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Multiresolution local smoothness detection in non-uniformly sampled multivariate signals

T0 review · 2 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Samplet coefficient decay rates determine local Hölder exponents on scattered, non-uniformly sampled signals.

desk verdict A clean samplet decay theorem wrapped around a slope-fitting algorithm whose central equality the theorem does not support; the numerics look good, but the theory overclaims. read the letter →

arxiv 2507.13480 v1 pith:YIREONJR submitted 2025-07-17 math.NA cs.CVcs.LGcs.NA

Sara Avesani , Gianluca Giacchi , Michael Multerer This is my paper · ORCID
classification math.NAcs.CVcs.LGcs.NA MSC 42C4065T60
keywords sampletslocalHölderexponentsmicrolocalspacesscattereddataedgedetectionmultiresolutionanalysisnon-uniformsamplingpointwiseregularity
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 claims that the local Hölder exponent of a signal sampled at scattered, non-uniformly spaced points can be read off from how fast its samplet coefficients decay along a multiresolution tree. Samplets are discrete signed measures, localized at data sites and built to annihilate low-degree polynomials; the paper proves that for a function in the microlocal space $C^\alpha(x_0)$, every samplet coefficient on a cluster containing $x_0$ satisfies $|(\sigma_{j,k}, f)| \lesssim \operatorname{diam}(\tau)^\alpha \sqrt{\#\tau}$. The proof turns this decay into a near-linear-time algorithm: walk down each branch of the $2^d$-tree, fit a line to log coefficient norm versus log cluster diameter, and read the slope as $\alpha + d/2$. If correct, this gives a deterministic, parameter-lean way to segment images, point clouds, and volumetric data by local smoothness, without structured grids or trained networks. The numerical experiments in one, two, and three dimensions support the claim across jumps, corners, and smooth regions.

What carries the argument

The load-bearing object is the samplet: a localized signed measure $\sigma_{j,k} = \sum_\ell \omega_\ell \delta_{x_\ell}$ with $\ell^2$-normalized weights, built from a hierarchical $2^d$-tree so that it has vanishing moments against polynomials of total degree $q$ and is orthonormal within each detail space. The fast samplet transform changes the data between Dirac-$\delta$ coordinates and samplet coordinates in linear time once the tree exists. The paper's main identity is the coefficient estimate $|(\sigma_{j,k}, f)| \lesssim \operatorname{diam}(\tau)^\alpha \sqrt{\#\tau}$, obtained by subtracting the approximating polynomial from $f$ and using Cauchy-Schwarz on the $\ell^1$ norm of the weights; the same estimate, specialized to balanced trees, gives the decay rate that the slope-fitting algorithm reads.

What would settle it

Take a known test signal $f(x) = |x-x_0|^\alpha$ sampled on scattered sites, run the branch slope fit for many values of $\alpha$ and $N$, and compare each recovered exponent to the true $\alpha$; if the fitted slope systematically deviates as $\alpha$ grows or as coarse clusters dominate the fit, the identification fails. A second check is to compute the coefficients for a $C^\infty$ bump, for which the fit will assign a large exponent, testing only the upper bound rather than the equality model.

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Extended reading notes

Core claim

The central discovery is a decay-to-regularity correspondence for samplets that mirrors the classical wavelet result. For any cluster $\tau$ containing $x_0$, if $f \in C^\alpha(x_0)$ and the samplets have vanishing moments of degree at least $\lfloor\alpha\rfloor$, then $|(\sigma_{j,k}, f)| \lesssim \operatorname{diam}(\tau)^\alpha \sqrt{\#\tau}$; on a balanced $2^d$-tree this becomes $\lesssim \sqrt{N}\, d^\alpha\, 2^{-j(\alpha+d/2)}$. The paper then proposes to treat this bound as an equality model $e_j \approx c\, (b_j)^{\alpha+d/2}$ on each branch and recover $\alpha+d/2$ by least-squares regression of $\log e_j$ against $\log b_j$. This turns regularity detection into a slope estimate and assigns a microlocal class $C^\alpha$ to every leaf cluster. Corollaries extend the decay estimate to H\"older and Sobolev-Slobodeckij classes, and experiments on grid and scattered data, images, the sphere, and point-cloud surfaces demonstrate the resulting edge and singularity charts.

