Illustration of a decomposition of a breast lesion into prominent components. (a) An ROI of a sonography containing a benign breast lesion. (b) A decomposition of a breast lesion into prominent components. In (b), a region enclosed by dotted lines is regarded to be a prominent component.
Tessellating a ROI into elementary cell, cell, and prominent component structures. (a) A ROI of a sonography. (b) Elementary cell tessellation by the first-pass watershed transformation. (c) Cell tessellation from the second-pass watershed transformation. (d) Prominent component tessellation by cell competition process.
The transformation process of the edge structure of a prominent component tessellation into corresponding c-graph. (a) A prominent component tessellation of a benign lesion. (b) The corresponding c-graph. In (b), a cycle constituted of a set of sequential darker graph nodes may be regarded as the desired boundary of the breast lesion.
Profiling the bilateral vicinities of a p-edgel. The bilateral profiles of the p-edgel can be obtained by morphological dilation with a specific size of structural element. is the profile of the left vicinity of the p-edgel while the right profile is .
Two types of p-edgel. (a) and (b) demonstrate cliff p-edgels with different slope orientations. (c) indicates a peak type p-edgel. It can be found that cliff type of p-edgel holds significant altitude difference in bilateral vicinities.
The inner lateral vicinities along a breast lesion boundary may appear darker than outer vicinities. and , , indicate outer and inner vicinities around the lesion boundary, respectively.
Scenarios of depth-first search scheme to concatenate p-edgels. (a) Demonstrations of the desired and undesired combination of p-edgels. p-edgel can possibly go to p-edgels , , and . The combination of p-edgels and violates the slope consistence rule and is excluded in the c-graph searching. (b) The traversing orientation of a closed curve can be determined by the sign of overall turning angles, i.e., . In (a) and (b), and are vertices interconnecting the p-edgels.
Boundary candidates proposed by ACCOMP algorithm for the benign lesion in Fig. 2. (a) Rough outline derived from the region competition algorithm. (b) The prominent component tessellation from the cell competition process. The initial p-edgel for the retrieval of cycles is indicated by the white dotted circle. [(c)–(g)] Five boundary candidates with respect to the five cost functions C1–C5. (h) A manual delineation confirmed by an experienced medical doctor.
Flow chart of the ACCOMP algorithm. The left column illustrates the major steps of the proposed algorithm. The right column diagrams the processes of cell-based contour grouping.
Comparison of the manual delineations and the boundaries generated by ACCOMP, thresholding-based, and level-set-based algorithms for a breast malignant lesion. The image in the first row is the ROI of the original sonography, while the images in the second, third, fourth, and fifth rows report the manual delineations and the boundaries generated by ACCOMP, thresholding-based, and level-set-based algorithms, respectively.
Four metrics, including the modified Williams index, percentage statistic, overlapping ratio, and difference ratio, for evaluation of the quality of the computer-generated boundaries with respect to the manually delineated boundaries.
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