3D Point Cloud Super-Resolution via Graph Total Variation on Surface Normals

Chinthaka Dinesh; Gene Cheung; Ivan V. Bajic

REVIEW 3 major objections 5 minor 42 references

3D Point Cloud Super-Resolution via Graph Total Variation on Surface Normals

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Point cloud super-resolution can be cast as a convex graph total variation problem on surface normals, and the resulting algorithm reports lower reconstruction error than two standard interpolation methods on six test models.

desk verdict Reasonable extension of the authors' denoising framework to point cloud SR, with solid but narrow experiments; the key affine normal model is unverified and the inserted points are unconstrained. read the letter →

arxiv 1908.06261 v1 pith:WHXG2ODO submitted 2019-08-17 eess.SP

Chinthaka Dinesh , Gene Cheung , Ivan V. Bajic This is my paper · ORCID

classification eess.SP

keywords pointcloudsuper-resolutiongraphtotalvariationsurfacenormalsbipartiteapproximationADMMconvexoptimizationpiecewisesmoothsurfaces3Dprocessing

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

This paper proposes a local, training-free algorithm for increasing the density of a 3D point cloud. The key move is to split the point cloud into two halves by bipartite graph approximation, so that each surface normal can be written as a linear function of its own point coordinates. That linearity turns super-resolution into a convex optimization problem: minimize graph total variation of surface normals, subject to keeping the original points fixed. The paper reports lower point-to-point and point-to-plane errors than two standard surface-fitting methods on all six test models, along with visually sharper edges.

What carries the argument

The load-bearing device is the bipartite graph approximation combined with the affine normal model. After a k-NN graph is built, nodes are split into red and blue sets so that each red node's normal can be computed from neighboring blue coordinates as $n_i = A_i p_i + b_i$; this makes the normal differences $m_{i,j} = n_i - n_j$ linear in the positions, $m = Bp + v$. The objective is the weighted $\ell^1$ graph total variation of the normals, $\sum_{i,j} w_{i,j} \Vert m_{i,j} \Vert_1$, enforced against the sampling constraint $Cp = q$ via an augmented Lagrangian. ADMM then alternates a closed-form $p$ update, a proximal soft-thresholding $m$ update, and a dual update, with the red and blue sets optimized alternately until convergence.

What would settle it

Take a ground-truth sphere or torus, downsample it to several densities, run the proposed algorithm, and compare each output surface normal to the analytic normal at that location; if the angular normal error grows noticeably in high-curvature or sparsely sampled regions, the affine normal model is the limiting assumption.

Watch

Extended reading notes

Core claim

The central claim is that point cloud super-resolution benefits from regularizing the surface normals, not the coordinates. The authors show that with a bipartite graph partition, normals of one color class become affine functions of coordinates, $n_i = A_i p_i + b_i$, so the piecewise-smoothness prior $\sum_{i,j} w_{i,j} \Vert n_i - n_j \Vert_1$ is convex in the positions. The resulting constrained minimization is solved by ADMM with a closed-form position update and a soft-thresholding normal update, alternating between the two color classes. On six test models, the method achieves the lowest C2C and C2P errors among the initial interpolated cloud, APSS, RIMLS, and the proposed output, and the visual comparisons show edges and fine features preserved rather than over-smoothed.

Load-bearing premise

The load-bearing premise is that each surface normal can be written as a linear function of its own point's coordinates using opposite-colored neighbors as fixed references; where curvature or sparse sampling breaks that linear model, the optimization minimizes a quantity that no longer reflects the true surface geometry.

Editorial extensions

If this is right

If the reported errors hold, the method offers a practical unsupervised alternative for upsampling low-cost scanner output, with no training data or learned priors.
Because the objective promotes piecewise smoothness in normals, the algorithm should preserve sharp creases and corners better than MLS-style interpolation, which the visual results support.
The convex formulation with ADMM gives the optimization convergence guarantees and a predictable per-iteration cost, making it suitable for local processing of large clouds.
The same bipartite-linearization trick could be reused inside other point-cloud optimization tasks, not only super-resolution.