Load-bearing premise

The algorithm assumes the decay rate in Theorem 3.1 is sharp enough that the slope of log coefficient norm versus log diameter equals $\alpha+d/2$; the theorem only proves an upper bound, and for coarse clusters the required condition $\operatorname{diam}(\tau) \leq R$ may fail.

Editorial extensions

If this is right

  • For a signal in $C^\alpha(x_0)$, every samplet coefficient on a cluster containing $x_0$ decays at least like $\operatorname{diam}(\tau)^\alpha \sqrt{\#\tau}$, provided the vanishing-moment order $q$ satisfies $q \geq \lfloor\alpha\rfloor$.
  • On balanced $2^d$-trees this means coefficient norms along a branch decay as $2^{-j(\alpha+d/2)}$, so $\alpha+d/2$ is exactly the slope in a log-log plot.
  • The same bound transfers to H\"older functions $C^{m,\vartheta}$ and to Sobolev-Slobodeckij spaces $W^{s,p}$ with $s > d/p$, yielding decay rates $m+\vartheta$ and $s-d/p-\varepsilon$, respectively.
  • A depth-first traversal of the tree plus one least-squares fit per branch yields a local regularity chart in essentially linear time once the cluster tree is available.
  • The experiments assign $C^0$ to jumps, $C^1$ to corners and nondifferentiable points, and high exponents to smooth regions in one, two, and three dimensions on both gridded and scattered data.

Reading between the lines

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

  • Because Theorem 3.1 is only an upper bound, the slope fit can overestimate $\alpha$ for functions that are smoother at $x_0$ than their formal microlocal exponent; a matching lower-bound or two-sided estimate would make the recovered exponent exact.
  • The same slope machinery should extend to any metric-measure setting where a hierarchical partition with diameter decay is available, even beyond the sphere and surface examples treated in the paper.
  • Thresholding the recovered slopes yields a multiscale edge detector whose scale sensitivity is controlled by the vanishing-moment order $q$; choosing $q$ adaptively could separate jumps from higher-order singularities without changing the algorithm.
  • The residual scatter in the log-log regression could provide empirical confidence intervals for the inferred H\"older exponent, although the paper does not discuss uncertainty quantification.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper develops a samplet-based method for detecting local Hölder regularity in non-uniformly sampled multivariate signals. It proves an upper decay bound for samplet coefficients of functions in Jaffard's microlocal spaces C^α(x0) (Theorem 3.1), derives corollaries for Hölder and Sobolev-Slobodeckij spaces, and proposes a near-linear-time algorithm (Algorithms 1 and 2) that fits the decay rate of samplet coefficient norms along tree branches to estimate the local Hölder exponent. The method is tested extensively on 1D, 2D, and 3D signals, including scattered point clouds and images.

Significance. If the algorithmic inference is justified, this is a valuable extension of wavelet-based edge detection to scattered and multivariate data, with an appealing near-linear practical cost. The upper bound in Theorem 3.1 is clean and correctly derived from the vanishing-moment property, and the numerical experiments cover a wide range of settings, including non-uniform point clouds. The central gap is that the algorithm relies on an equality between the fitted slope and α+d/2, whereas the paper only proves an upper bound; this undermines the theoretical support for the estimated exponents until a matching lower bound or characterization is supplied.

