Automatic extraction of vertebra regions from a spinal magnetic resonance (MR) image is normally required as the first step to an intelligent spinal MR image diagnosis system. In this work, we develop a fully automatic vertebra detection and segmentation system, which consists of three stages; namely, AdaBoost-based vertebra detection, detection refinement via robust curve fitting, and vertebra segmentation by an iterative normalized cut algorithm. In order to produce an efficient and effective vertebra detector, a statistical learning approach based on an improved AdaBoost algorithm is proposed. A robust estimation procedure is applied on the detected vertebra locations to fit a spine curve, thus refining the above vertebra detection results. This refinement process involves removing the false detections and recovering the miss-detected vertebrae. Finally, an iterative normalized-cut segmentation algorithm is proposed to segment the precise vertebra regions from the detected vertebra locations. In our implementation, the proposed AdaBoost-based detector is trained from 22 spinal MR volume images. The experimental results show that the proposed vertebra detection and segmentation system can achieve nearly 98% vertebra detection rate and 96% segmentation accuracy on a variety of testing spinal MR images. Our experiments also show the vertebra detection and segmentation accuracies by using the proposed algorithm are superior to those of the previous representative methods. The proposed vertebra detection and segmentation system is proved to be robust and accurate so that it can be used for advanced research and application on spinal MR images.

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In this paper, a problem, called "the density divergence problem" is explored. This problem is related to the phenomenon that the densities of the clusters vary in di erent subspace cardinalities. We take the densities into consideration in subspace clustering and explore an algorithm to adaptively determine di erent density thresholds to discover clusters in di erent subspace cardinalities.

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