2.8.** Figure 2.8: Implicit SDF for a wide range of reconstruction problems, from [PITH_FULL_IMAGE:figures/full_fig_p039_2_8.png]

**Figure 2.9.** Figure 2.9: Neural Radiance Field (at the left) alongside its extensions: 3D [PITH_FULL_IMAGE:figures/full_fig_p040_2_9.png]

**Figure 2.10.** Figure 2.10: The NICE-SLAM framework [288] tracks ego-body pose and [PITH_FULL_IMAGE:figures/full_fig_p041_2_10.png]

**Figure 3.1.** Figure 3.1: Illustration of pose orientation estimation from image frames on [PITH_FULL_IMAGE:figures/full_fig_p047_3_1.png]

**Figure 3.2.** Figure 3.2: Open source hardware setup. plane in the current frame with those in the reference frame. The compensation angles from various pipelines are then fed into the proposed particle filter presented in the Section below to obtain fusion orientations, further as input for…

**Figure 3.3.** Figure 3.3: Block diagram of the presented orientation estimation algorithm. [PITH_FULL_IMAGE:figures/full_fig_p048_3_3.png]

**Figure 3.4.** Figure 3.4: Failure case demo using traditional OpenCV pipeline. [PITH_FULL_IMAGE:figures/full_fig_p049_3_4.png]

**Figure 3.5.** Figure 3.5: Sample images and ground truth masks for training. [PITH_FULL_IMAGE:figures/full_fig_p050_3_5.png]

**Figure 3.6.** Figure 3.6: Segmented images for skyline search. Roll and pitch have a specific tolerance range to avoid unnecessary operations, so processing is only triggered when the movement is out of this range. Roll angle can be predicted from the slope m of the skyline, followed by pitc…

**Figure 3.7.** Figure 3.7: Arrows between them stand for transition conditions. In our [PITH_FULL_IMAGE:figures/full_fig_p055_3_7.png]

**Figure 3.8.** Figure 3.8: Simulation test setup on top of the building. [PITH_FULL_IMAGE:figures/full_fig_p057_3_8.png]

**Figure 3.** Figure 3: further validates the consistency of our method. The test is [PITH_FULL_IMAGE:figures/full_fig_p060_3.png]

**Figure 3.9.** Figure 3.9: The Green arrow is a mean error, the orange line is a median [PITH_FULL_IMAGE:figures/full_fig_p060_3_9.png]

**Figure 4.1.** Figure 4.1: Different Equivariant model designs. (a) is equivariant [PITH_FULL_IMAGE:figures/full_fig_p065_4_1.png]

**Figure 4.2.** Figure 4.2: (Left) Color image decomposed into superpixels of large size. [PITH_FULL_IMAGE:figures/full_fig_p068_4_2.png]

**Figure 4.3.** Figure 4.3: (Left) Color points cast from the depth map aligned with the [PITH_FULL_IMAGE:figures/full_fig_p069_4_3.png]

**Figure 4.4.** Figure 4.4: The network structure features a shared encoder for surfels (6 [PITH_FULL_IMAGE:figures/full_fig_p071_4_4.png]

**Figure 4.5.** Figure 4.5: Recovering discreteized SO(3) ′ from the quotient feature S 2 ′ by permutation order. The surfel undergoes convolution with two distinct symmetric kernels, κ1 and κ2, as shown in [PITH_FULL_IMAGE:figures/full_fig_p072_4_5.png]

**Figure 4.6.** Figure 4.6: Comparison results on KITTI [66]. For each dataset, the top [PITH_FULL_IMAGE:figures/full_fig_p076_4_6.png]

**Figure 4.7.** Figure 4.7: Huber loss learning curve under different thresholds. [PITH_FULL_IMAGE:figures/full_fig_p078_4_7.png]

**Figure 5.1.** Figure 5.1: Point cloud reconstructed from the extracted feature points of [PITH_FULL_IMAGE:figures/full_fig_p082_5_1.png]

