Pith. sign in

REVIEW 4 major objections 6 minor 55 references

Riemannian Complex Hermit Positive Definite Convolution Network for Polarimetric SAR Image Classification

T0 review · 4 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash

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

Pith's one-line read The paper claims that HPDNet, which processes PolSAR covariance matrices directly as complex Hermitian positive definite matrices on a Riemannian manifold before projecting them to Euclidean space, reaches the best reported accuracy on…

desk verdict The first complex HPD manifold network for PolSAR is a plausible new idea with consistent accuracy gains, but the fast eigendecomposition module (CM-ASQRT) as written cannot produce the eigenvectors and eigenvalues the ReEig/LogEig layers need, so the speedup claim is unsupported. read the letter →

arxiv 2502.08137 v2 pith:MIGZRLOG submitted 2025-02-12 cs.CV

Junfei Shi , Yuke Li , Mengmeng Nie , Fang Liu , Haiyan Jin , Junhuai Li , Weisi Lin This is my paper · ORCID
classification cs.CV
keywords PolSARimageclassificationHermitianpositivedefinitematrixRiemannianmanifoldlearningcomplex-valuedconvolutionalnetworkLogEiglayeriterativesquarerootcovariancegeometryremotesensing
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 paper tries to show that vectorizing PolSAR covariance matrices before feeding them to a neural network destroys exactly the structure that separates terrain classes. It proposes HPDNet, which treats each pixel's 3x3 complex covariance matrix as a Hermitian positive definite matrix on a Riemannian manifold, applies manifold-preserving mapping and rectifying layers, and only then projects to Euclidean space with a complex LogEig layer for a complex-valued 3D CNN. The claim is that this Riemannian-to-Euclidean pipeline beats vector-based complex CNNs and other state-of-the-art PolSAR classifiers, with the largest gains in heterogeneous regions such as buildings and roads. On the Xi'an, Oberpfaffenhofen, and Flevoland datasets, the paper reports overall accuracies of 96.90%, 90.94%, and 98.73%, with Kappa coefficients of 95.56%, 87.30%, and 98.32%, each above the compared methods.

What carries the argument

The load-bearing object is the complex HPD covariance matrix and its Riemannian geometry. The argument rests on three layers: the HPD mapping layer $X_k = W_k X_{k-1} W_k^H$ with a complex kernel, which moves matrices between HPD manifolds; the rectifying layer, which clamps eigenvalues below a threshold while preserving HPD structure; and the complex LogEig layer $X_k = U_{k-1}\operatorname{diag}(\log \Lambda_{k-1}) U_{k-1}^H$, which sends manifold points to the tangent space so a Euclidean complex 3D CNN can follow. Speeding all of this is CM-ASQRT, a complex version of the Newton-Schulz iteration for matrix square roots that replaces costly exact eigendecomposition with GPU-friendly matrix multiplications.

What would settle it

On a PolSAR dataset, replace the CM-ASQRT approximation in the rectifying and LogEig layers with exact complex Hermitian eigendecomposition, retrain with identical settings, and compare overall accuracy and Kappa; if exact decomposition does not match or beat the reported values, the approximation is not a faithful substitute. A direct check would compute the relative error between eigenvalues and eigenvectors recovered from the five CM-ASQRT iterations and those from exact decomposition on random complex HPD matrices to see whether the iteration converges at all.

Watch

Extended reading notes

Core claim

The central claim is that a complex Hermitian positive definite (HPD) matrix should be learned as a manifold-valued object, not flattened into a vector. The paper defines complex HPD mapping and rectifying layers that operate on the real and imaginary parts of the covariance matrix separately, keeping the output on the HPD manifold, and a complex LogEig layer that maps the manifold to a tangent space. Once in Euclidean space, a complex-valued 3D CNN extracts spatial and scattering context. The authors report that this Riemannian-to-Euclidean pipeline outperforms vector-based complex CNNs and other state-of-the-art PolSAR classifiers, and they attribute the gains to preserving the geometric structure of the covariance matrices rather than to any single Euclidean module.

Load-bearing premise

The results depend on the fast five-step approximation of the matrix square root behaving exactly like the true eigenvalue decomposition inside the network; if that approximation distorts the eigenvalues or eigenvectors, the reported accuracy and speed gains cannot be credited to the manifold design.

