This paper presents a shape-based curve-growing algorithm for object recognition in the field of medical imaging. The proposed curve growing process, modeled by a Bayesian network, is influenced by both image data and prior knowledge of the shape of the curve. A maximum a posteriori (MAP) solution is derived using an energy-minimizing mechanism. It is implemented in an adaptive regularization framework that balances the influence of image data and shape prior in estimating the curve, and reflects the causal dependencies in the Bayesian network. The method effectively alleviates over-smoothing, an effect that can occur with other regularization methods. Moreover, the proposed framework also addresses initialization and local minima problems. Robustness and performance of the proposed method are demonstrated by segmentation of pulmonary fissures in computed tomography (CT) images.