**Figure 5.2.** Figure 5.2: The rays emitted from an object placed at an axial distance [PITH_FULL_IMAGE:figures/full_fig_p087_5_2.png]

**Figure 5.3.** Figure 5.3: The overview of our proposed network, FocDepthFormer, is pre [PITH_FULL_IMAGE:figures/full_fig_p087_5_3.png]

**Figure 5.4.** Figure 5.4: To illustrate the LSTM module in our network, the initial step [PITH_FULL_IMAGE:figures/full_fig_p089_5_4.png]

**Figure 5.5.** Figure 5.5: Comparison of Transformer attention on the two left column [PITH_FULL_IMAGE:figures/full_fig_p090_5_5.png]

**Figure 5.6.** Figure 5.6: Qualitative evaluation of our model on DDFF 12-Scene dataset. [PITH_FULL_IMAGE:figures/full_fig_p096_5_6.png]

**Figure 5.7.** Figure 5.7: Qualitative evaluation of our model on Mobile Depth dataset. [PITH_FULL_IMAGE:figures/full_fig_p096_5_7.png]

**Figure 5.8.** Figure 5.8: Qualitative evaluation of our model on LightField4D dataset. [PITH_FULL_IMAGE:figures/full_fig_p096_5_8.png]

**Figure 5.9.** Figure 5.9: The top row is the input, and the bottom is the output disparity [PITH_FULL_IMAGE:figures/full_fig_p099_5_9.png]

**Figure 5.10.** Figure 5.10: Different model structures’ comparison. former + LSTM design proposed in the paper can predict a more detailed feature map with fine-grained details, while the naive concatenation of feature maps after the Transformer can not achieve the equivalent performance (as r…

**Figure 5.11.** Figure 5.11: Our model performance w.r.t. the frame size of one focal stack [PITH_FULL_IMAGE:figures/full_fig_p102_5_11.png]

**Figure 6.1.** Figure 6.1: 2D cross-section of the implicit SDF volume space, where red [PITH_FULL_IMAGE:figures/full_fig_p106_6_1.png]

**Figure 6.2.** Figure 6.2: Sampling points near the surface are generated to compute Signed [PITH_FULL_IMAGE:figures/full_fig_p107_6_2.png]

**Figure 6.3.** Figure 6.3: GT SDF value generation can be achieved using two main [PITH_FULL_IMAGE:figures/full_fig_p108_6_3.png]

**Figure 6.4.** Figure 6.4: 3D CNN-based UNet for shape point cloud completion, image [PITH_FULL_IMAGE:figures/full_fig_p111_6_4.png]

**Figure 6.5.** Figure 6.5: The implicit SDF model for shape reconstruction in the training [PITH_FULL_IMAGE:figures/full_fig_p112_6_5.png]

**Figure 6.6.** Figure 6.6: The implicit SDF model for shape reconstruction in the test [PITH_FULL_IMAGE:figures/full_fig_p112_6_6.png]

**Figure 6.7.** Figure 6.7: Our model is based on implicit triplane feature fusion for Signed [PITH_FULL_IMAGE:figures/full_fig_p115_6_7.png]

**Figure 6.8.** Figure 6.8: A three-stage preprocessing pipeline for distractor removal: (a) [PITH_FULL_IMAGE:figures/full_fig_p117_6_8.png]

**Figure 6.9.** Figure 6.9: (a) Raw image with distractor on the ground. (b) Inpainted image [PITH_FULL_IMAGE:figures/full_fig_p117_6_9.png]

**Figure 6.10.** Figure 6.10: Wavelet transform of the depth map in finest resolution, (a) is [PITH_FULL_IMAGE:figures/full_fig_p119_6_10.png]

**Figure 6.11.** Figure 6.11: Sampling points along the pixel ray r(t) starting from o for implicit triplane feature learning via projection. For Wavelet feature projection onto triplane. The ray r(t) starts from the camera origin o, then passes through a single unprojected point S. Dashed line…

