Algorithm 1. Implementation of the MCONVEF Model.
Fig 1.
Analysis of parameter sensitivity.
The gray dashed, black and red solid lines represent initialization, curve evolution and final result, respectively.
Fig 2.
Some common properties of the MCONVEF Snakes: Large capture range, initialization insensitivity, and subject contour connection.
Fig 3.
U-shape images corrupted with varying salt-and-pepper noises that are (a) 0.05, (b) 0.10, (c) 0.15, (d) 0.2, (e) 0.25, (f) 0.3. First row: results of the GVF snake with μ = 0.2. Second row: results of the VEF snake. Third row: results of the MCONVEF snake with h = 1.2, k = 100, L = 2. To note when the value of the parameter k is 100, gk(|∇f|) approaches 1, and the parameter h plays a primary role in noise resistance.
Fig 4.
Experiment on weak edge preservation.
(a) Original image. The segmentation results of (b) the GVF snake with μ = 0.05, (c) the VEF snake, and (d) the MCONVEF snake with k = 0.1, h = 0 and L = 2. The gray dash point circles are the initial contours, and the solid lines in red are the converged results.
Fig 5.
Weak edge preservation example.
(a) The moon image,(b) edge map, segmentation results of (c) the GVF snake with μ = 0.05, (d) the VEF snake, and (d) the MCONVEF snake with k = 0.01, h = 0 and L = 10. The gray dash point circles are the initial contours, and the solid lines in white are the converged results.
Fig 6.
Example of weak edge preservation and noise suppression.
(a) The noisy image,(b) edge map, segmentation results of (c) the GVF snake with μ = 0.1, (d) the VEF snake, and (d) the MCONVEF snake with k = 0.1, h = 1.2 and L = 2. The gray dash point circles are the initial contours, and the solid lines in red are the converged results.
Fig 7.
Example of weak edge preservation and noise suppression.
(a) The crescent image,(b) edge map with noise, (c) edge map without noise, segmentation results of (d) the GVF snake with μ = 0.1, (e) the VEF snake, and (f) the MCONVEF snake with k = 0.1, h = 1.2 and L = 2. The gray dash point circles are the initial contours, and the solid lines in red are the converged results.
Fig 8.
The segmentation results of (a) the GVF snakes with μ = 0.2, (b) the VEF snakes, and (c) the MCONVEF snakes with h = 0, k = 0.2, L = 2.
Fig 9.
(a) medical images, (b) edge maps, The segmentation results of (c) the GVF snakes with μ = 0.1, (d) the VEF snakes, and (e) the MCONVEF snakes with h = 0.3, k = 0.1, L = 10, (f) ground truth.
Table 1.
The comparison of quantitative indices on medical images.
Table 2.
Runtime comparison of the MCONVEF, GVF and VEF models in second.