Editorial extensions

If this is right

  • Treating PolSAR data as manifold-valued HPD matrices rather than as vectors should improve classification in heterogeneous regions such as buildings and roads, where vectorization loses phase and off-diagonal structure.
  • The Riemannian-to-Euclidean design means existing Euclidean deep networks can be reused after a LogEig projection, so manifold geometry and contextual features are combined rather than chosen between.
  • The CM-ASQRT iteration cuts training time on the Xi'an dataset from about 663 seconds to about 152 seconds, which makes the manifold layers practical for larger PolSAR scenes.
  • The ablation results imply that neither manifold learning alone (80.53% OA on Xi'an) nor a complex 3D CNN alone (93.36%) is sufficient; the reported gains come from the combination of both modules.

Reading between the lines

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

  • The paper leaves implicit that the same HPD manifold layers could be applied to other matrix-valued remote sensing data, such as coherency matrices from PolInSAR, or to any signal whose natural representation is a complex HPD matrix.
  • The paper states that five Newton-Schulz iterations give good performance but does not specify how eigenvectors are recovered from the iteration; a careful reader should check whether the approximate square root is differentiable and whether its gradients remain stable during backpropagation.
  • The training-split experiment (1% to 15%) suggests the method's advantage may be largest in low-label regimes, but the paper does not report per-class errors under extremely scarce training data.
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.

Referee Report

4 major / 6 minor

Summary. The paper proposes HPDNet, a two-module framework for PolSAR image classification. The first module operates on complex Hermitian positive definite (HPD) matrices directly in the Riemannian manifold, applying complex HPD mapping layers, a rectifying (ReEig) layer, and a LogEig layer that projects the manifold representation to a tangent space. The second module is a complex-valued 3D CNN that learns contextual features in Euclidean space. To reduce the cost of eigendecomposition, the authors introduce CM-ASQRT, an iterative complex matrix square-root method based on coupled Newton-Schulz iterations, and report that it accelerates training by a factor of roughly four. Experiments on the Xi'an, Oberpfaffenhofen, and Flevoland datasets report the highest overall accuracy and Kappa coefficient against six baselines, along with an ablation study and runtime comparison.

Significance. If the technical gaps described below are resolved, the paper would introduce a novel and useful direction: to the best of the authors' claim, it is the first complex HPD manifold network for PolSAR data, and the Riemannian-to-Euclidean design is a sensible way to combine manifold geometry with standard contextual deep learning. The reported accuracy gains are substantial on Xi'an and Oberpfaffenhofen, and the ablation study supports the contribution of the HPD module. The paper does not ship code or data, and the accuracy and runtime claims rest on single-run point estimates, so the empirical claims are not yet fully reproducible as written.

major comments (4)
  1. [III.B.2, Eq. (12)] The definition of the rectifying function is internally contradictory: both branches of max(τI, Λ_{k-1})_{ii} return (Λ_{k-1})_{ii}. The second branch should return τ, otherwise the ReEig layer is the identity on the eigenvalues and cannot perform the intended nonlinear thresholding. Please correct Eq. (12) and verify that the implemented layer matches the corrected formula.
  2. [III.B.4, Eqs. (14)-(18)] The claim that 'After several iterations, the SVD decomposition can be approximately obtained' is not supported. The coupled Newton-Schulz iteration computes only approximate C^{1/2} and C^{-1/2}; it does not directly provide the eigenvector matrix U and eigenvalue vector Λ required by the ReEig layer in Eq. (11) and the LogEig layer in Eq. (13). No formula is given that maps (X_k, Z_k) to (U, Λ). Please specify how the eigendecomposition is recovered, or revise the architecture so that the square-root approximation can be used where the eigendecomposition appears. Without this, the described network operations and the Table VI speedup claim are unsupported.
  3. [IV, Tables I-III and Table VI] All accuracy, Kappa, and runtime results are reported as single-run point estimates without error bars, confidence intervals, or repeated trials. This is particularly problematic for the Flevoland dataset, where the margin over PolMPCNN is only 0.64% OA and over HybridCVnet is 0.76% OA; these differences may be within run-to-run variability. Please provide multiple runs with means and standard deviations, or a statistical significance test, to support the claim of consistent superiority.
  4. [III.B.4, Eq. (14)] In the Z update, the variable Y_{k-1} appears but is never defined. If this is a typo for Z_{k-1}X_{k-1} or X_{k-1}Z_{k-1}, the equation should be corrected and the iteration restated. As written, the coupled iteration is incomplete and cannot be implemented.
minor comments (6)
  1. [Throughout] There are numerous typographical errors, including 'Hermit' for 'Hermitian', 'Remianian' for 'Riemannian', 'non-dialog' for 'non-diagonal', 'buidlings' for 'buildings', and 'dateset' for 'dataset'. A thorough language edit is needed.
  2. [IV.B-IV.D] The text refers to figures as 'Figs. 1(b)-(h)', 'Fig. 2(b)', and 'Figs. 2(b)-(h)', but the actual figures are numbered 5, 6, and 7. The figure cross-references should be corrected.
  3. [IV.A.2 and IV.E] The training ratio (10%) and patch size (13×13) are selected using the Xi'an dataset and then applied to the other two datasets. Please justify this transferability or report per-dataset tuning, since such selection can inflate reported performance.
  4. [IV.C.4] The MRF smoothing operation used to refine the classification result is mentioned but not described; no parameters, neighborhood size, or implementation details are provided, which hinders reproducibility.
  5. [References] References [22] and [44] are the same paper, as are [19] and [56]. Please consolidate or otherwise disambiguate them.
  6. [General] No code or trained models are released. Given the reliance on the CM-ASQRT implementation and the exact handling of complex HPD operations, providing code would substantially improve reproducibility.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the reported accuracies are empirical measurements against external baselines, and the few self-citations are not load-bearing.