Reading between the lines

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

Outside the paper: because the only geometric prior is normal-based graph total variation, the method should be tested on point clouds with thin structures or fine texture, where the linear normal model is most strained; a failure there would localize the assumption's limits.
Outside the paper: the bipartite partition makes the linear model depend on having enough opposite-color neighbors, so in very sparse regions the approximation quality degrades; an adaptive re-partitioning or a hierarchical scheme is a natural extension.
Outside the paper: the objective only constrains original point coordinates, so newly added points are free to drift; a mild fidelity term for the initial centroid positions could prevent the output from deviating too far in flat regions.
Outside the paper: comparing normal-angle errors against ground-truth normals, rather than only point-to-plane distances, would isolate whether the improvement comes from normal regularization or from the coordinate update.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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

The paper does one useful thing: it takes the authors' prior bipartite-graph GTV denoising framework and adapts it to point cloud super-resolution. New points are inserted at triangle centroids, the cloud is split into red/blue halves, and each half is optimized alternately to minimize graph total variation on surface normals while preserving the original low-res coordinates. The per-subproblem optimization is clearly derived: the p-update in (12) is a standard linear solve, the m-update is proximal gradient with soft-thresholding, and the ADMM update is standard. The experiments show consistent C2C and C2P improvements over APSS and RIMLS on all six test models, so the method delivers what it claims on clean synthetic downsampling.

Where the paper is soft is exactly where the stress-test note points. Equation (4), the affine normal model n_i = A_i p_i + b_i, is imported from [5] with no derivation or verification. The bipartite graph approximation has to guarantee enough opposite-color neighbors for the linear relation to be a faithful proxy for the surface normal. More importantly, the optimization minimizes GTV of these affine normals subject only to Cp=q; there is no term keeping the inserted points near their initialized positions or near the true surface. In principle the objective could be lowered by moving inserted points so that the affine normals become artificially smooth. The paper does not address this. The empirical results suggest the problem does not materialize on the six Stanford models, but the theoretical gap is real and the paper would be stronger if it either justified Eq. (4) or added a locality constraint.

Other missing pieces are evaluation details rather than fatal flaws: no code, no parameter sensitivity analysis, no experiments with noisy or real scanner data (despite the paper's motivation from low-cost scanners), and no comparison with the cited PU-Net baseline. The claim 'outperforms competing schemes' should be read as 'outperforms two classical surface-interpolation baselines on clean data.'

This is a legitimate extension of an established program, not a breakthrough. It is exactly the kind of work that deserves a serious referee for a conference; for a journal, it would need a more rigorous evaluation and a closer look at Eq. (4). If you work on point cloud SR, it's worth reading; if not, you can skip it.

Referee Report

3 major / 5 minor

Summary. This paper proposes a point cloud super-resolution method based on graph total variation (GTV) on surface normals. New points are inserted at centroids of Delaunay triangles of the low-resolution cloud; all points are connected via a k-NN graph and partitioned into two sets via bipartite graph approximation. Using the affine relation between each node's surface normal and its 3D coordinate (Eq. 4, imported from the authors' prior denoising work [5]), the authors formulate a convex ADMM optimization that minimizes a weighted l1 GTV of normal differences between nearby nodes, subject to preserving the original point coordinates. The optimization alternates between the two node sets, with a closed-form p update, a proximal-gradient m update, and a dual update. Numerical comparisons on six Stanford models report lower C2C and C2P errors than APSS, RIMLS, and the initial interpolated cloud, with visual results on Bunny and Armadillo.

Significance. If the proposed method works as claimed, it is a useful unsupervised alternative to learning-based point cloud upsampling: no training data is required, the formulation is convex, the update steps are explicit, and the reported gains are consistent across six standard models. The paper's strengths are a transparent optimization derivation with closed-form updates, standard ADMM/proximal machinery, and external evaluation against ground truth and several baselines. The main weakness is the unverified affine normal model, which is the theoretical foundation of the objective; without an independent derivation or a normalization/fidelity mechanism, the experimental gains are not yet fully supported by a sound optimality argument. The result is therefore promising but not fully established.

major comments (3)

