A 3D generalization of user-steered live-wire segmentation.

We have been developing user-steered image segmentation methods for situations which require considerable human assistance in object definition. In the past, we have presented two paradigms, referred to as live-wire and live-lane, for segmenting 2D/3D/4D object boundaries in a slice-by-slice fashion, and demonstrated that live-wire and live-lane are more repeatable, with a statistical significance level of P < 0.03, and are 1.5-2.5 times faster, with a statistical significance level of P < 0.02, than manual tracing. In this paper, we introduce a 3D generalization of the live-wire approach for segmenting 3D/4D object boundaries which further reduces the time spent by the user in segmentation. In a 2D live-wire, given a slice, for two specified points (pixel vertices) on the boundary of the object, the best boundary segment is the minimum-cost path between the two points, described as a set of oriented pixel edges. This segment is found via Dijkstra's algorithm as the user anchors the first point and moves the cursor to indicate the second point. A complete 2D boundary is identified as a set of consecutive boundary segments forming a "closed", "connected", "oriented" contour. The strategy of the 3D extension is that, first, users specify contours via live-wiring on a few slices that are orthogonal to the natural slices of the original scene. If these slices are selected strategically, then we have a sufficient number of points on the 3D boundary of the object to subsequently trace optimum boundary segments automatically in all natural slices of the 3D scene. A 3D object boundary may define multiple 2D boundaries per slice. The points on each 2D boundary form an ordered set such that when the best boundary segment is computed between each pair of consecutive points, a closed, connected, oriented boundary results. The ordered set of points on each 2D boundary is found from the way the users select the orthogonal slices. Based on several validation studies involving segmentation of the bones of the foot in MR images, we found that the 3D extension of live-wire is more repeatable, with a statistical significance level of P < 0.0001, and 2-6 times faster, with a statistical significance level of P < 0.01, than the 2D live-wire method, and 3-15 times faster than manual tracing.