full rationale

The paper's central claim is that HPDNet achieves higher OA/Kappa than six external baselines on three PolSAR datasets. These numbers are measured on held-out test pixels (10% training / 90% testing), not derived from the method's own assumptions, so no fitted parameter is renamed as a prediction. Hyperparameters such as patch size and training ratio are selected on Xi'an and then transferred, which is standard model selection and does not by construction force the Oberpfaffenhofen or Flevoland results. The Riemannian layers (HPD mapping, ReEig, LogEig) are standard SPDNet-style constructions extended to complex HPD matrices; the LogEig projection is a definitional use of eigendecomposition rather than a predicted outcome. The authors' self-citations ([25], [30]) appear only as related-work references to prior PolSAR methods and metrics and are not used to justify the architecture, uniqueness, or accuracy. The CM-ASQRT section is under-specified (the Newton-Schulz iteration computes matrix square roots, and the paper does not state how U and Lambda are recovered), which is a reproducibility/correctness risk rather than a circularity, because the claimed classification results remain independent empirical outputs. Overall, no load-bearing step reduces to its own input by construction.

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

The central claim rests on standard PolSAR domain assumptions plus one ad hoc computational assumption: the CM-ASQRT iteration accurately replaces exact eigendecomposition. The hyperparameters tau, iteration count, patch size, and training ratio are chosen by hand or by simple experiments, and their values are not reported completely.

free parameters (4)
  • rectifying threshold tau = not specified
    A positive threshold in Eq. (12) that clips small eigenvalues during rectification; the value is hand-chosen and never reported in the paper.
  • CM-ASQRT iteration count = 5
    Number of Newton-Schulz iterations used to approximate eigendecomposition; adopted from [51] without validation for complex HPD matrices.
  • patch size = 13 x 13
    Selected by experiment on the Xi'an dataset (Table V) and then used for all datasets without cross-validation.
  • training sample ratio = 10%
    Selected by experiment (Fig. 8) as the training fraction of labeled pixels.
assumptions (4)
  • domain assumption The PolSAR multi-look covariance matrix C is a complex Hermitian positive definite matrix.
    Section III-A, Eqs. (8-9). This is standard PolSAR theory, though in practice the matrix may be only positive semidefinite without regularization.
  • standard math The congruence mapping W X W^H preserves HPD-ness when W is full-rank.
    Section III-B1, citing [46]. Congruence preserves positive definiteness, so the mapping layer keeps outputs on the manifold.
  • domain assumption The log-Euclidean metric is a suitable distance for the HPD manifold.
    Section II-A, citing [27]. Used to motivate the LogEig layer and the claim that manifold distances are more discriminative than Euclidean distances.
  • ad hoc to paper A five-iteration Newton-Schulz iteration accurately approximates the complex matrix square root and the eigendecomposition used in ReEig and LogEig layers.
    Section III-B4. The paper asserts this without specifying how eigenvectors are extracted from the coupled iteration or validating approximation error.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Riemannian Complex Hermit Positive Definite Convolution Network for Polarimetric SAR Image Classification." pith.science (2026). https://pith.science/paper/MIGZRLOG

@misc{pith2026250208137,
  author       = {Pith},
  title        = {Pith review of: Riemannian Complex Hermit Positive Definite Convolution Network for Polarimetric SAR Image Classification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MIGZRLOG}},
  note         = {Machine review of arXiv:2502.08137}
}
read the original abstract

