We present a novel framework for the simultaneous segmentation of multiple interacting surfaces belonging
to multiple mutually interacting objects. The method is a non-trivial extension of our previously reported
optimal multi-surface segmentation. Considering an example application of knee-cartilage segmentation, the
framework consists of the following main steps: 1) Shape model construction: Building a mean shape
for each bone of the joint (femur, tibia, patella) from interactively segmented volumetric datasets. Using the
resulting mean-shape model - identification of cartilage, non-cartilage, and transition areas on the mean-shape
bone model surfaces. 2) Presegmentation: Employment of iterative optimal surface detection method to
achieve approximate segmentation of individual bone surfaces. 3) Cross-object surface mapping: Detection
of inter-bone equidistant separating sheets to help identify corresponding vertex pairs for all interacting surfaces.
4) Multi-object, multi-surface graph construction and final segmentation: Construction of a single
multi-bone, multi-surface graph so that two surfaces (bone and cartilage) with zero and non-zero intervening
distances can be detected for each bone of the joint, according to whether or not cartilage can be locally absent
or present on the bone. To define inter-object relationships, corresponding vertex pairs identified using the
separating sheets were interlinked in the graph. The graph optimization algorithm acted on the entire multiobject,
multi-surface graph to yield a globally optimal solution.
The segmentation framework was tested on 16 MR-DESS knee-joint datasets from the Osteoarthritis Initiative
database. The average signed surface positioning error for the 6 detected surfaces ranged from 0.00 to 0.12 mm.
When independently initialized, the signed reproducibility error of bone and cartilage segmentation ranged from
0.00 to 0.26 mm. The results showed that this framework provides robust, accurate, and reproducible segmentation
of the knee joint bone and cartilage surfaces of the femur, tibia, and patella. As a general segmentation
tool, the developed framework can be applied to a broad range of multi-object segmentation problems.