[Section 3.1, Eq. (4)] The affine normal model n_i = A_i p_i + b_i is the single most important assumption in the paper, but it is not derived or validated here. Citing [5] is insufficient for the super-resolution setting: in denoising the points are near the true surface, whereas here the inserted points are initialized at triangle centroids and then moved by the optimization. The only active constraint, C p = q, fixes the original points; the inserted points are unconstrained except through the GTV objective. Because the normals in Eq. (4) are not required to be unit length, minimizing ||n_i - n_j||_1 can be satisfied by moving inserted points so that the affine outputs become artificially uniform, even if the points leave the true surface. The authors should provide (a) a derivation of Eq. (4) with an explicit validity region, (b) a unit-norm projection or re-estimation step after each p update, (c) a position-fidelity term for inserted points relative to their initialization, or (d) an experimental validation that optimized inserted points remain close to the ground-truth surface. This issue is load-bearing for the central claim.
[Section 3.3, Eq. (12)] The claim that (B^T B + C^T C) is positive definite is not substantiated. For the SR problem, C^T C is a diagonal projection onto the original points and is singular on the subspace of inserted points, so the definiteness rests on B^T B. With edge differences m_{i,j} = A_i p_i - A_j p_j + b_i - b_j, a nonzero displacement of inserted points that is annihilated by B would make the linear system singular and the closed-form update (12) invalid. The authors should give a proof of the positive-definiteness claim for their particular A_i, or add a small regularization term (e.g., epsilon I) and report its value. As written, the numerical-stability discussion does not resolve the possibility of rank deficiency.
[Section 4] The experimental section omits several details needed to assess the central claim. The value of sigma_p in the edge weight (2) is not reported; the stopping criterion and maximum number of alternating iterations are not given; and it is not stated how APSS and RIMLS, which produce point-set surfaces rather than point clouds of specified cardinality, are used to obtain exactly the same number of points as the ground truth. These omissions make it difficult to reproduce the comparison and to gauge the sensitivity of the reported gains to the chosen parameters.

minor comments (5)

[Section 3.3, Eq. (18)] The dual update is written with A and b, but the paper defines H, s, and d in Eq. (6); the notation should be made consistent, e.g., y^{k+1} = y^k + rho(H s^{k+1} - d).
[Abstract and Section 3.3] There is a typo: 'proximal gradient decent' should read 'proximal gradient descent', and 'state-of-art' should read 'state-of-the-art'.
[Section 4] In the visual-results discussion, 'and the fingers' appears as 'and and the fingers'; this should be corrected.
[Section 2] The clause 'M, M < N' is awkward; it should simply read 'M < N'.
[Section 4] The parameter sigma_p that appears in the edge-weight definition (2) is missing from the list of selected parameters; a sensitivity study for rho, t, k, and sigma_p would strengthen the paper.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the reported SR improvements are measured against external ground truth and external baselines, and no fitted parameter is renamed as a prediction.

full rationale

The derivation chain in Section 3 is an unsupervised optimization routine: new points are centroids of Delaunay triangles; the objective is graph total variation of surface normals (Eq. 7) subject to the sampling constraint Cp = q (Eq. 6). No parameter is fitted to the C2C/C2P metrics or to the ground-truth clouds. The hyperparameters (rho=5, t=0.1, k=8) are fixed across all six models and are not selected to minimize the reported errors, so the comparisons in Tables 1 and 2 are external evidence rather than a consequence of the optimization. The affine normal-coordinate relation n_i = A_i p_i + b_i (Eq. 4) is imported from the authors' prior denoising work [5], but this is a stated modeling assumption and does not make the SR output equivalent to its input; the cited prior work is not invoked as a uniqueness theorem that forces the algorithm's success. The paper does not hide a fitted parameter or rename the input as output, so no circular reduction is exhibited.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The algorithm relies on several unstated or underspecified choices. The bipartite graph linearization is imported from the authors' own prior work, the noiseless-input assumption is in tension with the paper's motivation, and the graph weight parameter sigma_p is never specified. The optimization hyperparameters are fixed by hand without sensitivity analysis, so the reported performance may depend on favorable settings.

free parameters (2)

