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.
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.
@cite_26 @cite_1 @cite_6
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In this work, we extend a common framework for graph-based image segmentation that includes the graph cuts, random walker, and shortest path optimization algorithms. Viewing an image as a weighted graph, these algorithms can be expressed by means of a common energy function with differing choices of a parameter q acting as an exponent on the differences between neighboring nodes. Introducing a new parameter p that fixes a power for the edge weights allows us to also include the optimal spanning forest algorithm for watershed in this same framework. We then propose a new family of segmentation algorithms that fixes p to produce an optimal spanning forest but varies the power q beyond the usual watershed algorithm, which we term the power watershed. In particular, when q=2, the power watershed leads to a multilabel, scale and contrast invariant, unique global optimum obtained in practice in quasi-linear time. Placing the watershed algorithm in this energy minimization framework also opens new possibilities for using unary terms in traditional watershed segmentation and using watershed to optimize more general models of use in applications beyond image segmentation. Watershed cuts are among the fastest segmentation algorithms and therefore well suited for interactive segmentation of very large 3D data sets. To minimize the number of user interactions (“seeds”) required until the result is correct, we want the computer to actively query the human for input at the most critical locations, in analogy to active learning. These locations are found by means of suitable uncertainty measures. We propose various such measures for watershed cuts along with a theoretical analysis of some of their properties. Extensive evaluation on two types of 3D electron microscopic volumes of neural tissue shows that measures which estimate the non-local consequences of new user inputs achieve performance close to an oracle endowed with complete knowledge of the ground truth. 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. 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.