major comments (2)
  1. [§4, Eq. (15)] The model e_j ≈ c (b_j)^{α+d/2} assumes that samplet coefficients decay at the exact rate α+d/2, but Theorem 3.1 provides only the upper bound |(σ_{j,k}, f)| ≲ diam(τ)^α √#τ. There is no matching lower bound or converse theorem showing that the rate is attained. A concrete failure mode is a function such as f(x) = x·1_Q(x) + x^{q+1} at x0=0 (a variant of Remark 2.2): on any floating-point grid the data equal x + x^{q+1}, and with q vanishing moments the polynomial part is annihilated, so the coefficients decay like 2^{-j(q+1+1/2)} and the fitted exponent is near q+1 rather than the true local Hölder exponent 1. The paper must either prove a lower bound or characterize the decay rate, or clearly reframe the slope-fitting step as a heuristic whose accuracy is only empirically validated.
  2. [Theorem 3.1, proof] The proof begins by assuming 'diam(τ) ≤ R', where R is the radius in the definition of C^α(x0), but this hypothesis is absent from the theorem statement. Algorithm 2 uses coefficients from all levels of the tree, including coarse clusters for which diam(τ) may exceed R and which may contain multiple singularities. This gap means the theoretical justification for applying the decay bound to the full branch is incomplete; the statement should include the condition diam(τ) ≤ R, or the algorithm should restrict the fit to clusters satisfying it.
minor comments (4)
  1. [Corollary 3.5] The statement contains 'x0 ∈ Ω ⊆ Ω', which appears to be a typo; it should likely read 'x0 ∈ Ω′ ⊆ Ω'.
  2. [Lemma 3.4, proof] In the last sentence, 'the las claim' should be 'the last claim'.
  3. [Algorithm 1] The lines 'er ← [ ]' and 'br ← [ ]' appear after the function definition and read as global initializations; please clarify the intended scope of these variables (e.g., by moving them into the main routine or annotating them as global).
  4. [Table 1] For the 3D experiments, the entry '28 × 28 × 28' seems small compared with the other settings; please clarify whether these are grid dimensions, cluster-tree depths, or another quantity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the samplet decay bound is derived directly from the C^alpha definition and vanishing moments, and the slope-fit routine is a modeling assumption rather than a fitted input relabeled as a prediction.

full rationale

The paper's central theoretical result (Theorem 3.1, Eq. (11)) is derived in the text directly from the definition of the microlocal space C^alpha(x0), the vanishing-moment property (5), the l1/l2 estimate for samplet coefficient vectors (Remark 2.6), and the diameter/cardinality scaling of the cluster. No fitted parameter or target quantity enters that derivation, so the decay estimate is not circular. The algorithm in Section 4 then fits the model e_j approximately c (b_j)^(alpha+d/2) (Eq. (15)) to the computed coefficient norms; this is an explicit heuristic ansatz, not a claim that Theorem 3.1 is an equality or a characterization. Numerical validation in Section 5 is carried out against known test functions with known singularities, not against the algorithm's own fitted outputs. The skeptic's concern that Theorem 3.1 supplies only an upper bound, so the fitted exponent can overestimate alpha for functions whose coefficients decay faster than the bound, is a genuine correctness or robustness limitation of the estimator, but it is not a circular reduction: the fitted slope is not forced by the theorem or by the definition of the input. Self-citations to the samplet literature are appropriate because samplets are the object of study, and the cited constructions ([2,11]) are independent of the present decay claim. Overall, no step in the paper reduces to its own inputs by definition or by construction.

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

The algorithm's correctness depends on the balance and quasi-uniformity assumptions, on the vanishing-moment construction, and on the unproven assumption that fitted slopes equal Hölder exponents. No new entities are introduced.

free parameters (2)
  • edge detection threshold = 1.75
    In Section 5.3, slopes below 1.75 are plotted as edges; the threshold is chosen by hand, not derived.
  • vanishing moment degree q = q+1 = 5 (1D), q+1 = 3 (others)
    Section 5 chooses the polynomial degree q of samplet vanishing moments per experiment; this sets the maximum detectable regularity.
assumptions (4)
  • domain assumption Data sites X are quasi-uniform
    Section 2.2 states this assumption to ensure balanced 2^d-trees.
  • domain assumption Cluster tree is balanced with #τ ∼ N 2^{-jd}
    Used in deriving the explicit decay rate (12); real point clouds may violate this.
  • domain assumption Signal f is a continuous function on Ω so that Dirac evaluations are meaningful
    Section 2.2 represents the signal as a sum of Dirac measures; this requires f ∈ C(Ω) for point evaluations.
  • standard math Samplets satisfy the vanishing moment condition (5) for degree q
    This is a construction property of samplets (Section 2.2), used in the proof of Theorem 3.1.

