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Convolutional virtual electric field for image segmentation using active contours.

Wang Y, Zhu C, Zhang J, Jian Y - PLoS ONE (2014)

Bottom Line: Gradient vector flow (GVF) is an effective external force for active contours; however, it suffers from heavy computation load.Meanwhile, the CONVEF model can also be implemented in real-time by using FFT.Experimental results illustrate these advantages of the CONVEF model on both synthetic and natural images.

View Article: PubMed Central - PubMed

Affiliation: School of Computer Science, Tianjin University of Technology, Tianjin, China.

ABSTRACT
Gradient vector flow (GVF) is an effective external force for active contours; however, it suffers from heavy computation load. The virtual electric field (VEF) model, which can be implemented in real time using fast Fourier transform (FFT), has been proposed later as a remedy for the GVF model. In this work, we present an extension of the VEF model, which is referred to as CONvolutional Virtual Electric Field, CONVEF for short. This proposed CONVEF model takes the VEF model as a convolution operation and employs a modified distance in the convolution kernel. The CONVEF model is also closely related to the vector field convolution (VFC) model. Compared with the GVF, VEF and VFC models, the CONVEF model possesses not only some desirable properties of these models, such as enlarged capture range, u-shape concavity convergence, subject contour convergence and initialization insensitivity, but also some other interesting properties such as G-shape concavity convergence, neighboring objects separation, and noise suppression and simultaneously weak edge preserving. Meanwhile, the CONVEF model can also be implemented in real-time by using FFT. Experimental results illustrate these advantages of the CONVEF model on both synthetic and natural images.

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Related in: MedlinePlus

Segmentation results of the noisy images in Fig. 2 using the CONVEF snake and comparisons with the VFC snake.Columns (a) and (b) are the results using CONVEF snakes, those in columns (c) and (d) are the results using VFC snakes with m1(x,y) and those in columns (e) and (f) are the results using VFC snakes with m2(x,y). Before calculating all the VFC fields, the noisy images are preprocessed using a 2D Gaussian function with standard deviation σ. Although the VFC model prefers small γ for noise suppression, we increased γ to preserve edges in these experiments. The corresponding parameters are listed in the subcaption of each subfigure.
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pone-0110032-g005: Segmentation results of the noisy images in Fig. 2 using the CONVEF snake and comparisons with the VFC snake.Columns (a) and (b) are the results using CONVEF snakes, those in columns (c) and (d) are the results using VFC snakes with m1(x,y) and those in columns (e) and (f) are the results using VFC snakes with m2(x,y). Before calculating all the VFC fields, the noisy images are preprocessed using a 2D Gaussian function with standard deviation σ. Although the VFC model prefers small γ for noise suppression, we increased γ to preserve edges in these experiments. The corresponding parameters are listed in the subcaption of each subfigure.

Mentions: Since the VFC, VEF and GVF snake fails to extract the U shape in the noisy images in Fig. 2, the CONVEF snake is employed for this task. Through the observations in Fig. 1, we can increase the value of h to suppress noise and increase the value of n to preserve edges. The results of CONVEF snakes at some combinations of h and n are shown in columns (a) and (b) in Fig. 5. These results are satisfactory even though the noise is very heavy in the fourth row. Although the VFC snake fails to overcome the three handicaps in extracting the U-shape objects in Fig. 2, we propose to presmooth the noisy images using a 2D Gaussian function with standard deviation σ,. The results of VFC snakes with combined with are shown in columns (c) and (d). It is clear this combination would work well when the noise is not very heavy, see the first and second rows in columns (c) and (d). However, when the noise is as heavy as that in the fourth row, it would fail. Although the result in Fig. 5(c3) is fairly good, the result is sensitive to parameters γ and σ. We have tried many combinations of γ and σ for the noisy image in the third row, the values of γ are {1.8,1.9,2.0,2.5,3.0,4.0}, σ varies in a wide range by step 0.1, we found that there are only two combinations, i.e., {, }, {, }, at which the results are acceptable. However, the CONVEF snake is more robust to the parameters h and n, for example, when , h can vary from 9 to 13, at which the results are fairly good. The results of VFC snakes with combined with are shown in columns (e) and (f). However, the Gaussian filter didn't help much. The effectiveness of a Gaussian filter is similar to that of increasing ζ in . For example, the result in Fig. 5(f2) () is similar to the result in Fig. 2(e2)().


