Framelet-Based Algorithm for Segmentation of Tubular Structures

Cai, Xiaohao; Chan, Raymond H.; Morigi, Serena; Sgallari, Fiorella

doi:10.1007/978-3-642-24785-9_35

Cited by 15 publications

(11 citation statements)

References 24 publications

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“…We note that our method converges in 9 iterations, see the third column in Table I. 9 (a) (b) (c) volumetric data set has been extracted from a 120 × 448 × 540 MRA image of the brain-neck vasculature system, see Fig. 5(a).…”

Section: Numerical Examplesmentioning

confidence: 99%

Vessel Segmentation in Medical Imaging Using a Tight-Frame--Based Algorithm

Cai¹,

Chan²,

Morigi³

et al. 2013

SIAM J. Imaging Sci.

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Tight-frame, a generalization of orthogonal wavelets, has been used successfully in various problems in image processing, including inpainting, impulse noise removal, super-resolution image restoration, etc. Segmentation is the process of identifying object outlines within images. There are quite a few efficient algorithms for segmentation that depend on the variational approach and the partial differential equation (PDE) modeling. In this paper, we propose to apply the tight-frame approach to automatically identify tube-like structures such as blood vessels in Magnetic Resonance Angiography (MRA) images. Our method iteratively refines a region that encloses the possible boundary or surface of the vessels. In each iteration, we apply the tight-frame algorithm to denoise and smooth the possible boundary and sharpen the region. We prove the convergence of our algorithm. Numerical experiments on real 2D/3D MRA images demonstrate that our method is very efficient with convergence usually within a few iterations, and it outperforms existing PDE and variational methods as it can extract more tubular objects and fine details in the images.

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Section: Numerical Examplesmentioning

confidence: 99%

Vessel Segmentation in Medical Imaging Using a Tight-Frame--Based Algorithm

Cai¹,

Chan²,

Morigi³

et al. 2013

SIAM J. Imaging Sci.

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“…6. The results show that the measures of the maximum and mean of the line integral (i.e., eqn (8) and eqn (12)) perform similarly, acting as generic low-pass filters with no distinctly selective curve enhancement, see (a)-(b) in Fig. 5 and Fig.…”

Section: A Performance In 2dmentioning

confidence: 93%

3D Orientation Field Transform

Yeung,

Cai,

Liang

et al. 2020

Preprint

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The two-dimensional (2D) orientation field transform has been proved to be effective at enhancing 2D contours and curves in images by means of top-down processing. It, however, has no counterpart in three-dimensional (3D) images due to the extremely complicated orientation in 3D compared to 2D. Practically and theoretically, the demand and interest in 3D can only be increasing. In this work, we modularise the concept and generalise it to 3D curves. Different modular combinations are found to enhance curves to different extents and with different sensitivity to the packing of the 3D curves. In principle, the proposed 3D orientation field transform can naturally tackle any dimensions. As a special case, it is also ideal for 2D images, owning simpler methodology compared to the previous 2D orientation field transform. The proposed method is demonstrated with several transmission electron microscopy tomograms ranging from 2D curve enhancement to, the more important and interesting, 3D ones.

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“…In additional to the methods above, approaches based on wavelets and tight frames [6,14,15,74] have been proposed for segmentation. In [14,15], a tight-frame based segmentation method was designed for a vessel segmentation problem in medical imaging. The major advantage of this method is the ability to segment twisted, convoluted and occluded structures without user interactions.…”

mentioning

confidence: 99%

“…In this paper, we devise an iterative framework for segmenting spherical images using wavelets defined on the sphere, extending the method proposed in [14,15]. The first stage of the method, as a preprocessing step, suppresses noise in the given data by soft thresholding wavelet coefficients.…”

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confidence: 99%

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Wavelet-based segmentation on the sphere

Cai

Wallis

Chan

et al. 2020

Pattern Recognition

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Segmentation is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational approach and partial differential equation modelling. Wavelets have been used successfully in various problems in image processing, including segmentation, inpainting, noise removal, super-resolution image restoration, and many others. Wavelets on the sphere have been developed to solve such problems for data defined on the sphere, which arise in numerous fields such as cosmology and geophysics. In this work, we propose a wavelet-based method to segment images on the sphere, accounting for the underlying geometry of spherical data. Our method is a direct extension of the tight-frame based segmentation method used to automatically identify tube-like structures such as blood vessels in medical imaging. It is compatible with any arbitrary type of wavelet frame defined on the sphere, such as axisymmetric wavelets, directional wavelets, curvelets, and hybrid wavelet constructions. Such an approach allows the desirable properties of wavelets to be naturally inherited in the segmentation process. In particular, directional wavelets and curvelets, which were designed to efficiently capture directional signal content, provide additional advantages in segmenting images containing prominent directional and curvilinear features. We present several numerical experiments, applying our wavelet-based segmentation method, as well as the common K-means method, on realworld spherical images, including an Earth topographic map, a light probe image, solar data-sets, and spherical retina images. These experiments demonstrate the superiority of our method and show that it is capable of segmenting different kinds of spherical images, including those with prominent directional features. Moreover, our algorithm is efficient with convergence usually within a few iterations.

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Framelet-Based Algorithm for Segmentation of Tubular Structures

Cited by 15 publications

References 24 publications

Vessel Segmentation in Medical Imaging Using a Tight-Frame--Based Algorithm

Vessel Segmentation in Medical Imaging Using a Tight-Frame--Based Algorithm

3D Orientation Field Transform

Wavelet-based segmentation on the sphere

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