Deep learning has been extensively utilized for PolSAR image classification. However, most existing methods transform the polarimetric covariance matrix into a real- or complex-valued vector to comply with standard deep learning frameworks in Euclidean space. This approach overlooks the inherent structure of the covariance matrix, which is a complex Hermitian positive definite (HPD) matrix residing in the Riemannian manifold. Vectorization disrupts the matrix structure and misrepresents its geometric properties. To mitigate this drawback, we propose HPDNet, a novel framework that directly processes HPD matrices on the Riemannian manifold. The HPDnet fully considers the complex phase information by decomposing a complex HPD matrix into the real- and imaginarymatrices. The proposed HPDnet consists of several HPD mapping layers and rectifying layers, which can preserve the geometric structure of the data and transform them into a more separable manifold representation. Subsequently, a complex LogEig layer is developed to project the manifold data into a tangent space, ensuring that conventional Euclidean-based deep learning networks can be applied to further extract contextual features for classification. Furthermore, to optimize computational efficiency, we design a fast eigenvalue decomposition method for parallelized matrix processing. Experiments conducted on three real-world PolSAR datasets demonstrate that the proposed method outperforms state-of-the-art approaches, especially in heterogeneous regions.

Figures

Figures reproduced from arXiv: 2502.08137 by the authors.

Figure 1
Figure 1. The framework of the proposed Riemannian complex HPD convolution network. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. The complex HPD mapping layer. 2)Complex HPD Rectifying layer After matrix mapping layer, the original HPD matrix is converted to a new manifold feature space. However, the HPD mapping layer is similar to the linear mapping in SPDnet. A non-linear rectifying is necessary to enhance the discriminat￾ing ability of the mapping features. With non-linear rectifying, the original HPD matrix can be mapped to a new space wi… view at source ↗
Figure 3
Figure 3. The complex HPD Rectifying layer. The complex HPD mapping layer and rectifying layer can be considered as the convolution and ReLu layer similar to CNN. However, they transfer complex HPD matrix from one manifold to another. After applying multiple mapping and rectifying layers, a discriminating feature in Riemannian space can be achieved, which maintains the geometric structure of the PolSAR data and increases the … view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Three datasets with their PauliRGB images and corresponding label [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Classification results of different method on Xi’an area; (a)The label map; (b) CV-CNN; (c) Super [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Classification results of different method on Oberpfaffenhofen area; (a)The label map; (b) CV-CNN; (c) Super [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Classification results of different method on Flevoland area; (a)The label map; (b) CV-CNN; (c) Super [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: The effect of ratio of training samples on classification accuracy. [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 8
Figure 8. Figure 8: Fig.8. It is observed that there is a significant improvement in [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

55 extracted references · 53 canonical work pages

  1. [51]

    Towards faster training of global covariance pooling networks by iterative matrix square root normalization,

    P. Li, J. Xie, Q. Wang, and Z. Gao, “Towards faster training of global covariance pooling networks by iterative matrix square root normalization,” in Proceedings of the IEEE conference on computer vision and pattern recognition , 2018, pp. 947–955

    work page 2018

  2. [1]

    Remote sensing scene classification via multi-branch local attention network,

    S.-B. Chen, Q.-S. Wei, W.-Z. Wang, J. Tang, B. Luo, and Z.-Y . Wang, “Remote sensing scene classification via multi-branch local attention network,” IEEE Transactions on Image Processing, vol. 31, pp. 99–109, 2022

    work page 2022

  3. [2]

    Cdfnet: Cross-domain feature fusion network for polsar terrain classification,

    S. Wang, Z. Sun, T. Bian, Y . Guo, L. Dai, Y . Guo, and L. Jiao, “Cdfnet: Cross-domain feature fusion network for polsar terrain classification,” IEEE Transactions on Geoscience and Remote Sensing , vol. 63, pp. 1– 15, 2025

    work page 2025

  4. [3]

    New generation deep learning for video object detection: A survey,

    L. Jiao, R. Zhang, F. Liu, S. Yang, B. Hou, L. Li, and X. Tang, “New generation deep learning for video object detection: A survey,” IEEE Transactions on Neural Networks and Learning Systems , vol. 33, no. 8, pp. 3195–3215, 2022. JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, JULY 2023 12 TABLE VI RUNNING TIME OF DIFFERENT METHODS ON XI’AN DATA SET (s) tim...