Convolutional virtual electric field for image segmentation using active contours.

Wang Y, Zhu C, Zhang J, Jian Y - PLoS ONE (2014)

Segmentation results of the noisy images in Fig. 2 using the CONVEF snake and comparisons with the VFC snake.Columns (a) and (b) are the results using CONVEF snakes, those in columns (c) and (d) are the results using VFC snakes with m1(x,y) and those in columns (e) and (f) are the results using VFC snakes with m2(x,y). Before calculating all the VFC fields, the noisy images are preprocessed using a 2D Gaussian function with standard deviation σ. Although the VFC model prefers small γ for noise suppression, we increased γ to preserve edges in these experiments. The corresponding parameters are listed in the subcaption of each subfigure.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4216009&req=5

pone-0110032-g005: Segmentation results of the noisy images in Fig. 2 using the CONVEF snake and comparisons with the VFC snake.Columns (a) and (b) are the results using CONVEF snakes, those in columns (c) and (d) are the results using VFC snakes with m1(x,y) and those in columns (e) and (f) are the results using VFC snakes with m2(x,y). Before calculating all the VFC fields, the noisy images are preprocessed using a 2D Gaussian function with standard deviation σ. Although the VFC model prefers small γ for noise suppression, we increased γ to preserve edges in these experiments. The corresponding parameters are listed in the subcaption of each subfigure.
Mentions: Since the VFC, VEF and GVF snake fails to extract the U shape in the noisy images in Fig. 2, the CONVEF snake is employed for this task. Through the observations in Fig. 1, we can increase the value of h to suppress noise and increase the value of n to preserve edges. The results of CONVEF snakes at some combinations of h and n are shown in columns (a) and (b) in Fig. 5. These results are satisfactory even though the noise is very heavy in the fourth row. Although the VFC snake fails to overcome the three handicaps in extracting the U-shape objects in Fig. 2, we propose to presmooth the noisy images using a 2D Gaussian function with standard deviation σ,. The results of VFC snakes with combined with are shown in columns (c) and (d). It is clear this combination would work well when the noise is not very heavy, see the first and second rows in columns (c) and (d). However, when the noise is as heavy as that in the fourth row, it would fail. Although the result in Fig. 5(c3) is fairly good, the result is sensitive to parameters γ and σ. We have tried many combinations of γ and σ for the noisy image in the third row, the values of γ are {1.8,1.9,2.0,2.5,3.0,4.0}, σ varies in a wide range by step 0.1, we found that there are only two combinations, i.e., {, }, {, }, at which the results are acceptable. However, the CONVEF snake is more robust to the parameters h and n, for example, when , h can vary from 9 to 13, at which the results are fairly good. The results of VFC snakes with combined with are shown in columns (e) and (f). However, the Gaussian filter didn't help much. The effectiveness of a Gaussian filter is similar to that of increasing ζ in . For example, the result in Fig. 5(f2) () is similar to the result in Fig. 2(e2)().

Bottom Line: Gradient vector flow (GVF) is an effective external force for active contours; however, it suffers from heavy computation load.Meanwhile, the CONVEF model can also be implemented in real-time by using FFT.Experimental results illustrate these advantages of the CONVEF model on both synthetic and natural images.

View Article: PubMed Central - PubMed

Affiliation: School of Computer Science, Tianjin University of Technology, Tianjin, China.

ABSTRACT
Gradient vector flow (GVF) is an effective external force for active contours; however, it suffers from heavy computation load. The virtual electric field (VEF) model, which can be implemented in real time using fast Fourier transform (FFT), has been proposed later as a remedy for the GVF model. In this work, we present an extension of the VEF model, which is referred to as CONvolutional Virtual Electric Field, CONVEF for short. This proposed CONVEF model takes the VEF model as a convolution operation and employs a modified distance in the convolution kernel. The CONVEF model is also closely related to the vector field convolution (VFC) model. Compared with the GVF, VEF and VFC models, the CONVEF model possesses not only some desirable properties of these models, such as enlarged capture range, u-shape concavity convergence, subject contour convergence and initialization insensitivity, but also some other interesting properties such as G-shape concavity convergence, neighboring objects separation, and noise suppression and simultaneously weak edge preserving. Meanwhile, the CONVEF model can also be implemented in real-time by using FFT. Experimental results illustrate these advantages of the CONVEF model on both synthetic and natural images.

Show MeSH
Related in: MedlinePlus