Learned boundary maps are known to outperform hand- crafted 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 con- volutional (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.
Alternatively, one can employ the edge-based watershed algorithm and learn boundary probabilities for the grid graph's edges. The corresponding ground truth simply indicates if the end points of each edge are supposed to be in different segments or not. From a theoretical perspective, the distinction between node- and edge-based watersheds is not very significant because both can be transformed into each other @cite_25 . However, the algorithmic details differ considerably. Edge-based altitude learning was first proposed in @cite_26 , who used hand-crafted features and logistic regression. Subsequently, @cite_32 employed a CNN to learn features and boundary probabilities simultaneously. Watershed superpixel generation and clustering on the basis of these altitudes was investigated in @cite_2 .
@cite_26 @cite_32 @cite_25 @cite_2
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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. 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. This work reviews the watershed in the graph framework of a shortest-path forest problem using a lexicographic path cost formulation. This formulation reflects the behavior of the ordered queue-based watershed algorithm. This algorithm is compared with our proposed shortest-path forest (IFT-Image Foresting Transform), concluding that the watershed is a special case of that. Recently many different watershed approaches are being used. We point out that in some cases the watershed algorithm does not keep the optimality of the shortest-path forest solution unless the IFT algorithm is used. The main difference between the algorithms is related to permanently labeling a pixel when inserting or removing it from the queue. The watershed based on the pixel dissimilarity using IFT can segment one-pixel width regions while keeping the optimality of the shortest-path forest solution.