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A chance-constrained programming level set method for longitudinal segmentation of lung tumors in CT

This paper presents a novel stochastic level set method for the longitudinal tracking of lung tumors in computed tomography (CT). The proposed model addresses the limitations of registration based and segmentation based methods for longitudinal tumor tracking. It combines the advantages of each approach using a new probabilistic framework, namely Chance-Constrained Programming (CCP). Lung tumors can shrink or grow over time, which can be reflected in large changes of shape, appearance and volume in CT images. Traditional level set methods with a priori knowledge about shape are not suitable since the tumors are undergoing random and large changes in shape. Our CCP level set model allows to introduce a flexible prior to track structures with a highly variable shape by permitting a constraint violation of the prior up to a specified probability level. The chance constraints are computed from two given points by the user or from segmented tumors from a reference image. The reference image can be one of the images studied or an external template. We present a numerical scheme to approximate the solution of the proposed model and apply it to track lung tumors in CT. Finally, we compare our approach with a Bayesian level set. The CCP level set model gives the best results: it is more coherent with the manual segmentation.