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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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Convergence of the CONVEF snakes with different initial contours.
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pone-0110032-g008: Convergence of the CONVEF snakes with different initial contours.

Mentions: There are other demonstrations in Fig. 2. Resembling the noisy image in Fig. 8 in [48], the impulse noise is added to the U-shape image by using MATLAB function imnoise(U, 'salt&pepper', Var) with Var varying from 0.1 to 0.4 with step 0.1 in from the first row to the fourth row in Fig. 2, respectively. The goal in these examples is to extract the U-shape object from the noisy images. There are three handicaps in achieving this goal: (1) the evolving contour would get trapped in local minima arising from noise; (2) since the object boundary may be broken by noise, the evolving contour would leak out; (3) it is difficult for the contour to converge to the noisy concavity. Since the noises in the present examples are much heavier than those in [48], it is more difficult for the snakes to converge correctly to the concavities. We also let the noisy image stay intact as done in [48]. The results of VFC snake using are shown in columns (b) and (c), those using are in columns (d) and (e). The corresponding values of the parameters in and ,i.e., γ and ζ, respectively, are shown in the subcaption of each subfigure. These values are chosen so that they are justifiable, for example, in Fig. 2(b1), γ is 1.6 but the contour leaks out; when γ is 1.5 the leakage is more serious. Therefore, we set γ to 1.7 to resist leakage in Fig. 2(c1), however the concavity convergence is poorer than that in Fig. 2(b1) and the contour converges more poorly when γ is 1.8. Consequently, the results of and are chosen for demonstration. The values for ζ are also chosen in the same way. The increasing step is 0.1 for γ and 1.0 for ζ. We found when the step for ζ is 0.5, there is usually no significant change in the result, for example, when , the converged result is similar to that in Fig. 2 (d1) where , so in Fig. 2 (e1). It is obvious that the VFC model using cannot conquer the above mentioned three handicaps at all, the model using performs slightly better; however, the result are not satisfactory especially in the third and fourth rows in Fig. 2. What's more, we will demonstrate that the VFC model using behaves clumsily on G-shape convergence in the next section. The results of the GVF snake are presented in column (f). The noisy images are smoothed using Gaussian filter of standard deviation to calculate the GVF field, and the initial contours are very close to the u-shapes, especially in the 3rd and 4th rows, however, the results are far from satisfactory. Since the VEF is equal to the VFC using with , the results in column (g) are not better, if not worse, than those in column (c) where γ is 1.7 or 1.8.


Convolutional virtual electric field for image segmentation using active contours.

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

Convergence of the CONVEF snakes with different initial contours.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0110032-g008: Convergence of the CONVEF snakes with different initial contours.
Mentions: There are other demonstrations in Fig. 2. Resembling the noisy image in Fig. 8 in [48], the impulse noise is added to the U-shape image by using MATLAB function imnoise(U, 'salt&pepper', Var) with Var varying from 0.1 to 0.4 with step 0.1 in from the first row to the fourth row in Fig. 2, respectively. The goal in these examples is to extract the U-shape object from the noisy images. There are three handicaps in achieving this goal: (1) the evolving contour would get trapped in local minima arising from noise; (2) since the object boundary may be broken by noise, the evolving contour would leak out; (3) it is difficult for the contour to converge to the noisy concavity. Since the noises in the present examples are much heavier than those in [48], it is more difficult for the snakes to converge correctly to the concavities. We also let the noisy image stay intact as done in [48]. The results of VFC snake using are shown in columns (b) and (c), those using are in columns (d) and (e). The corresponding values of the parameters in and ,i.e., γ and ζ, respectively, are shown in the subcaption of each subfigure. These values are chosen so that they are justifiable, for example, in Fig. 2(b1), γ is 1.6 but the contour leaks out; when γ is 1.5 the leakage is more serious. Therefore, we set γ to 1.7 to resist leakage in Fig. 2(c1), however the concavity convergence is poorer than that in Fig. 2(b1) and the contour converges more poorly when γ is 1.8. Consequently, the results of and are chosen for demonstration. The values for ζ are also chosen in the same way. The increasing step is 0.1 for γ and 1.0 for ζ. We found when the step for ζ is 0.5, there is usually no significant change in the result, for example, when , the converged result is similar to that in Fig. 2 (d1) where , so in Fig. 2 (e1). It is obvious that the VFC model using cannot conquer the above mentioned three handicaps at all, the model using performs slightly better; however, the result are not satisfactory especially in the third and fourth rows in Fig. 2. What's more, we will demonstrate that the VFC model using behaves clumsily on G-shape convergence in the next section. The results of the GVF snake are presented in column (f). The noisy images are smoothed using Gaussian filter of standard deviation to calculate the GVF field, and the initial contours are very close to the u-shapes, especially in the 3rd and 4th rows, however, the results are far from satisfactory. Since the VEF is equal to the VFC using with , the results in column (g) are not better, if not worse, than those in column (c) where γ is 1.7 or 1.8.

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