Efficient Color Image Segmentation via Quaternion-based $$L_1/L_2$$ Regularization

Wu, Tingting; Mao, Zhihui; Li, Zeyu; Zeng, Yonghua; Zeng, Tieyong

doi:10.1007/s10915-022-01970-0

Cited by 10 publications

(6 citation statements)

References 44 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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“…Voronin et al [59] proposed an automated segmentation analysis based on the modified Chan and Vese method using the quaternion anisotropic TV algorithm under Merced data (https://vision.ucmerced.edu/datasets/, accessed on 1 March 2023). Wu et al [18] extended the l 1 /l 2 regularizer to the quaternion domain for image segmentation under the Weizmann (https://www.wisdom.weizmann. ac.il/vision/Seg_Evaluation_DB/dl.html, accessed on 1 March 2023) and Berkeley (https: //www2.eecs.berkeley.edu/Research/Projects/CS/vision/grouping/segbench/, accessed on 1 March 2023) datasets.…”

Section: Tv-based Modelsmentioning

confidence: 99%

“…Then we can represent a color pixel as a quaternion number, i.e., u = u 0 + u r i + u g j + u b k. Please see Figure 1 for a better understanding. As quaternions have a real part u 0 and imaginary parts (u r , u g , u b ), the quaternion representation for color pixels should be the pure quaternion u = u r i + u g j + u b k. However, in basic tasks such as image denoising or other tasks with simple methods, e.g., [18], we do not affect the real part of the quaternion. Therefore, for better understanding, we use the quaternion representation u = u 0 + u r i + u g j + u b k. In some works, such as singular value decomposition, the real part of the quaternion is iterated to be nonzero; thus, a zero constraint is needed for the real part.…”

Section: Introductionmentioning

confidence: 99%

Review of Quaternion-Based Color Image Processing Methods

Huang

Gao

2023

Mathematics

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Images are a convenient way for humans to obtain information and knowledge, but they are often destroyed throughout the collection or distribution process. Therefore, image processing evolves as the need arises, and color image processing is a broad and active field. A color image includes three distinct but closely related channels (red, green, and blue (RGB)). Compared to directly expressing color images as vectors or matrices, the quaternion representation offers an effective alternative. There are several papers and works on this subject, as well as numerous definitions, hypotheses, and methodologies. Our observations indicate that the quaternion representation method is effective, and models and methods based on it have rapidly developed. Hence, the purpose of this paper is to review and categorize past methods, as well as study their efficacy and computational examples. We hope that this research will be helpful to academics interested in quaternion representation.

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“…The color channel of a pixel can be denoted as the imaginary parts of the quaternion number: (𝑢 ; , 𝑢 < , 𝑢 = ), then the colored pixel as a quaternion number will look like: 𝑢̇= 𝑢 / + 𝑢 ; 𝑖 + 𝑢 < 𝑗 + 𝑢 = 𝑘, where 𝑖, 𝑗, 𝑘 are the quaternion unit basis, 𝑢 / -is a real part. For basic tasks, such as, for example, [14], the real part of the quaternion is not affected, then the color pixel, as the number of the quaternion, will look: 𝑢̇= 𝑢 ; 𝑖 + 𝑢 < 𝑗 + 𝑢 = 𝑘 [15] (Fig. 3).…”

Section: Gabor Quaternionic Fourier Transformmentioning

confidence: 99%

Action recognition algorithm from multimodal images for human-robot collaboration systems

Voronin¹,

Zhdanova²,

Semenishchev³

et al. 2023

Multimodal Sensing and Artificial Intelligence: Technologies and Applications III

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Automation of production processes using robots is a priority for developing many industrial enterprises. Human-machine interaction is a key component of such control infrastructure. The proposed algorithm is a four-stage procedure: (a) fusion information from multimodal sensors based on the quaternion model, (b) image preprocessing using a 3D Gabor filter, (c) a descriptor calculation using 3D local binary dense micro-block difference with skeleton points, and (d) classification. The proposed algorithm is based on capturing 3D sub-volumes located inside a video sequence patch and calculating the difference in intensities between these sub-volumes; for intensified motion, used the convolution with a bank of 3D arbitrarily oriented Gabor filters and calculating 3D local binary dense micro-block difference. A program was developed for transmitting information about the target points of the robot's movement through a virtual TCP / IP port and a script for working out the target points in the simulation environment. To test the effectiveness of the proposed algorithm, we simulate an action recognition system for Human-robot collaboration in the RoboGuide environment.

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Efficient Color Image Segmentation via Quaternion-based $$L_1/L_2$$ Regularization

Cited by 10 publications

References 44 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

Review of Quaternion-Based Color Image Processing Methods

Action recognition algorithm from multimodal images for human-robot collaboration systems

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