Journal of Mathematical Imaging and Vision
On maximum weight objects decomposable into based rectilinear convex objects
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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In this work, we address the problem of segmenting multiple objects, under possible occlusions, in a level set framework. A variational energy that incorporates a piecewise constant representation of the image in terms of the object regions and the object spatial order is proposed. To resolve occluded boundaries, prior knowledge of the shape of objects is also introduced within the segmentation energy. By minimizing the above energy, we solve the segmentation with depth problem, i.e., estimating the object boundaries, the object intensities, and the spatial order. The segmentation with depth problem was originally dealt with by the Nitzberg-Mumford-Shiota (NMS) variational formulation, which proposes segmentation energies for each spatial order. We discuss the relationships and show the computational advantages of our formulation over the NMS model, mainly due to our treatment of spatial order estimation within a single energy. A novelty here is that the spatial order information available in the image model is used to dynamically impose prior shape constraints only to occluded boundaries. Also presented are experiments on synthetic and real images that have promising results.