Two-stage image segmentation based on nonconvex<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si18.svg"><mml:mrow><mml:msub><mml:mi>ℓ</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mspace width="0.16em"/><mml:mo linebreak="goodbreak">−</mml:mo><mml:mspace width="0.16em"/><mml:msub><mml:mi>ℓ</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow></mml:math>approximation and thresholding

Wu, Tingting; Shao, Jinbo; Gu, Xiaoyu; Ng, Michael K.; Zeng, Tieyong

doi:10.1016/j.amc.2021.126168

Cited by 16 publications

(8 citation statements)

References 52 publications

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“…In our numerical experiments, the AITV Poisson SaT/SLaT yielded high-quality segmentation results within seconds for various grayscale and color images corrupted with Poisson noise and/or blur. For future directions, we are interested in other nonconvex regularization, such as ℓ 1 /ℓ 2 on the gradient (Wang et al, 2021(Wang et al, , 2022Wu et al, 2022a), ℓ p , 0 < p < 1, on the gradient (Hintermüller and Wu, 2013;Li Y. et al, 2020;Wu et al, 2021b), and transformed total variation (Huo et al, 2022), as alternatives to AITV. On the other hand, we can develop AITV variants of weighted TV or adaptive TV (Wu et al, 2021a; Zhang et al, 2022).…”

Section: Discussionmentioning

confidence: 99%

Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise

Bui

Lou

Park

et al. 2023

Front. Comput. Sci.

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In this paper, we aim to segment an image degraded by blur and Poisson noise. We adopt a smoothing-and-thresholding (SaT) segmentation framework that finds a piecewise-smooth solution, followed by k-means clustering to segment the image. Specifically for the image smoothing step, we replace the least-squares fidelity for Gaussian noise in the Mumford-Shah model with a maximum posterior (MAP) term to deal with Poisson noise and we incorporate the weighted difference of anisotropic and isotropic total variation (AITV) as a regularization to promote the sparsity of image gradients. For such a nonconvex model, we develop a specific splitting scheme and utilize a proximal operator to apply the alternating direction method of multipliers (ADMM). Convergence analysis is provided to validate the efficacy of the ADMM scheme. Numerical experiments on various segmentation scenarios (grayscale/color and multiphase) showcase that our proposed method outperforms a number of segmentation methods, including the original SaT.

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Section: Discussionmentioning

confidence: 99%

Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise

Bui

Lou

Park

et al. 2023

Front. Comput. Sci.

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“…Empirical studies [33], [59] demonstrate that for p ∈ [1/2, 1), as p decreases, the solution becomes sparser by p minimization, but for p ∈ (0, 1/2), the performance becomes no longer significant. Moreover, it is used in image deconvolution [60], [61], hyperspectral unmixing [62], computed topography reconstruction [63], and image segmentation [64], [65]. Numerically, in compressed sensing, a small value is added to z i to avoid blowup in the subgradient when z i = 0.…”

Section: B Regularization Penaltymentioning

confidence: 99%

Improving Network Slimming With Nonconvex Regularization

et al. 2021

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Convolutional neural networks (CNNs) have developed to become powerful models for various computer vision tasks ranging from object detection to semantic segmentation. However, most of the state-of-the-art CNNs cannot be deployed directly on edge devices such as smartphones and drones, which need low latency under limited power and memory bandwidth. One popular, straightforward approach to compressing CNNs is network slimming, which imposes 1 regularization on the channel-associated scaling factors via the batch normalization layers during training. Network slimming thereby identifies insignificant channels that can be pruned for inference. In this paper, we propose replacing the penalty with an alternative nonconvex, sparsity-inducing penalty in order to yield a more compressed and/or accurate CNN architecture. We investigate p (0 < p < 1), transformed 1 (T 1 ), minimax concave penalty (MCP), and smoothly clipped absolute deviation (SCAD) due to their recent successes and popularity in solving sparse optimization problems, such as compressed sensing and variable selection. We demonstrate the effectiveness of network slimming with nonconvex penalties on VGGNet, Densenet, and Resnet on standard image classification datasets. Based on the numerical experiments, T 1 preserves model accuracy against channel pruning, 1/2,3/4 yield better compressed models with similar accuracies after retraining as 1 , and MCP and SCAD provide more accurate models after retraining with similar compression as 1 . Network slimming with T 1 regularization also outperforms the latest Bayesian modification of network slimming in compressing a CNN architecture in terms of memory storage while preserving its model accuracy after channel pruning.INDEX TERMS Convolutional neural networks (CNN), machine learning, deep learning, network pruning, nonconvex optimization

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“…Note that the convex approximation of the length term in (1) by Ω |∇u| dx in (3) is not optimal, since the Hausdorff measure is nonconvex. For a better approximation, Wu et al [71] adopted a nonconvex term Ω |∇u| p dx for (0 < p < 1), referred to as TV p , leading to a nonconvex problem,…”

Section: Introductionmentioning

confidence: 99%

A Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-Isotropic Total Variation

Bui¹,

Lou²,

Park³

et al. 2022

Preprint

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In this paper, we propose a multi-stage image segmentation framework that incorporates a weighted difference of anisotropic and isotropic total variation (AITV). The segmentation framework generally consists of two stages: smoothing and thresholding, thus referred to as SaT. In the first stage, a smoothed image is obtained by an AITV-regularized Mumford-Shah (MS) model, which can be solved efficiently by the alternating direction method of multipliers (ADMM) with a closed-form solution of a proximal operator of the 1 − α 2 regularizer. Convergence of the ADMM algorithm is analyzed. In the second stage, we threshold the smoothed image by k-means clustering to obtain the final segmentation result. Numerical experiments demonstrate that the proposed segmentation framework is versatile for both grayscale and color images, efficient in producing high-quality segmentation results within a few seconds, and robust to input images that are corrupted with noise, blur, or both. We compare the AITV method with its original convex and nonconvex TV p (0 < p < 1) counterparts, showcasing the qualitative and quantitative advantages of our proposed method.

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Two-stage image segmentation based on nonconvexℓ2−ℓpapproximation and thresholding

Cited by 16 publications

References 52 publications

Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise

Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise

Improving Network Slimming With Nonconvex Regularization

A Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-Isotropic Total Variation

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