(a) The calculation of the gradient likelihood function. The dotted line represents the partition boundary, while the black and gray arrows represent the boundary normal vectors and local gradient vectors, respectively. (b) The computation of local gradient vector, which is conducted by sampling the gradient in eight directions distributed spherically.
The initial segmentation used for the stochastic region competition. The region outside the outer circle is assigned as the background region, while the region inside the inner one is the object region. The region in between is the unknown region. The solid line represents the object of interest, which has supplying vessels crossing its boundary.
The optimization process of the stochastic region competition algorithm with Z R = 5 and Z C = 10: (a) the initial setting, (b)–(d) intermediate result of the competition, and (e) final result. The overall computation time for this image is 3.26 s. The unknown region between the outer background region and inner object region is gradually replaced by other two regions, and the final result converges to the boundary of the object even though a supplying vessel crosses the object boundary.
The reproducibility of algorithm-generated boundaries in comparison to the manual delineations. The first column lists the original Doppler sonograms, whereas the second and third columns list the algorithm-generated boundaries (Z R = 5, Z C = 10) and manual delineations, respectively. The four different colors represent four different contours generated from the algorithm (second column) and manual delineation (third column). Even under the influence of the color-coded pixels, the algorithm is able to achieve as good reproducibility as the manual delineations.
The effect of the parameters Z R and Z C on the segmentation results. A higher value of Z R results in smoother boundaries, whereas a higher value of Z C results in higher sensitivity to local gradient. If a fixed Z C to Z R ratio is used, lower values in both constants are equivalent to a higher weighting in histogram likelihood, which results in more homogeneous intensity within the segmented region.
The average distance (±standard deviation) and William index between algorithm-generated boundaries (C 1, C 2, C 3, and C 4) and manual delineations (O 1, O 2, O 3, and O 4).
The overlap ratios between algorithm-generated boundaries (C 1, C 2, C 3, and C 4) and manual delineations (O 1, O 2, O 3, and O 4).
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