    work page 2022

  5. [4]

    Saan: Similarity-aware attention flow network for change detection with vhr remote sensing images,

    H. Guo, X. Su, C. Wu, B. Du, and L. Zhang, “Saan: Similarity-aware attention flow network for change detection with vhr remote sensing images,” IEEE Transactions on Image Processing , vol. 33, pp. 2599– 2613, 2024

    work page 2024

  6. [5]

    Generalized polarimetric entropy: Polarimetric in- formation quantitative analyses of model-based incoherent polarimetric decomposition,

    W. An and M. Lin, “Generalized polarimetric entropy: Polarimetric in- formation quantitative analyses of model-based incoherent polarimetric decomposition,” IEEE Transactions on Geoscience and Remote Sensing, vol. 59, no. 3, pp. 2041–2057, 2021

    work page 2021

  7. [6]

    Model-based polarimetric sar target decomposition: A scheme to introduce repeat-pass polinsar coherence,

    D. Zhuang, L. Zhang, and B. Zou, “Model-based polarimetric sar target decomposition: A scheme to introduce repeat-pass polinsar coherence,” IEEE Transactions on Geoscience and Remote Sensing , vol. 62, pp. 1– 16, 2024

    work page 2024

  8. [7]

    Variational learning of mixture wishart model for polsar image classification,

    Q. Wu, B. Hou, Z. Wen, and L. Jiao, “Variational learning of mixture wishart model for polsar image classification,” IEEE Transactions on Geoscience and Remote Sensing , vol. 57, no. 1, pp. 141–154, 2019

    work page 2019

Show all 55 references
  1. [8]

    Enhanced pga for dual- polarized isar imaging by exploiting cloude-pottier decomposition,

    Y . Zhang, W. Wang, Z. Guo, and N. Li, “Enhanced pga for dual- polarized isar imaging by exploiting cloude-pottier decomposition,” IEEE Geoscience and Remote Sensing Letters , vol. 21, pp. 1–5, 2024

    2024

  2. [9]

    A reflection symmetry approximation of multilook polarimetric sar data and its application to freeman–durden decomposi- tion,

    W. An and M. Lin, “A reflection symmetry approximation of multilook polarimetric sar data and its application to freeman–durden decomposi- tion,” IEEE Transactions on Geoscience and Remote Sensing , vol. 57, no. 6, pp. 3649–3660, 2019

    2019

  3. [10]

    A variational model for polsar data speckle reduction based on the wishart distribution,

    X. Nie, H. Qiao, and B. Zhang, “A variational model for polsar data speckle reduction based on the wishart distribution,” IEEE Transactions on Image Processing , vol. 24, no. 4, pp. 1209–1222, 2015

    2015

  4. [11]

    Multiscale deep learning for detection and recognition: A comprehensive survey,

    L. Jiao, M. Wang, X. Liu, L. Li, F. Liu, Z. Feng, S. Yang, and B. Hou, “Multiscale deep learning for detection and recognition: A comprehensive survey,” IEEE Transactions on Neural Networks and Learning Systems, vol. 36, no. 4, pp. 5900–5920, 2025

    2025

  5. [12]

    Dual-branch cnn incorporating multiscale svd profile for polsar image classification,

    N. Das, A. Bortiew, S. Patra, and L. Bruzzone, “Dual-branch cnn incorporating multiscale svd profile for polsar image classification,” IEEE Transactions on Geoscience and Remote Sensing , vol. 62, pp. 1–12, 2024

    2024

  6. [13]

    Contrastive learning-based dual dynamic gcn for sar image scene classification,

    F. Liu, X. Qian, L. Jiao, X. Zhang, L. Li, and Y . Cui, “Contrastive learning-based dual dynamic gcn for sar image scene classification,” IEEE Transactions on Neural Networks and Learning Systems , vol. 35, no. 1, pp. 390–404, 2024

    2024

  7. [14]

    Psat-gan: Efficient adversarial attacks against holistic scene understanding,

    L. Wang and K.-J. Yoon, “Psat-gan: Efficient adversarial attacks against holistic scene understanding,” IEEE Transactions on Image Processing , vol. 30, pp. 7541–7553, 2021

    2021

  8. [15]

    Efficient swin transformer for remote sensing image super-resolution,

    X. Kang, P. Duan, J. Li, and S. Li, “Efficient swin transformer for remote sensing image super-resolution,” IEEE Transactions on Image Processing, vol. 33, pp. 6367–6379, 2024

