On the Equivalence Between Hierarchical Segmentations and Ultrametric Watersheds
Journal of Mathematical Imaging and Vision
Generalized hard constraints for graph segmentation
SCIA'11 Proceedings of the 17th Scandinavian conference on Image analysis
Incremental algorithm for hierarchical minimum spanning forests and saliency of watershed cuts
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Surface reconstruction using power watershed
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Global relabeling for continuous optimization in binary image segmentation
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Carving: scalable interactive segmentation of neural volume electron microscopy images
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Interactive image segmentation by matching attributed relational graphs
Pattern Recognition
Closed-Form relaxation for MRF-MAP tissue classification using discrete laplace equations
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Computer Vision and Image Understanding
Knot segmentation in noisy 3d images of wood
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
New software developments for quality mesh generation and optimization from biomedical imaging data
Computer Methods and Programs in Biomedicine
Random walks in directed hypergraphs and application to semi-supervised image segmentation
Computer Vision and Image Understanding
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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.