We present an end-to-end learned algorithm for seeded segmentation. Our method is based on the Random Walker algorithm, where we predict the edge weights of the underlying graph using a convolutional neural network. This can be interpreted as learning context-dependent diffusivities for a linear diffusion process. Besides calculating the exact gradient for optimizing these diffusivities, we also propose simplifications that sparsely sample the gradient and still yield competitive results. The proposed method achieves the currently best results on a seeded version of the CREMI neuron segmentation challenge.
@cite_26: Learned boundary maps are known to outperform handcrafted ones as a basis for the watershed algorithm. We show, for the first time, how to train watershed computation jointly with boundary map prediction. The estimator for the merging priorities is cast as a neural network that is convolutional (over space) and recurrent (over iterations). The latter allows learning of complex shape priors. The method gives the best known seeded segmentation results on the CREMI segmentation challenge.
@cite_1: We recently introduced watershed cuts, a notion of watershed in edge-weighted graphs. In this paper, our main contribution is a thinning paradigm from which we derive three algorithmic watershed cut strategies: The first one is well suited to parallel implementations, the second one leads to a flexible linear-time sequential implementation, whereas the third one links the watershed cuts and the popular flooding algorithms. We state that watershed cuts preserve a notion of contrast, called connection value, on which several morphological region merging methods are (implicitly) based. We also establish the links and differences between watershed cuts, minimum spanning forests, shortest path forests, and topological watersheds. Finally, we present illustrations of the proposed framework to the segmentation of artwork surfaces and diffusion tensor images.
@cite_6: This paper describes a general method for interactive segmentation, Smart Paint. The user interaction is inspired by the way an airbrush is used, objects are segmented by "sweeping" with the mouse ...
Such fragility is especially pronounced for watershed-type methods that base dissimilarities on a minimax criterion @cite_1 . Even so, such methods have been used successfully in biomedical @cite_6 and other applications. Recent work has sought to mitigate this limitation by learning the edge weights for watershed seeded segmentation in a structured fashion, just as we do, and moreover making the algorithm adaptive @cite_26 , the cost for the latter being a somewhat involved recurrent neural net formulation. The experiments in section show that we can supersede the learned watershed in spite of our simpler architecture.