**Figure 6.** Figure 6: illustrates the feature extraction process along a pixel ray [PITH_FULL_IMAGE:figures/full_fig_p121_6.png]

**Figure 6.12.** Figure 6.12: The results of 3D UNet model for point cloud completion, where [PITH_FULL_IMAGE:figures/full_fig_p124_6_12.png]

**Figure 6.13.** Figure 6.13: The shape reconstruction results from 3D voxel input via im [PITH_FULL_IMAGE:figures/full_fig_p125_6_13.png]

**Figure 6.14.** Figure 6.14: Baseline comparison results on five targets from DTU ([103]), [PITH_FULL_IMAGE:figures/full_fig_p129_6_14.png]

**Figure 6.15.** Figure 6.15: Ablation study on 3D reconstruction. From left to right: (1) Re [PITH_FULL_IMAGE:figures/full_fig_p130_6_15.png]

**Figure 6.16.** Figure 6.16: Visualization of learned wavelet encoder feature maps at the [PITH_FULL_IMAGE:figures/full_fig_p132_6_16.png]

**Figure 6.17.** Figure 6.17: Ablation study visualizations of different design combinations [PITH_FULL_IMAGE:figures/full_fig_p134_6_17.png]

**Figure 8.** Figure 8: illustrates pose estimation from camera images based on track [PITH_FULL_IMAGE:figures/full_fig_p144_8.png]

**Figure 8.1.** Figure 8.1: Camera pose is calculated from the live-streaming images, demo [PITH_FULL_IMAGE:figures/full_fig_p145_8_1.png]

**Figure 8.2.** Figure 8.2: Experimental Hardware Test Setup: Our camera pose estima [PITH_FULL_IMAGE:figures/full_fig_p145_8_2.png]

**Figure 8.3.** Figure 8.3: Camera pose estimation system tested both on the ground and [PITH_FULL_IMAGE:figures/full_fig_p146_8_3.png]

**Figure 8.** Figure 8: shows the registration of head scans in the body scan of terracotta [PITH_FULL_IMAGE:figures/full_fig_p148_8.png]

**Figure 8.4.** Figure 8.4: Registration of source and target scans of Terracotta Warriors [PITH_FULL_IMAGE:figures/full_fig_p148_8_4.png]

**Figure 8.5.** Figure 8.5: Depth estimation for the planar sculpture of Marigold. The [PITH_FULL_IMAGE:figures/full_fig_p150_8_5.png]

**Figure 8.6.** Figure 8.6: Depth prediction from focal stack technique applied to heritage [PITH_FULL_IMAGE:figures/full_fig_p151_8_6.png]

**Figure 8.7.** Figure 8.7: 3D AR Guides overlaid with the real temple. The image was [PITH_FULL_IMAGE:figures/full_fig_p154_8_7.png]

**Figure 8.** Figure 8: demonstrates the beautiful interior of a historic cathedral with [PITH_FULL_IMAGE:figures/full_fig_p154_8.png]

**Figure 8.8.** Figure 8.8: The demo image is from public website link. [PITH_FULL_IMAGE:figures/full_fig_p155_8_8.png]

**Figure 8.** Figure 8: exhibits another critical application of how 3D digital recon [PITH_FULL_IMAGE:figures/full_fig_p155_8.png]

**Figure 8.9.** Figure 8.9: Chinese 3A Video Game, Black-myth Wukong, with many cul [PITH_FULL_IMAGE:figures/full_fig_p156_8_9.png]

**Figure 8.11.** Figure 8.11: This can prove the great usage potential of our reconstruction [PITH_FULL_IMAGE:figures/full_fig_p156_8_11.png]

**Figure 8.10.** Figure 8.10: 3D printed copy of Dunhuang Mogao Grottes inside the moun [PITH_FULL_IMAGE:figures/full_fig_p157_8_10.png]

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