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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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Results on a synthetic image.(a) Synthetic edge map containing an impulse, a strong edge and a weak one; streamlines generated from (b) GVF using μ = 0.2,#iteration = 200, (c) VFC using m1 with , (d) VFC using m1 with , (e) VFC using m2 with , (f) VFC using m2 with ; (g) CONVEF with n = 1.0, h = 20.0, (h) CONVEF with n = 1.0, h = 25.0.
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pone-0110032-g001: Results on a synthetic image.(a) Synthetic edge map containing an impulse, a strong edge and a weak one; streamlines generated from (b) GVF using μ = 0.2,#iteration = 200, (c) VFC using m1 with , (d) VFC using m1 with , (e) VFC using m2 with , (f) VFC using m2 with ; (g) CONVEF with n = 1.0, h = 20.0, (h) CONVEF with n = 1.0, h = 25.0.

Mentions: For the VFC model using , the authors encouraged decreasing γ to suppress noise, therefore, is employed for all the experiments and excellent performance over GVF on noise suppression has been exemplified in [48]. As pointed out in [57], “a significant advantage in using the VFC force as opposed to standard formulations of external forces or more sophisticated formulations such as the gradient vector flow field (GVF) is that the VFC force is robust to spurious edges and noise in the image and provides a large capture range.” However, further studies show that the VFC model would also smooth away weak edges while suppressing noise. Fig. 1 shows an example similar to that in Fig. 3 in [48]. There are an impulse, a strong edge and a weak edge in this synthetic image where black is zero and white is unitary. The magnitudes of the strong edge and the impulse are zero and that of the weak edge is 0.85. The streamlines generated from the VFC using with and are shown in Figs.1 (c) and (d), respectively, where it can be observed that the force generated from the impulse always plays an important role in the left part of the strong edge even though the weak edge is overwhelmed in Fig. 1 (d). Similar observations also occurred in [48]. Therefore, there is a dilemma for the VFC snake to eliminate noise and preserve weak edges simultaneously. The streamlines of the VFC model using with and are shown in Figs.1 (e) and (f), respectively. Although the result in Fig. 1(f) is satisfactory, the VFC using fails when the noise distribution is more complicated. The streamlines of the GVF model is shown in Fig. 1 (b), it is also obvious that the impulse noise dominates the left part of the GVF field. Since VEF is equal to the VFC using with , it is clear that the VEF cannot overwhelm the impulse noise as well.


Convolutional virtual electric field for image segmentation using active contours.

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

Results on a synthetic image.(a) Synthetic edge map containing an impulse, a strong edge and a weak one; streamlines generated from (b) GVF using μ = 0.2,#iteration = 200, (c) VFC using m1 with , (d) VFC using m1 with , (e) VFC using m2 with , (f) VFC using m2 with ; (g) CONVEF with n = 1.0, h = 20.0, (h) CONVEF with n = 1.0, h = 25.0.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0110032-g001: Results on a synthetic image.(a) Synthetic edge map containing an impulse, a strong edge and a weak one; streamlines generated from (b) GVF using μ = 0.2,#iteration = 200, (c) VFC using m1 with , (d) VFC using m1 with , (e) VFC using m2 with , (f) VFC using m2 with ; (g) CONVEF with n = 1.0, h = 20.0, (h) CONVEF with n = 1.0, h = 25.0.
Mentions: For the VFC model using , the authors encouraged decreasing γ to suppress noise, therefore, is employed for all the experiments and excellent performance over GVF on noise suppression has been exemplified in [48]. As pointed out in [57], “a significant advantage in using the VFC force as opposed to standard formulations of external forces or more sophisticated formulations such as the gradient vector flow field (GVF) is that the VFC force is robust to spurious edges and noise in the image and provides a large capture range.” However, further studies show that the VFC model would also smooth away weak edges while suppressing noise. Fig. 1 shows an example similar to that in Fig. 3 in [48]. There are an impulse, a strong edge and a weak edge in this synthetic image where black is zero and white is unitary. The magnitudes of the strong edge and the impulse are zero and that of the weak edge is 0.85. The streamlines generated from the VFC using with and are shown in Figs.1 (c) and (d), respectively, where it can be observed that the force generated from the impulse always plays an important role in the left part of the strong edge even though the weak edge is overwhelmed in Fig. 1 (d). Similar observations also occurred in [48]. Therefore, there is a dilemma for the VFC snake to eliminate noise and preserve weak edges simultaneously. The streamlines of the VFC model using with and are shown in Figs.1 (e) and (f), respectively. Although the result in Fig. 1(f) is satisfactory, the VFC using fails when the noise distribution is more complicated. The streamlines of the GVF model is shown in Fig. 1 (b), it is also obvious that the impulse noise dominates the left part of the GVF field. Since VEF is equal to the VFC using with , it is clear that the VEF cannot overwhelm the impulse noise as well.

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