    2024

  9. [16]

    Evolutionary complex- valued cnn for polsar image classification,

    M. Zhang, J. Shi, L. Liu, X. Wang, and L. Jiao, “Evolutionary complex- valued cnn for polsar image classification,” in 2024 International Joint Conference on Neural Networks (IJCNN) , 2024, pp. 1–8

    2024

  10. [17]

    Polsar image classification via complex-valued multi-scale convolutional neural network,

    L. Zhang, S. Zhang, H. Dong, and D. Lu, “Polsar image classification via complex-valued multi-scale convolutional neural network,” in IGARSS 2020 - 2020 IEEE International Geoscience and Remote Sensing Sym- posium, 2020, pp. 200–203

    2020

  11. [18]

    Spectral–spatial classification of hyper- spectral imagery with 3d convolutional neural network,

    Y . Li, H. Zhang, and Q. Shen, “Spectral–spatial classification of hyper- spectral imagery with 3d convolutional neural network,”Remote Sensing, vol. 9, no. 1, pp. 1–20, 2017

    2017

  12. [20]

    c2n2: Complex-valued contourlet neural network,

    M. Liu, L. Jiao, X. Liu, L. Li, F. Liu, S. Yang, Y . Guo, and P. Chen, “c2n2: Complex-valued contourlet neural network,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing , vol. 17, pp. 4478–4491, 2024

    2024

  13. [21]

    Unsupervised classification of polarimetric sar images via riemannian sparse coding,

    N. Zhong, W. Yang, A. Cherian, X. Yang, G.-S. Xia, and M. Liao, “Unsupervised classification of polarimetric sar images via riemannian sparse coding,” IEEE Transactions on Geoscience and Remote Sensing , vol. 55, no. 9, pp. 5381–5390, 2017

    2017

  14. [22]

    A riemannian network for spd matrix learning,

    Z. Huang and L. Van Gool, “A riemannian network for spd matrix learning,” Proceedings of the AAAI Conference on Artificial Intelligence, vol. 31, no. 1, Feb. 2017

    2017

  15. [23]

    U-spdnet: An spd manifold learning-based neural network for visual classification,

    R. Wang, X.-J. Wu, T. Xu, C. Hu, and J. Kittler, “U-spdnet: An spd manifold learning-based neural network for visual classification,” Neural networks, vol. 161, pp. 382–396, 2023

    2023

  16. [24]

    Deep manifold-to-manifold transforming network for skeleton-based action recognition,

    T. Zhang, W. Zheng, Z. Cui, Y . Zong, C. Li, X. Zhou, and J. Yang, “Deep manifold-to-manifold transforming network for skeleton-based action recognition,” IEEE transactions on multimedia , vol. 22, no. 11, pp. 2926–2937, 2020

    2020

  17. [25]

    Riemannian nearest-regularized subspace classifica- tion for polarimetric sar images,

    J. Shi and H. Jin, “Riemannian nearest-regularized subspace classifica- tion for polarimetric sar images,” IEEE Geoscience and Remote Sensing Letters, vol. 19, pp. 1–5, 2022

    2022

  18. [26]

    Log-determinant divergences revisited: Alpha-beta and gamma log-det divergences,

    A. Cichocki, S. Cruces, and S.-i. Amari, “Log-determinant divergences revisited: Alpha-beta and gamma log-det divergences,” Entropy, vol. 17, no. 5, pp. 2988–3034, 2015

    2015

  19. [27]

    H. Q. Minh and V . Murino, Covariances in computer vision and machine learning. Morgan & Claypool Publishers, 2017

    2017

  20. [28]

    Polsar target recognition with cnns optimizing discrete polarimetric correlation pattern,

    H. Lin, J. Yang, and F. Xu, “Polsar target recognition with cnns optimizing discrete polarimetric correlation pattern,” IEEE Transactions on Geoscience and Remote Sensing , vol. 62, pp. 1–14, 2024

    2024

  21. [29]

    Mfnet: A novel gnn-based multi-level feature network with superpixel priors,

    S. Li, F. Liu, L. Jiao, P. Chen, X. Liu, and L. Li, “Mfnet: A novel gnn-based multi-level feature network with superpixel priors,” IEEE Transactions on Image Processing , vol. 31, pp. 7306–7321, 2022

    2022

  22. [30]

    Cnn-improved superpixel-to- pixel fuzzy graph convolution network for polsar image classification,