Optimization parameters (rho, t, k) = rho=5, t=0.1, k=8
Set by hand in Sec 4 with no sensitivity analysis or justification; the reported performance could depend on favorable settings.
Edge weight scale sigma_p = not specified
Appears in Eq (2) for k-NN graph weights but its value is never given in the paper, leaving the graph construction incompletely specified.

assumptions (4)

domain assumption The low-resolution point cloud q is noiseless (Sec 2: 'We assume that the observed low-res q is noiseless.').
Conflicts with the stated motivation of low-cost 3D scanners, which produce noisy measurements; the algorithm is neither formulated nor tested for noisy input.
domain assumption Surface normals can be written as a linear function of point coordinates using opposite-color neighbors, n_i = A_i p_i + b_i (Eq 4).
Imported from the authors' prior denoising paper [5]; this linearization is the foundation of the convex optimization. If it is inaccurate, the solver optimizes the wrong objective.
domain assumption The underlying 2D surface is piecewise smooth, so GTV on surface normals is the correct prior (Sec 3.1).
The entire objective promotes small normal differences between neighbors; objects with fine texture or high-frequency detail may be over-smoothed, though the authors claim detail preservation.
standard math ADMM and proximal gradient converge to the optimum of the convex reformulation.
The objective is convex and the constraint is linear, but the paper does not analyze convergence behavior for this specific problem or give stopping criteria.

how reviews work

0 comments

Cite this review

Pith. "Pith review of 3D Point Cloud Super-Resolution via Graph Total Variation on Surface Normals." pith.science (2026). https://pith.science/paper/WHXG2ODO

@misc{pith2026190806261,
  author       = {Pith},
  title        = {Pith review of: 3D Point Cloud Super-Resolution via Graph Total Variation on Surface Normals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WHXG2ODO}},
  note         = {Machine review of arXiv:1908.06261}
}

read the original abstract

Point cloud is a collection of 3D coordinates that are discrete geometric samples of an object's 2D surfaces. Using a low-cost 3D scanner to acquire data means that point clouds are often in lower resolution than desired for rendering on high-resolution displays. Building on recent advances in graph signal processing, we design a local algorithm for 3D point cloud super-resolution (SR). First, we initialize new points at centroids of local triangles formed using the low-resolution point cloud, and connect all points using a k-nearestneighbor graph. Then, to establish a linear relationship between surface normals and 3D point coordinates, we perform bipartite graph approximation to divide all nodes into two disjoint sets, which are optimized alternately until convergence. For each node set, to promote piecewise smooth (PWS) 2D surfaces, we design a graph total variation (GTV) objective for nearby surface normals, under the constraint that coordinates of the original points are preserved. We pursue an augmented Lagrangian approach to tackle the optimization, and solve the unconstrained equivalent using the alternating method of multipliers (ADMM). Extensive experiments show that our proposed point cloud SR algorithm outperforms competing schemes objectively and subjectively for a large variety of point clouds.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

42 extracted references · 41 canonical work pages

[5]

Speciﬁcally, we ﬁrst initialize new points at centroids of local triangles, and construct a k-nearest-neighbor graph to connect all 3D points

CONCLUSION We pursue a graph-based approach to tackle the point cloud super- resolution (SR) problem, where the density of the point cloud is increased while preserving piecewise smoothness (PWS) of the in- tended object’s 2D surface. Speciﬁcally, we ﬁrst initialize new points at centroids of local triangles, and construct a k-nearest-neighbor graph to co...

work page
[1]

Unlike 3D meshes, a point cloud is an unstructured list of 3D coordinates, and low-level processing tasks like compression [2–4] and denoising [5, 6] are challenging

INTRODUCTION Point cloud, acquired directly by off-the-shelf 3D scanners like Microsoft Kinect or estimated indirectly via stereo-matching al- gorithms [1], is a recently popular 3D visual signal representation for free viewpoint image rendering, and is investigated in indus- trial standards like MPEG 1. Unlike 3D meshes, a point cloud is an unstructured ...

work page 2016
[2]

