Efficient numerical schemes for gradient vector flow

Boukerroui, Djamal

doi:10.1016/j.patcog.2011.07.007

Cited by 13 publications

(8 citation statements)

References 26 publications

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“…Furthermore, in homogeneous regions where the intensity is nearly constant, the magnitudes of gradient vectors are close to zero. Several researchers point out this limitations and propose alternative solutions to increase the capture range of the external force [18]. The most popular solution is the gradient vector flow [19].…”

Section: Gradient Vector Flowmentioning

confidence: 99%

Watershed based intelligent scissors

Więcławek

Piętka

2015

Computerized Medical Imaging and Graphics

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Section: Gradient Vector Flowmentioning

confidence: 99%

Watershed based intelligent scissors

Więcławek

Piętka

2015

Computerized Medical Imaging and Graphics

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“…Equations (25) and (26) are the sign function. Therefore, the CN-GGVF field is simply rewritten as v cn−ggvf (x, y) = sgn (u (x, y)) , sgn (v (x, y)) (27) where sgn (·) denotes the sign function.…”

Section: A Component-normalized Ggvf Fieldmentioning

confidence: 99%

“…Additionally, automatic initialization methods of the GVF snake can be found in [22] and [23]. Efficient numerical schemes are applied to speed up the GVF computation [24], [25].…”

mentioning

confidence: 99%

Generalized Gradient Vector Flow for Snakes: New Observations, Analysis, and Improvement

Qin

Zhu

Zhao

et al. 2013

IEEE Trans. Circuits Syst. Video Technol.

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Snakes, or active contours, have been widely used in image processing applications. An external force for snakes called gradient vector flow (GVF) attempts to address traditional snake problems of initialization sensitivity and poor convergence to concavities, while generalized GVF (GGVF) aims to improve GVF snake convergence to long and thin indentations (LTIs). In this paper, we find and show that both GVF and GGVF snakes essentially yield the same performance in capturing LTIs of odd widths, and generally neither can converge to even-width LTIs. Based on a thorough investigation of the GVF and GGVF fields within the LTI during their iterative processes, we identify the crux of the convergence problem, and accordingly propose a novel external force termed as component-normalized GGVF (CN-GGVF) to eliminate the problem. CN-GGVF is obtained by normalizing each component of initial GGVF vectors with respect to its own magnitude. Experimental results and comparisons against GGVF snakes show that the proposed CN-GGVF snakes can capture LTIs regardless of odd or even widths with a remarkably faster convergence speed, while preserving other desirable properties of GGVF snakes with lower computational complexity in vector normalization.

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“…Xu and Prince [2] adopted an explicit difference scheme. Boukerroui [12] tested several other numerical schemes, including the alternating direction explicit scheme (ADES), the additive operating splitting (AOS), and the locally one dimensional (LOD) methods, and showed that ADES was more appropriate for fast GVF computation.…”

Section: Gradient Vector Flowmentioning

confidence: 99%

“…Several fast numerical schemes, e.g., multiresolution method [10] and multigrid method [11], have been proposed for fast GVF computation. Most recently, Boukerroui [12] compared several efficient numerical schemes for GVF computation, and showed that the alternating direction explicit scheme (ADES) may be a suitable alternative to the multigrid method.…”

Section: Introductionmentioning

confidence: 99%

An augmented Lagrangian method for fast gradient vector flow computation

Zuo

Zhao

et al. 2011

2011 18th IEEE International Conference on Image Processing

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Gradient vector flow (GVF) and its generalization have been widely applied in many image processing applications. The high cost of GVF computation, however, has restricted their potential applications to images with large size. In this paper, motivated by progress in fast image restoration algorithms, we reformulate the GVF computation problem as a convex optimization model with an equality constraint, and solve it using a fast algorithm, inexact augmented Lagrangian method (ALM). With fast Fourier transform (FFT), we provide a novel simple and efficient algorithm for GVF computation. Experimental results show that the proposed method can improve the computational speed by an order of magnitude, and is even more efficient for images with large sizes.

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Efficient numerical schemes for gradient vector flow

Cited by 13 publications

References 26 publications

Watershed based intelligent scissors

Watershed based intelligent scissors

Generalized Gradient Vector Flow for Snakes: New Observations, Analysis, and Improvement

An augmented Lagrangian method for fast gradient vector flow computation

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