    J. Shi, T. He, S. Ji, M. Nie, and H. Jin, “Cnn-improved superpixel-to- pixel fuzzy graph convolution network for polsar image classification,” IEEE Transactions on Geoscience and Remote Sensing , vol. 61, pp. 1– 18, 2023

    2023

  23. [31]

    Vtae: Variational transformer autoencoder with manifolds learning,

    P. Shamsolmoali, M. Zareapoor, H. Zhou, D. Tao, and X. Li, “Vtae: Variational transformer autoencoder with manifolds learning,” IEEE Transactions on Image Processing , vol. 32, pp. 4486–4500, 2023

    2023

  24. [32]

    Uiu-net: U-net in u-net for infrared small object detection,

    X. Wu, D. Hong, and J. Chanussot, “Uiu-net: U-net in u-net for infrared small object detection,” IEEE Transactions on Image Processing, vol. 32, pp. 364–376, 2023

    2023

  25. [33]

    Polarimetric sar image classification based on hierarchical scattering-spatial interaction transformer,

    J. Geng, Y . Zhang, and W. Jiang, “Polarimetric sar image classification based on hierarchical scattering-spatial interaction transformer,” IEEE Transactions on Geoscience and Remote Sensing , vol. 62, pp. 1–14, 2024

    2024

  26. [34]

    Three-channel convolutional neural network for polarimetric sar images classification,

    W. Hua, W. Xie, and X. Jin, “Three-channel convolutional neural network for polarimetric sar images classification,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing , vol. 13, pp. 4895–4907, 2020

    2020

  27. [35]

    Incremental land cover classification via label strategy and adap- tive weights,

    B. Ren, Z. Wang, B. Hou, B. Liu, Z. Wu, J. Chanussot, and L. Jiao, “Incremental land cover classification via label strategy and adap- tive weights,” IEEE Transactions on Geoscience and Remote Sensing , vol. 61, pp. 1–15, 2023

    2023

  28. [36]

    A novel causal inference-guided feature enhancement framework for polsar image classification,

    H. Dong, L. Si, W. Qiang, L. Zhang, J. Yu, Y . Wu, C. Zheng, and F. Sun, “A novel causal inference-guided feature enhancement framework for polsar image classification,” IEEE Transactions on Geoscience and Remote Sensing, vol. 62, pp. 1–16, 2024

    2024

  29. [37]

    Multiscale superpixel-guided weighted graph convolutional network for polarimetric sar image classification,

    R. Wang, Y . Nie, and J. Geng, “Multiscale superpixel-guided weighted graph convolutional network for polarimetric sar image classification,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 17, pp. 3727–3741, 2024

    2024

  30. [38]

    Complex-valued 3- d convolutional neural network for polsar image classification,

    X. Tan, M. Li, P. Zhang, Y . Wu, and W. Song, “Complex-valued 3- d convolutional neural network for polsar image classification,” IEEE Geoscience and Remote Sensing Letters , vol. 17, no. 6, pp. 1022–1026, 2020

    2020

  31. [39]

    Complex contourlet- cnn for polarimetric sar image classification,

    L. Li, L. Ma, L. Jiao, F. Liu, Q. Sun, and J. Zhao, “Complex contourlet- cnn for polarimetric sar image classification,” Pattern Recognition, vol. 100, p. 107110, 2020

    2020

  32. [40]

    Unsupervised complex- valued sparse feature learning for polsar image classification,

    Y . Jiang, M. Li, P. Zhang, X. Tan, and W. Song, “Unsupervised complex- valued sparse feature learning for polsar image classification,” IEEE Transactions on Geoscience and Remote Sensing , vol. 60, pp. 1–16, 2022

    2022

  33. [41]

    Unified classification framework for multipolarization and dual-frequency sar,

    M. Liu, Y . Deng, D. Wang, X. Liu, and C. Wang, “Unified classification framework for multipolarization and dual-frequency sar,” IEEE Trans- actions on Geoscience and Remote Sensing , vol. 61, pp. 1–13, 2023. JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, JULY 2023 13

    2023

  34. [42]

    Riemannian-gradient-based learning on the complex matrix- hypersphere,

    S. Fiori, “Riemannian-gradient-based learning on the complex matrix- hypersphere,” IEEE transactions on neural networks , vol. 22, no. 12, pp. 2132–2138, 2011

    2011

  35. [43]

    Recursive frechet mean computa- tion on the grassmannian and its applications to computer vision,

    R. Chakraborty and B. C. Vemuri, “Recursive frechet mean computa- tion on the grassmannian and its applications to computer vision,” in Proceedings of the IEEE International Conference on Computer Vision , 2015, pp. 4229–4237