3D Point Cloud Super-Resolution via Graph Total Variation on Surface Normals

PRELIMINARIES 3D Point Cloud: We deﬁne a point cloud as a set of (roughly uni- form) discrete samples of 3D coordinates on an object’s 2D surface in 3D space. Denote by p = [ p⊤ 1 ... p⊤ N ]⊤ ∈ R3N the posi- tion vector for a full-resolution point cloud, where pi∈ R3 is the 3D coordinate of a point i, and N is the number of points in the point cloud. Simi...

work page Pith review arXiv 2019
[3]

Algorithm Overview We begin by adding a set of new interior points to the low-res point cloud q to populate the target full-res point cloud p

PROPOSED ALGORITHM 3.1. Algorithm Overview We begin by adding a set of new interior points to the low-res point cloud q to populate the target full-res point cloud p. Speciﬁcally, we construct a triangular mesh using Delaunay triangulation using points in q, and then insert new points at the centroids of those tri- angles. Given an interpolated point clou...

work page
[4]

The weight deﬁnition in (2) is similar to bilateral ﬁlter weights deﬁned in [23] with domain and range ﬁlters

otherwise. The weight deﬁnition in (2) is similar to bilateral ﬁlter weights deﬁned in [23] with domain and range ﬁlters. Surface Normals: A surface normal ni∈ R3 of nodei is a vector that is perpendicular to the tangent plane at pointi. Typically coordi- nates of thek nearest neighbors ofi are used to compute ni [24–28]. The most popular method is to ﬁt ...

work page
[6]

We can thus rewrite (8) as min m,p ∑ i,j wi,j‖mi,j‖1 + y⊤ 1 (Bp + v− m)+ y⊤ 2 (Cp− q) +ρ 2‖Bp + v− m‖2 2 + ρ 2‖Cp− q‖2 2

(9) Similarly, according to (6), y⊤(Hs− d) can be rewritten as y⊤(Hs− d) = y⊤ 1 (Bp + v− m) + y⊤ 2 (Cp− q), (10) where y⊤ = [y⊤ 1 y⊤ 2 ]. We can thus rewrite (8) as min m,p ∑ i,j wi,j‖mi,j‖1 + y⊤ 1 (Bp + v− m)+ y⊤ 2 (Cp− q) +ρ 2‖Bp + v− m‖2 2 + ρ 2‖Cp− q‖2 2. (11) As typically done in ADMM approaches, we solve (11) by al- ternately minimizing p and m and ...

work page
[7]

=−ρ(Bpk+1 + v− m)− yk

work page
[8]

C2C (×10−1) of different models Model Low APSS RIMLS Initial Prop

(14) We can now deﬁne a proximal mapping prox g,t(m) for a con- vex, non-differentiable functiong() with step sizet as: proxg,t(m) = arg min θ { g(θ) + 1 t||θ− m||2 2 } (15) Table 1. C2C (×10−1) of different models Model Low APSS RIMLS Initial Prop. Bunny 1.47 1.31 1.22 1.27 1.14 Dragon 1.52 1.43 1.34 1.45 1.25 Armadillo 1.49 1.38 1.30 1.37 1.21 Buddha 1....

work page

Show all 42 references

[9]

Point cloud models we use are Bunny, Dragon, Armadillo, Happy Buddha, Asian Dragon, and Lucy, pro- vided in [30]

EXPERIMENTAL RESULTS The computed SR point clouds are compared against point cloud models obtained using competing schemes APSS [13] and RIMLS [14], as well as initial point cloud (after adding new points to the centroids of triangles). Point cloud models we use are Bunny, Dra...
[10]

Real-time super-resolution for digital zooming using ﬁnite kernel-based edge orientation estimation and truncated image restoration,

W. Kang, J. Jeon, E. Lee, C. Cho, J. Jung, T. Kim, A. K. Kat- saggelos, and J. Paik, “Real-time super-resolution for digital zooming using ﬁnite kernel-based edge orientation estimation and truncated image restoration,” inICIP, Sep. 2013, pp. 1311– 1315

2013
[11]

Surfacenet: An end-to-end 3D neural network for multiview stereopsis,

M. Ji, J. Gall, H. Zheng, Y . Liu, and L. Fang, “Surfacenet: An end-to-end 3D neural network for multiview stereopsis,”arXiv preprint arXiv: 1708.01749, 2017