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Cite this review

Pith. "Pith review of Multiresolution local smoothness detection in non-uniformly sampled multivariate signals." pith.science (2026). https://pith.science/paper/YIREONJR

@misc{pith2026250713480,
  author       = {Pith},
  title        = {Pith review of: Multiresolution local smoothness detection in non-uniformly sampled multivariate signals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YIREONJR}},
  note         = {Machine review of arXiv:2507.13480}
}
read the original abstract

Inspired by edge detection based on the decay behavior of wavelet coefficients, we introduce a (near) linear-time algorithm for detecting the local regularity in non-uniformly sampled multivariate signals. Our approach quantifies regularity within the framework of microlocal spaces introduced by Jaffard. The central tool in our analysis is the fast samplet transform, a distributional wavelet transform tailored to scattered data. We establish a connection between the decay of samplet coefficients and the pointwise regularity of multivariate signals. As a by product, we derive decay estimates for functions belonging to classical H\"older spaces and Sobolev-Slobodeckij spaces. While traditional wavelets are effective for regularity detection in low-dimensional structured data, samplets demonstrate robust performance even for higher dimensional and scattered data. To illustrate our theoretical findings, we present extensive numerical studies detecting local regularity of one-, two- and three-dimensional signals, ranging from non-uniformly sampled time series over image segmentation to edge detection in point clouds.

Figures

Figures reproduced from arXiv: 2507.13480 by the authors.

Figure 1
Figure 1. Examples of 2 d -trees in dimensions d = 1, 2, 3. For a balanced 2 d -tree, we obtain J ∼ d log2 N levels. At each level j, all N points are split into 2 jd clusters, and the division can be performed with linear cost. Hence, the overall cost for the construction of the 2 d -tree is O(JN) = O(N log N) in this case. If further structural details are available on X, e.g., in case that X refers to the pixels of an imag… view at source ↗
Figure 2
Figure 2. Illustration of a fixed branch in the samplet tree (left) and its corresponding nested regions in the computational domain (right). Each node along the branch is associated with the Euclidean norms of the samplet coefficients and a bounding box whose diameter reflects the local resolution. where A =    1 log b r 0 . . . . . . 1 log b r J    ∈ R (J+1)×2 , x =  log c α + d/2  ∈ R 2 , y =    log e r 0 . . . … view at source ↗
Figure 3
Figure 3. Top: Original function f plot. Bottom: Local Hölder expo￾nents. Our algorithm assigns the microlocal space C 0.5− d 2 = C 0 to clusters intersecting a jump; the space C 1.5− d 2 = C 1 to clusters intersecting the corners; finally, it assigns C 2.5− d 2 = C 2 to clusters intersecting singularities on the second derivative we detect. bottom row shows the obtained smoothness chart. As can be seen, all types of singular… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Top: Two-dimensional (left) and three-dimensional (right) plots of the corner function on the unit square Ω. Bottom: Local Hölder expo￾nents, displayed with linear (left) and structured (right) colormaps. Our algorithm assigns the space C 2− d 2 = C 1 to clusters inter…
Figure 5
Figure 5. Figure 5: Top: Two-dimensional (left) and three-dimensional (right) plots of the function g defined in (17) on the unit square Ω. Bottom: Local Hölder exponents, displayed with linear (left) and structured (right) col￾ormaps. We observe that g is in C 1− d 2 [PITH_FULL_IMAGE:fi…
Figure 6
Figure 6. Figure 6: Top: Phantom function plot. Bottom: Local Hölder exponents, displayed with linear (left) and structured (right) colormaps. Our algo￾rithm assigns the microlocal space C 1− d 2 = C 0 to clusters intersecting the singularity [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 7
Figure 7. Figure 7: Top: Visionteam picture from Matlab. Bottom left: local Hölder exponents, where the image noise introduces spurious high-frequency exponents. Bottom right: thresholded coefficient map showing only values below 1.75, which reduces noise and better reveals the true bound…
Figure 8
Figure 8. Figure 8: Top: photograph of the city of Lugano, Switzerland. Bottom left: local Hölder exponents, where the image noise introduces spurious high-frequency exponents. Bottom right: thresholded coefficient map show￾ing only values below 1.75, which reduces noise and better reveal…
Figure 9
Figure 9. Figure 9: Left: Plots of the analyzed function on the unit sphere. Right: Local Hölder exponents. Our algorithm assigns the microlocal space C 1− d 2 = C 0 to clusters intersecting the singularity. yields the Hölder exponent of 0. We also consider a more complex surface: the Sta…
Figure 10
Figure 10. Figure 10: Top: Different angles of the Lucy domain with a jump and a corner function. Bottom: Local Hölder exponents. Our algorithm assigns the microlocal space C 1.5− d 2 = C 0 to clusters intersecting the jump, and C 2.5− d 2 = C 1 to clusters intersecting the corner. the fig…
Figure 11
Figure 11. Figure 11: Top: Bunny embedded in the unit cube (left) and jump func￾tion (right). Bottom: Local Hölder exponents, displayed with linear (left) and structured (right) colormaps. Our algorithm assigns the microlocal space C 1.5− d 2 = C 0 to those clusters intersecting the singul…