    2015

  36. [44]

    A riemannian network for spd matrix learn- ing,

    Z. Huang and L. Van Gool, “A riemannian network for spd matrix learn- ing,” in Proceedings of the AAAI conference on artificial intelligence , vol. 31, no. 1, 2017

    2017

  37. [45]

    A statistical recurrent model on the manifold of symmetric positive definite matrices,

    R. Chakraborty, C.-H. Yang, X. Zhen, M. Banerjee, D. Archer, D. Vail- lancourt, V . Singh, and B. Vemuri, “A statistical recurrent model on the manifold of symmetric positive definite matrices,” Advances in neural information processing systems , vol. 31, 2018

    2018

  38. [46]

    Symnet: A simple symmetric positive definite manifold deep learning method for image set classification,

    R. Wang, X.-J. Wu, and J. Kittler, “Symnet: A simple symmetric positive definite manifold deep learning method for image set classification,” IEEE Transactions on Neural Networks and Learning Systems , vol. 33, no. 5, pp. 2208–2222, 2021

    2021

  39. [47]

    Neural architecture search of spd manifold net- works.(2021),

    R. SUKTHANKER, Z. HUANG, S. KUMAR, E. ENDSJO, Y . WU, and G. L. V AN, “Neural architecture search of spd manifold net- works.(2021),” in Proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI-21), Montreal , 2021, pp. 19–26

    2021

  40. [48]

    Multiple riemannian manifold-valued descriptors based image set classification with multi- kernel metric learning,

    R. Wang, X.-J. Wu, K.-X. Chen, and J. Kittler, “Multiple riemannian manifold-valued descriptors based image set classification with multi- kernel metric learning,” IEEE Transactions on Big Data , vol. 8, no. 3, pp. 753–769, 2020

    2020

  41. [49]

    Manifoldnet: A deep neural network for manifold-valued data with applications,

    R. Chakraborty, J. Bouza, J. H. Manton, and B. C. Vemuri, “Manifoldnet: A deep neural network for manifold-valued data with applications,” IEEE Transactions on Pattern Analysis and Machine Intelligence , vol. 44, no. 2, pp. 799–810, 2020

    2020

  42. [50]

    Rie- mannian local mechanism for spd neural networks,

    Z. Chen, T. Xu, X.-J. Wu, R. Wang, Z. Huang, and J. Kittler, “Rie- mannian local mechanism for spd neural networks,” in Proceedings of the AAAI Conference on Artificial Intelligence , vol. 37, no. 6, 2023, pp. 7104–7112

    2023

  43. [52]

    Superpixel-based crop- land classification of sar image with statistical texture and polarization features,

    Q. Chen, W. Cao, J. Shang, J. Liu, and X. Liu, “Superpixel-based crop- land classification of sar image with statistical texture and polarization features,” IEEE Geoscience and Remote Sensing Letters , vol. 19, pp. 1–5, 2022

    2022

  44. [53]

    Deep fuzzy graph convolutional networks for polsar imagery pixelwise classification,

    H. Liu, T. Zhu, F. Shang, Y . Liu, D. Lv, and S. Yang, “Deep fuzzy graph convolutional networks for polsar imagery pixelwise classification,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 14, pp. 504–514, 2021

    2021

  45. [54]

    Adaptive mask sampling and manifold to euclidean subspace learning with distance covariance representation for hyperspectral image classification,

    M. Li, W. Li, Y . Liu, Y . Huang, and G. Yang, “Adaptive mask sampling and manifold to euclidean subspace learning with distance covariance representation for hyperspectral image classification,”IEEE Transactions on Geoscience and Remote Sensing , vol. 61, pp. 1–18, 2023

    2023

  46. [55]

    Polarimetric multipath convolutional neural network for polsar image classification,

    Y . Cui, F. Liu, L. Jiao, Y . Guo, X. Liang, L. Li, S. Yang, and X. Qian, “Polarimetric multipath convolutional neural network for polsar image classification,” IEEE Transactions on Geoscience and Remote Sensing , vol. 60, pp. 1–18, 2022

    2022

  47. [56]

    Polsar image classification using a hybrid complex- valued network (hybridcvnet),

    M. Q. Alkhatib, “Polsar image classification using a hybrid complex- valued network (hybridcvnet),” IEEE Geoscience and Remote Sensing Letters, vol. 21, pp. 1–5, 2024

    2024

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.