2017 arXiv
[12]

Progressive graph-signal sampling and encoding for static 3d geometry rep- resentation,

M. Zhao, G. Cheung, D. Florencio, and X. Ji, “Progressive graph-signal sampling and encoding for static 3d geometry rep- resentation,” inICIP, Sep. 2017, pp. 735–739

2017
[13]

Intra-frame context-based octree coding for point-cloud geometry,

D. C. Garcia and R. L. de Queiroz, “Intra-frame context-based octree coding for point-cloud geometry,” in ICIP, Oct 2018, pp. 1807–1811

2018
[14]

Compression of plenoptic point clouds,

G. Sandri, R. L. de Queiroz, and P. A. Chou, “Compression of plenoptic point clouds,” IEEE Trans. Image Process., vol. 28, no. 3, pp. 1419–1427, March 2019

2019
[15]

However, [15] is ad-hoc in methodology and still suffers from over-smoothing, albeit to a lesser extent

proposed an edge-aware point upsampling method by ﬁrst sam- pling away from object boundaries, and then progress towards object edges and corners. However, [15] is ad-hoc in methodology and still suffers from over-smoothing, albeit to a lesser extent. Recently a deep learning ...
[16]

Local 3D point cloud denoising via bipartite graph approximation & total variation,

C. Dinesh, G. Cheung, I. V . Bajic, and G. Yang, “Local 3D point cloud denoising via bipartite graph approximation & total variation,” inMMSP, 2018

2018
[17]

3D point cloud denois- ing via bipartite graph approximation and reweighted graph laplacian,

C. Dinesh, G. Cheung, and I. V . Bajic, “3D point cloud denois- ing via bipartite graph approximation and reweighted graph laplacian,”arXiv preprint arXiv:1812.07711, 2018

2018 arXiv
[18]

Super-resolution fourier transforms by optimisa- tion, and isar imaging,

G. Zweig, “Super-resolution fourier transforms by optimisa- tion, and isar imaging,” IEE Proceedings-Radar, Sonar and Navigation, vol. 150, no. 4, pp. 247–, Aug 2003

2003
[19]

Multi-scale patch-based image restoration,

V . Papyan and M. Elad, “Multi-scale patch-based image restoration,” IEEE Trans. Image Process. , vol. 25, no. 1, pp. 249–261, Jan 2016

2016
[20]

Hierarchical segmentation based point cloud attribute compression,

K. Zhang, W. Zhu, and Y . Xu, “Hierarchical segmentation based point cloud attribute compression,” inICASSP, 2018

2018
[21]

Laser scanner super- resolution

Y . Y . J. Kil, B. Mederos, and N. Amenta, “Laser scanner super- resolution.” inSPBG, 2006, pp. 9–15

2006
[22]

Computing and rendering point set surfaces,

M. Alexa, J. Behr, D. Cohen-Or, S. Fleishman, D. Levin, and C. T. Silva, “Computing and rendering point set surfaces,” IEEE Trans. Vis. Comput. Graphics , vol. 9, no. 1, pp. 3–15, Jan 2003

2003
[23]

Algebraic point set surfaces,

G. Guennebaud and M. Gross, “Algebraic point set surfaces,” ACM Trans. Graph., vol. 26, no. 3, p. 23, 2007

2007
[24]

Feature pre- serving point set surfaces based on non-linear kernel regres- sion,

A. C. ¨Oztireli, G. Guennebaud, and M. Gross, “Feature pre- serving point set surfaces based on non-linear kernel regres- sion,” in Computer Graphics Forum, vol. 28, no. 2, 2009, pp. 493–501

2009
[25]

Edge-aware point set resampling,

H. Huang, S. Wu, M. Gong, D. Cohen-Or, U. Ascher, and H. R. Zhang, “Edge-aware point set resampling,” ACM Trans. Graph., vol. 32, no. 1, p. 9, 2013

2013
[26]

PU-Net: Point cloud upsampling network,

L. Yu, X. Li, C. W. Fu, D. Cohen-Or, and P. N. Heng, “PU-Net: Point cloud upsampling network,” in CVPR, 2018, pp. 2790– 2799

2018
[27]