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Reference graph

Works this paper leans on

34 extracted references · 32 canonical work pages · cited by 1 Pith paper

  1. [1]

    Multiscale scattered data analysis in samplet coordinates

    S. Avesani, R. Kempf, M. Multerer, and H. Wendland. Multiscale scattered data analysis in samplet coordinates. arXiv:2409.14791, 2024. (to appear in SIAM J. Sci. Comput.)

    work page Pith review arXiv 2024

  2. [2]

    Balazs and M

    P. Balazs and M. Multerer. Construction of generalized samplets in Banach spaces.arXiv:2412.00954, 2024

    arXiv 2024

  3. [3]

    Baroli, H

    D. Baroli, H. Harbrecht, and M. Multerer. Samplet basis pursuit: Multiresolution scattered data approximation with sparsity constraints.IEEE Trans. Signal Process., 72:1813–1823, 2024

    work page 2024

  4. [4]

    Bertasius, J

    G. Bertasius, J. Shi, and L. Torresani. Deepedge: A multi-scale bifurcated deep network for top-down contour detection. InProc. IEEE Conf. Comput. Vis. Pattern Recognit. (CVPR), pages 4380–4389, 2015

    work page 2015

  5. [5]

    De Marchi, W

    S. De Marchi, W. Erb, F. Marchetti, E. Perracchione, and M. Rossini. Shape-driven interpolation with discontinuous kernels: Error analysis, edge extraction, and applications in magnetic particle imaging. SIAM J. Sci. Comput., 42(2):B472–B491, 2020

    work page 2020

  6. [6]

    Demengel

    F. Demengel. Functional Spaces for the Theory of Elliptic Partial Differential Equations. Springer, London, UK, 2012

    work page 2012

  7. [7]

    Dorafshan, R

    S. Dorafshan, R. J. Thomas, and M. Maguire. Comparison of deep convolutional neural networks and edge detectors for image-based crack detection in concrete.Constr. Build. Mater., 186:1031–1045, 2018

    work page 2018

  8. [8]

    Elharrouss, Y

    O. Elharrouss, Y. Hmamouche, A. K. Idrissi, B. El Khamlichi, and A. El Fallah-Seghrouchni. Re- fined edge detection with cascaded and high-resolution convolutional network. Pattern Recognit., 138:109361, 2023

    work page 2023

Show all 34 references
  1. [9]

    Ganin and V

    Y. Ganin and V. Lempitsky.N 4-fields: Neural network nearest neighbor fields for image transforms. In Asian Conf. Comput. Vis. (ACCV), pages 536–551. Springer, 2014

    2014

  2. [10]

    Grossmann

    A. Grossmann. Wavelet transforms and edge detection. InStoch. Process. Phys. Eng., pages 149–157. Springer, 1988. MULTIRESOLUTION LOCAL SMOOTHNESS DETECTION 21

    1988

  3. [11]

    Harbrecht and M

    H. Harbrecht and M. Multerer. Samplets: Construction and scattered data compression.J. Comput. Phys., 471:111616, 2022

    2022

  4. [12]

    H.Harbrecht, M.Multerer, O.Schenk, andCh.Schwab.Multiresolutionkernelmatrixalgebra. Numer. Math., 156(3):1085–1114, 2024

    2024

  5. [13]

    Pattern Recognit., 164:111551, 2025

    W.Huang, M.Valsecchi, andM.Multerer.Anisotropicmultiresolutionanalysesfordeepfakedetection. Pattern Recognit., 164:111551, 2025

    2025

  6. [14]

    Hwang and T.-L

    J.-J. Hwang and T.-L. Liu. Pixel-wise deep learning for contour detection.arXiv:1504.01989, 2015

    2015 arXiv

  7. [15]

