Shape Representation for Efficient Landmark-based Segmentation in 3-d

In this paper, we propose a novel approach to landmark-based shape representation that is based on transportation theory, where landmarks are considered as sources and destinations, all possible landmark connections as roads, and established landmark connections as goods transported via these roads. Landmark connections, which are selectively established, are identified through their statistical properties describing the shape of the object of interest, and indicate the least costly roads for transporting goods from sources to destinations. From such a perspective, we introduce three novel shape representations that are combined with an existing landmark detection algorithm based on game theory. To reduce computational complexity, which results from the extension from 2-D to 3-D segmentation, landmark detection is augmented by a concept known in game theory as strategy dominance. The novel shape representations, game-theoretic landmark detection and strategy dominance are combined into a segmentation framework that was evaluated on 3-D computed tomography images of lumbar vertebrae and femoral heads. The best shape representation yielded symmetric surface distance of 0.75 mm and 1.11 mm, and Dice coefficient of 93.6% and 96.2% for lumbar vertebrae and femoral heads, respectively. By applying strategy dominance, the computational costs were further reduced for up to three times.