Graph spectral image processing,

G. Cheung, E. Magli, Y . Tanaka, and M. Ng, “Graph spectral image processing,” Proc. IEEE, vol. 106, no.5, pp. 907–930, May 2018

2018
[28]

Graph signal processing: Overview, challenges, and applications,

A. Ortega, P. Frossard, J. Kovacevic, J. M. Moura, and P. Van- dergheynst, “Graph signal processing: Overview, challenges, and applications,” Proc. IEEE, vol. 106, no. 5, pp. 808–828, 2018

2018
[29]

Bipartite approximation for graph wavelet signal decomposition,

J. Zeng, G. Cheung, and A. Ortega, “Bipartite approximation for graph wavelet signal decomposition,” IEEE Trans. Signal Process., vol. 65, no. 20, pp. 5466–5480, Oct 2017

2017
[30]

Dis- tributed optimization and statistical learning via the alternat- ing direction method of multipliers,

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Dis- tributed optimization and statistical learning via the alternat- ing direction method of multipliers,”Foundation and Trends in Machine Learning, vol. 3, no. 1, pp. 1–122, Jan. 2011

2011
[31]

Proximal algorithms,

N. Parikh and S. Boyd, “Proximal algorithms,” Foundations and Trends® in Optimization, vol. 1, no. 3, pp. 127–239, 2013

2013
[32]

Wang, Geometric structure of high-dimensional data and di- mensionality reduction

J. Wang, Geometric structure of high-dimensional data and di- mensionality reduction. Springer, 2011

2011
[33]

Bilateral ﬁltering for gray and color images,

C. Tomasi and R. Manduchi, “Bilateral ﬁltering for gray and color images,” inICCV, Bombay, India, 1998

1998
[34]

Automatic data segmentation for geometric feature extraction from unorganized 3-d coordinate points,

J. Huang and C. H. Menq, “Automatic data segmentation for geometric feature extraction from unorganized 3-d coordinate points,” IEEE Trans. Robot. Autom. , vol. 17, no. 3, pp. 268– 279, Jun 2001

2001
[35]

Kanatani, Statistical optimization for geometric computa- tion: theory and practice

K. Kanatani, Statistical optimization for geometric computa- tion: theory and practice. Courier Corporation, 2005

2005
[36]

On the normal vector estimation for point cloud data from smooth surfaces,

D. OuYang and H. Y . Feng, “On the normal vector estimation for point cloud data from smooth surfaces,” Computer-Aided Design, vol. 37, no. 10, pp. 1071–1079, 2005

2005
[37]

Continuous shading of curved surfaces,

H. Gouraud, “Continuous shading of curved surfaces,” IEEE Trans. Comput., vol. C-20, no. 6, pp. 623–629, June 1971

1971
[38]

A comparison of algorithms for vertex normal computation,

S. Jin, R. R. Lewis, and D. West, “A comparison of algorithms for vertex normal computation,”The Visual Computer, vol. 21, no. 1-2, pp. 71–82, 2005

2005
[39]

Piecewise linear regularized solution paths,

S. Rosset and J. Zhu, “Piecewise linear regularized solution paths,”The Annals of Statistics, pp. 1012–1030, 2007

2007
[40]

The Stanford 3D scanning repository,

M. Levoy, J. Gerth, B. Curless, and K. Pull, “The Stanford 3D scanning repository,” [Online] https://graphics.stanford.edu/data/3Dscanrep/
[41]

Geo- metric distortion metrics for point cloud compression,

D. Tian, H. Ochimizu, C. Feng, R. Cohen, and A. Vetro, “Geo- metric distortion metrics for point cloud compression,” inICIP, Sept 2017, pp. 3460–3464

2017
[42]

Meshlab: an open-source mesh pro- cessing tool

P. Cignoni, M. Callieri, M. Corsini, M. Dellepiane, F. Ganov- elli, and G. Ranzuglia, “Meshlab: an open-source mesh pro- cessing tool.” in Eurographics Italian Chapter Conference , 2008, pp. 129–136

2008

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [5]

Speciﬁcally, we ﬁrst initialize new points at centroids of local triangles, and construct a k-nearest-neighbor graph to connect all 3D points

