© RSNA, 2006
Liver Metastases: 3D Shape–based Analysis of CT Scans for Detection of Local Recurrence after Radiofrequency Ablation
Appendix E1
Watershed algorithms segment images into "catchment basins" (1). ITK implementation (National Library of Medicine's Insight Segmentation and Registration toolkit; http://www.itk.org) uses a top-down gradient descent strategy for watershed computation. If a function f is a continuous height function defined over an image domain, then a catchment basin is defined as the set of points whose paths of steepest descent terminate at the same local minimum of f. A height function f suitable for many applications is the gradient magnitude of the image to be segmented, so that higher positive values correspond to object boundaries (Fig E1).
 |
| Figure E1. Principle of watershed segmentation: conventional algorithm. (a) Schematic example of an ablated tumor. (b) Catchment basins defined by the gradient magnitude of the postablation image. Basin 1 represents the liver parenchyma background, and basins 2, 3, 4, and 5 represent the ablated area. Basins 3, 4, and 5 are a schematic example of a nodular recurrence composed of three heterogeneous areas. (c) One-dimensional schematic view of the gradient magnitude profile across all catchment basins. All possible fusions between adjacent basins are indicated, together with the corresponding segmentation level. Note: The reference level (100%) corresponds to the deepest basin in the image. (d) Example of successive segmentation results corresponding to increasing segmentation levels indicated in c. Basins are merged when basin depths are inferior to the specified segmentation level. |
Watershed algorithms typically produce oversegmented images, each local minimum in the image being associated with a distinct catchment basin. Users can prevent oversegmentation by interactively choosing a particular segmentation level: The watershed algorithm will sequentially merge neighboring catchment basins whose depths fall below the segmentation level, until all the basins are of sufficient depth (Fig E1).
The ITK conventional algorithm has been adapted with the introduction of the semiautomated "tagged watershed" algorithm. Through specific graphical interface and cursor interactions, the user can select regions in the image and tag them as part of the liver parenchyma or of the ablated tumor. The algorithm is designed so that it prevents fusion between two catchment basins if one is tagged as liver and the other as ablated tumor. This algorithm also adjusts the segmentation level scale according to the liver and ablated tumor merging level (Fig E2). Figure E3 shows a comparison of conventional and tagged watershed algorithms.
 |
| Figure E2. Semiautomated tagged watershed algorithm. User has selected a point (+) in region 1 as part of the liver parenchyma and a point (+) in region 2 as part of the ablated tumor. (a) The tagged watershed algorithm prevents fusion between basins 1 and 2, and relabels fusions accordingly. (b) Segmentation results corresponding to different segmentation levels. Note: Segmentation levels have been rescaled so that the tagged basins 1 and 2 merging level is given the reference value 50%. |
 |
| Figure E3a-c. Comparison of conventional and semiautomated tagged watershed algorithms. (a) Transverse CT view shows a locally recurrent heterogeneous tumor. Note: While image processing was achieved in 3D, only one section is shown here. (b) Smoothing of the image with a "curvature flow" filter. (c) Results of a conventional watershed segmentation. A correct segmentation level is difficult to achieve, since the ablated tumor is incompletely segmented at the 3.9% level, whereas the tumor disappears by merging with the surrounding liver at the 4.2% level. |
 |
| Figure E3d-f. Comparison of conventional and semiautomated tagged watershed algorithms. (d) User interactively selects tagging points (+) for liver and ablated tumor. (e) Results of semiautomated tagged watershed segmentation. The segmentation level values demonstrate that the level scale has been correctly adjusted for this tumor segmentation. (f) The default value (100%) provides the segmentation result without any additional user interaction. |
Images are preprocessed before the use of the tagged watershed algorithm. A 3D curvature flow filter performs an edge-preserving smoothing (Fig E3a, E3b). A nonlinear intensity mapping is then performed with a sigmoid filter to enhance contrast between the liver and ablated area before gradient magnitude computation. The slope and minimum and maximum values of the sigmoid filter are automatically adjusted to the user-designated liver and post–tumor ablation pixel attenuation values.
Reference
1. Vincent L, Soille P. Watersheds in digital spaces: an efficient algorithm based on immersion simulation. IEEE Trans Pattern Anal Machine Intell 1991;13:583-598.
