Leveraging point annotations in segmentation learning with boundary loss

This paper investigates the combination of intensity-based distance maps with boundary loss for point-supervised semantic segmentation. By design the boundary loss imposes a stronger penalty on the false positives the farther away from the object they occur. Hence it is intuitively inappropriate for weak supervision, where the ground truth label may be much smaller than the actual object and a certain amount of false positives (w.r.t. the weak ground truth) is actually desirable. Using intensity-aware distances instead may alleviate this drawback, allowing for a certain amount of false positives without a significant increase to the training loss. The motivation for applying the boundary loss directly under weak supervision lies in its great success for fully supervised segmentation tasks, but also in not requiring extra priors or outside information that is usually required -- in some form -- with existing weakly supervised methods in the literature. This formulation also remains potentially more attractive than existing CRF-based regularizers, due to its simplicity and computational efficiency. We perform experiments on two multi-class datasets; ACDC (heart segmentation) and POEM (whole-body abdominal organ segmentation). Preliminary results are encouraging and show that this supervision strategy has great potential. On ACDC it outperforms the CRF-loss based approach, and on POEM data it performs on par with it. The code for all our experiments is openly available.

Fast Graph-Cut Based Optimization for Practical Dense Deformable Registration of Volume Images

Objective: Deformable image registration is a fundamental problem in medical image analysis, with applications such as longitudinal studies, population modeling, and atlas based image segmentation. Registration is often phrased as an optimization problem, i.e., finding a deformation field that is optimal according to a given objective function. Discrete, combinatorial, optimization techniques have successfully been employed to solve the resulting optimization problem. Specifically, optimization based on $\alpha$-expansion with minimal graph cuts has been proposed as a powerful tool for image registration. The high computational cost of the graph-cut based optimization approach, however, limits the utility of this approach for registration of large volume images. Methods: Here, we propose to accelerate graph-cut based deformable registration by dividing the image into overlapping sub-regions and restricting the $\alpha$-expansion moves to a single sub-region at a time. Results: We demonstrate empirically that this approach can achieve a large reduction in computation time -- from days to minutes -- with only a small penalty in terms of solution quality. Conclusion: The reduction in computation time provided by the proposed method makes graph cut based deformable registration viable for large volume images. Significance: Graph cut based image registration has previously been shown to produce excellent results, but the high computational cost has hindered the adoption of the method for registration of large medical volume images. Our proposed method lifts this restriction, requiring only a small fraction of the computational cost to produce results of comparable quality.

PDNet: Semantic Segmentation integrated with a Primal-Dual Network for Document binarization

Binarization of digital documents is the task of classifying each pixel in an image of the document as belonging to the background (parchment/paper) or foreground (text/ink). Historical documents are often subjected to degradations, that make the task challenging. In the current work a deep neural network architecture is proposed that combines a fully convolutional network with an unrolled primal-dual network that can be trained end-to-end to achieve state of the art binarization on four out of seven datasets. Document binarization is formulated as an energy minimization problem. A fully convolutional neural network is trained for semantic segmentation of pixels that provides labeling cost associated with each pixel. This cost estimate is refined along the edges to compensate for any over or under estimation of the foreground class using a primal-dual approach. We provide necessary overview on proximal operator that facilitates theoretical underpinning required to train a primal-dual network using a gradient descent algorithm. Numerical instabilities encountered due to the recurrent nature of primal-dual approach are handled. We provide experimental results on document binarization competition dataset along with network changes and hyperparameter tuning required for stability and performance of the network. The network when pre-trained on synthetic dataset performs better as per the competition metrics.

When can $l_p$-norm objective functions be minimized via graph cuts?

Techniques based on minimal graph cuts have become a standard tool for solving combinatorial optimization problems arising in image processing and computer vision applications. These techniques can be used to minimize objective functions written as the sum of a set of unary and pairwise terms, provided that the objective function is submodular. This can be interpreted as minimizing the $l_1$-norm of the vector containing all pairwise and unary terms. By raising each term to a power $p$, the same technique can also be used to minimize the $l_p$-norm of the vector. Unfortunately, the submodularity of an $l_1$-norm objective function does not guarantee the submodularity of the corresponding $l_p$-norm objective function. The contribution of this paper is to provide useful conditions under which an $l_p$-norm objective function is submodular for all $p\geq 1$, thereby identifying a large class of $l_p$-norm objective functions that can be minimized via minimal graph cuts.