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_22: We present a new approach for the discriminative training of continuous-valued Markov Random Field (MRF) model parameters. In our approach we train the MRF model by optimizing the parameters so that the minimum energy solution of the model is as similar as possible to the ground-truth. This leads to parameters which are directly optimized to increase the quality of the MAP estimates during inference. Our proposed technique allows us to develop a framework that is flexible and intuitively easy to understand and implement, which makes it an attractive alternative to learn the parameters of a continuous-valued MRF model. We demonstrate the effectiveness of our technique by applying it to the problems of image denoising and in-painting using the Field of Experts model. In our experiments, the performance of our system compares favourably to the Field of Experts model trained using contrastive divergence when applied to the denoising and in-painting tasks.
@cite_11: A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with user-defined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels. By assigning each pixel to the label for which the greatest probability is calculated, a high-quality image segmentation may be obtained. Theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits. This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension on arbitrary graphs
In computer vision, linear diffusion has been proposed for seeded segmentation in the seminal work of Grady @cite_11 . In semantic segmentation and image-valued regression tasks, @cite_22 have shown how to learn context-dependent potentials for GMRFs. These authors did not explore seeded segmentation, and the number of parameters learned was in the hundreds, not hundreds of thousands as in our case.