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_15: Large-scale training for semantic segmentation is challenging due to the expense of obtaining training data for this task relative to other vision tasks. We propose a novel training approach to address this difficulty. Given cheaply-obtained sparse image labelings, we propagate the sparse labels to produce guessed dense labelings. A standard CNN-based segmentation network is trained to mimic these labelings. The label-propagation process is defined via random-walk hitting probabilities, which leads to a differentiable parameterization with uncertainty estimates that are incorporated into our loss. We show that by learning the label-propagator jointly with the segmentation predictor, we are able to effectively learn semantic edges given no direct edge supervision. Experiments also show that training a segmentation network in this way outperforms the naive approach.
In recent work, Vernaza and Chandraker @cite_15 have proposed a first-order approximation of the derivative for backpropagation. We show in section that this approximation is not well-behaved for the kind of sparse seeds considered here.