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
2137276306 2169805405 2006227270 1507090658
The paper studies the problem of combining region and boundary cues for natural image segmentation. We employ a large database of manually segmented images in order to learn an optimal affinity function between pairs of pixels. These pairwise affinities can then be used to cluster the pixels into visually coherent groups. Region cues are computed as the similarity in brightness, color, and texture between image patches. Boundary cues are incorporated by looking for the presence of an "intervening contour", a large gradient along a straight line connecting two pixels. We first use the dataset of human segmentations to individually optimize parameters of the patch and gradient features for brightness, color, and texture cues. We then quantitatively measure the power of different feature combinations by computing the precision and recall of classifiers trained using those features. The mutual information between the output of the classifiers and the same-segment indicator function provides an alternative evaluation technique that yields identical conclusions. As expected, the best classifier makes use of brightness, color, and texture features, in both patch and gradient forms. We find that for brightness, the gradient cue outperforms the patch similarity. In contrast, using color patch similarity yields better results than using color gradients. Texture is the most powerful of the three channels, with both patches and gradients carrying significant independent information. Interestingly, the proximity of the two pixels does not add any information beyond that provided by the similarity cues. We also find that the convexity assumptions made by the intervening contour approach are supported by the ecological statistics of the dataset. Many image segmentation algorithms first generate an affinity graph and then partition it. We present a machine learning approach to computing an affinity graph using a convolutional network (CN) trained using ground truth provided by human experts. The CN affinity graph can be paired with any standard partitioning algorithm and improves segmentation accuracy significantly compared to standard hand-designed affinity functions. We apply our algorithm to the challenging 3D segmentation problem of reconstructing neuronal processes from volumetric electron microscopy (EM) and show that we are able to learn a good affinity graph directly from the raw EM images. Further, we show that our affinity graph improves the segmentation accuracy of both simple and sophisticated graph partitioning algorithms. In contrast to previous work, we do not rely on prior knowledge in the form of hand-designed image features or image preprocessing. Thus, we expect our algorithm to generalize effectively to arbitrary image types. The watershed is an efficient and versatile segmentation tool, as it partitions the images into disjoint catchment basins. We study the watershed on node or edge weighted graphs. We do not aim at constructing a partition of the nodes but consider the catchment zones, i.e., the attraction zones of a drop of water. Often, such zones largely overlap. In a first part, we show how to derive from a node or edge weighted graph a flooding graph with the same trajectories of a drop of water, whether one considers its node weights alone or its edge weights alone. In a second part we show how to reduce the number of possible trajectories of a drop of water in order to generate watershed partitions. We present a method for hierarchical image segmentation that defines a disaffinity graph on the image, over-segments it into watershed basins, defines a new graph on the basins, and then merges basins with a modified, size-dependent version of single linkage clustering. The quasilinear runtime of the method makes it suitable for segmenting large images. We illustrate the method on the challenging problem of segmenting 3D electron microscopic brain images.