A Weighted Difference of Anisotropic and Isotropic Total Variation for Relaxed Mumford--Shah Color and Multiphase Image Segmentation

Bui, Kevin; Park, Fredrick; Lou, Yifei; Xin, Jack

doi:10.1137/20m1337041

Cited by 15 publications

(18 citation statements)

References 65 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, we propose a new SaT/SLaT framework by replacing the convex TV term in the original formulation (3) with the AITV regularization for a better approximation of the curve length. As reported in our earlier work [7], AITV is effective in preserving edges and corners along the boundaries of the segmentation especially under the presence of noise and blur. To enhance the efficiency of the AITV-regularized segmentation model, we utilize the closed-form solution [49] of the proximal operator for 1 − α 2 to avoid nested loops of DCA as considered in [7].…”

Section: Introductionsupporting

confidence: 64%

“…As reported in our earlier work [7], AITV is effective in preserving edges and corners along the boundaries of the segmentation especially under the presence of noise and blur. To enhance the efficiency of the AITV-regularized segmentation model, we utilize the closed-form solution [49] of the proximal operator for 1 − α 2 to avoid nested loops of DCA as considered in [7]. The main contributions of this paper are summarized as follows:…”

Section: Introductionsupporting

confidence: 64%

“…We show that our model ( 7) admits a global solution in Section 3.1. To find a solution to (7), we describe in Section 3.2 the ADMM scheme with its convergence analysis conducted in Section 3.3. The overall AITV SaT/SLaT framework for segmentation is summarized in Algorithm 1.…”

Section: Final Stage: Thresholdingmentioning

confidence: 99%

“…In Theorem 3.1 we establish the existence of a global solution to (7) by showing that its objective function F is coercive in Lemma 3.1.…”

Section: Model Analysismentioning

confidence: 99%

“…AITV is robust against impulsive noise for image reconstruction [45]. AITV also yields satisfactory segmentation results in the CV model and the fuzzy region competition model [7]. However, these models are solved by a difference-of-convex algorithm (DCA) [41,57,58] that requires solving a TV-type subproblem iteratively, thus being computationally expensive.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Bui¹,

Lou²,

Park³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionsupporting

confidence: 64%

Section: Introductionsupporting

confidence: 64%

Section: Final Stage: Thresholdingmentioning

confidence: 99%

“…In Theorem 3.1 we establish the existence of a global solution to (7) by showing that its objective function F is coercive in Lemma 3.1.…”

Section: Model Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Bui¹,

Lou²,

Park³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Adaptive‐weighted high order TV algorithm for sparse‐view CT reconstruction

Zhou

et al. 2023

Medical Physics

View full text Add to dashboard Cite

BackgroundWith the development of low‐dose computed tomography (CT), incomplete data reconstruction has been widely concerned. The total variation (TV) minimization algorithm can accurately reconstruct images from sparse or noisy data.PurposeHowever, the traditional TV algorithm ignores the direction of structures in images, leading to the loss of edge information and block artifacts when the object is not piecewise constant. Since the anisotropic information can facilitate preserving the edge and detail information in images, we aim to improve the TV algorithm in terms of reconstruction accuracy via this approach.MethodsIn this paper, we propose an adaptive‐weighted high order total variation (awHOTV) algorithm. We construct the second order TV‐norm using the second order gradient, adapt the anisotropic edge property between neighboring image pixels, adjust the local image‐intensity gradient to keep edge information, and design the corresponding Chambolle‐Pock (CP) solving algorithm. Implementing the proposed algorithm, comprehensive studies are conducted in the ideal projection data experiment where the Structural similarity (SSIM), Root Mean Square Error (RMSE), Contrast to noise ratio (CNR), and modulation transform function (MTF) curves are utilized to evaluate the quality of reconstructed images in statism, structure, spatial resolution, and contrast, respectively. In the noisy data experiment, we further use the noise power spectrum (NPS) curve to evaluate the reconstructed images and compare it with other three algorithms.ResultsWe use the 2D slice in the XCAT phantom, 2D slice in TCIA Challenge data and FORBILD phantom as simulation phantoms and use real bird data for real verification. The results show that, compared with the traditional TV and FBP algorithms, the awHOTV has better performance in terms of RMSE, SSIM, and Pearson correlation coefficient (PCC) under the projected data with different sparsity. In addition, the awHOTV algorithm is robust against the noise of different intensities.ConclusionsThe proposed awHOTV method can reconstruct the images with high accuracy under sparse or noisy data. The awHOTV solves the strip artifacts caused by sparse data in the FBP method. Compared with the TV method, the awHOTV can effectively suppress block artifacts and has good detail protection ability.

show abstract