    S. Jaffard. Pointwise smoothness, two-microlocalization and wavelet coefficients. Publ. Mat., 35(1):155–168, 1991

    1991

  8. [16]

    Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions, volume 587

    S.JaffardandY.Meyer. Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions, volume 587. Amer. Math. Soc., Providence, 1996

    1996

  9. [17]

    Jawerth and W

    B. Jawerth and W. Sweldens. An overview of wavelet based multiresolution analyses.SIAM Rev., 36(3):377–412, 1994

    1994

  10. [18]

    J. Jing, S. Liu, G. Wang, W. Zhang, and C. Sun. Recent advances on image edge detection: A comprehensive review.Neurocomputing, 503:259–271, 2022

    2022

  11. [19]

    J. H. Jung and V. R. Durante. An iterative adaptive multiquadric radial basis function method for the detection of local jump discontinuities.Appl. Numer. Math., 59(7):1449–1466, 2009

    2009

  12. [20]

    L.LenarduzziandR.Schaback.Kernel-basedadaptiveapproximationoffunctionswithdiscontinuities. Appl. Math. Comput., 307:113–123, 2017

    2017

  13. [21]

    J. Li. A Wavelet Approach to Edge Detection. PhD thesis, Sam Houston State Univ., M.Sc. Thesis, 2003

    2003

  14. [22]

    Mallat.A Wavelet Tour of Signal Processing

    S. Mallat.A Wavelet Tour of Signal Processing. Elsevier, San Diego, US, 1999

    1999

  15. [23]

    Mallat and S

    S. Mallat and S. Zhong. Characterization of signals from multiscale edges.IEEE Trans. Pattern Anal. Mach. Intell., 14(7):710–732, 1992

    1992

  16. [24]

    P. Perona. Steerable-scalable kernels for edge detection and junction analysis. InProc. Eur. Conf. Comput. Vis. (ECCV), pages 3–18. Springer, 1992

    1992

  17. [25]

    W. Shen, X. Wang, Y. Wang, X. Bai, and Z. Zhang. Deepcontour: A deep convolutional feature learned by positive-sharing loss for contour detection. InProc. IEEE Conf. Comput. Vis. Pattern Recognit. (CVPR), pages 3982–3991, 2015

    2015

  18. [26]

    Soria, A

    X. Soria, A. Sappa, P. Humanante, and A. Akbarinia. Dense extreme inception network for edge detection. Pattern Recognit., 139:109461, 2023

    2023

  19. [27]

    J. Sun, D. Gu, Y. Chen, and S. Zhang. A multiscale edge detection algorithm based on wavelet domain vector hidden markov tree model.Pattern Recognit., 37(7):1315–1324, 2004

    2004

  20. [28]

    R. Sun, T. Lei, Q. Chen, Z. Wang, X. Du, W. Zhao, and A. K. Nandi. Survey of image edge detection. Front. Signal Process., 2:826967, 2022

    2022

  21. [29]

    R. Tarjan. Depth-first search and linear graph algorithms.SIAM J. Comput., 1(2):146–160, 1972

    1972

  22. [30]

    Torre and T

    V. Torre and T. A. Poggio. On edge detection.IEEE Trans. Pattern Anal. Mach. Intell., 2:147–163, 1986

    1986

  23. [31]

    R. Wang. Edge detection using convolutional neural network. InInt. Symp. Neural Netw., pages 12–20. Springer, 2016

    2016

  24. [32]

    Xie and Z

    S. Xie and Z. Tu. Holistically-nested edge detection. InProc. IEEE Int. Conf. Comput. Vis. (ICCV), pages 1395–1403, 2015

    2015

  25. [33]

    Zhang and P

    L. Zhang and P. Bao. Edge detection by scale multiplication in wavelet domain.Pattern Recognit. Lett., 23(14):1771–1784, 2002

    2002

  26. [34]

    Zhang, Y

    W. Zhang, Y. Zhao, T. P. Breckon, and L. Chen. Noise robust image edge detection based upon the automatic anisotropic gaussian kernels.Pattern Recognit., 63:193–205, 2017. 22 SARA A VESANI, GIANLUCA GIACCHI, AND MICHAEL MULTERER Sara A vesani, IDSIA USI-SUPSI, Università della...

    2017

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