CONCLUSION We pursue a graph-based approach to tackle the point cloud super- resolution (SR) problem, where the density of the point cloud is increased while preserving piecewise smoothness (PWS) of the in- tended object’s 2D surface. Speciﬁcally, we ﬁrst initialize new points at centroids of local triangles, and construct a k-nearest-neighbor graph to co...

work page

[2] [1]

Unlike 3D meshes, a point cloud is an unstructured list of 3D coordinates, and low-level processing tasks like compression [2–4] and denoising [5, 6] are challenging

INTRODUCTION Point cloud, acquired directly by off-the-shelf 3D scanners like Microsoft Kinect or estimated indirectly via stereo-matching al- gorithms [1], is a recently popular 3D visual signal representation for free viewpoint image rendering, and is investigated in indus- trial standards like MPEG 1. Unlike 3D meshes, a point cloud is an unstructured ...

work page 2016

[3] [2]

3D Point Cloud Super-Resolution via Graph Total Variation on Surface Normals

PRELIMINARIES 3D Point Cloud: We deﬁne a point cloud as a set of (roughly uni- form) discrete samples of 3D coordinates on an object’s 2D surface in 3D space. Denote by p = [ p⊤ 1 ... p⊤ N ]⊤ ∈ R3N the posi- tion vector for a full-resolution point cloud, where pi∈ R3 is the 3D coordinate of a point i, and N is the number of points in the point cloud. Simi...

work page Pith review arXiv 2019

[4] [3]

Algorithm Overview We begin by adding a set of new interior points to the low-res point cloud q to populate the target full-res point cloud p

PROPOSED ALGORITHM 3.1. Algorithm Overview We begin by adding a set of new interior points to the low-res point cloud q to populate the target full-res point cloud p. Speciﬁcally, we construct a triangular mesh using Delaunay triangulation using points in q, and then insert new points at the centroids of those tri- angles. Given an interpolated point clou...

work page

[5] [4]

The weight deﬁnition in (2) is similar to bilateral ﬁlter weights deﬁned in [23] with domain and range ﬁlters

otherwise. The weight deﬁnition in (2) is similar to bilateral ﬁlter weights deﬁned in [23] with domain and range ﬁlters. Surface Normals: A surface normal ni∈ R3 of nodei is a vector that is perpendicular to the tangent plane at pointi. Typically coordi- nates of thek nearest neighbors ofi are used to compute ni [24–28]. The most popular method is to ﬁt ...

work page

[6] [6]

We can thus rewrite (8) as min m,p ∑ i,j wi,j‖mi,j‖1 + y⊤ 1 (Bp + v− m)+ y⊤ 2 (Cp− q) +ρ 2‖Bp + v− m‖2 2 + ρ 2‖Cp− q‖2 2

(9) Similarly, according to (6), y⊤(Hs− d) can be rewritten as y⊤(Hs− d) = y⊤ 1 (Bp + v− m) + y⊤ 2 (Cp− q), (10) where y⊤ = [y⊤ 1 y⊤ 2 ]. We can thus rewrite (8) as min m,p ∑ i,j wi,j‖mi,j‖1 + y⊤ 1 (Bp + v− m)+ y⊤ 2 (Cp− q) +ρ 2‖Bp + v− m‖2 2 + ρ 2‖Cp− q‖2 2. (11) As typically done in ADMM approaches, we solve (11) by al- ternately minimizing p and m and ...

work page

[7] [7]

=−ρ(Bpk+1 + v− m)− yk

work page

[8] [8]

C2C (×10−1) of different models Model Low APSS RIMLS Initial Prop

(14) We can now deﬁne a proximal mapping prox g,t(m) for a con- vex, non-differentiable functiong() with step sizet as: proxg,t(m) = arg min θ { g(θ) + 1 t||θ− m||2 2 } (15) Table 1. C2C (×10−1) of different models Model Low APSS RIMLS Initial Prop. Bunny 1.47 1.31 1.22 1.27 1.14 Dragon 1.52 1.43 1.34 1.45 1.25 Armadillo 1.49 1.38 1.30 1.37 1.21 Buddha 1....

work page