For 3D images, segmentation via fitting surface meshes to object boundaries provides an efficient way to handle large images and enforce geometric prior knowledge. Furthermore, fitting such meshes with graph cuts has proven to be a versatile and robust framework. However, when segmenting multiple distinct objects in one image, current methods do not allow the natural constraint that objects should not overlap. In this paper, we present an extension to graph cut based methods which can provide a globally optimal segmentation of thousands of objects while guaranteeing no overlap. Our method works by separating objects with planes whose positions are determined as part of the graph cut. To demonstrate the general applicability of our method, we apply it to several 3D microscopy data sets from both biology and materials science. Our results show both quantitative and qualitative improvements.

Minimum cut / maximum flow (min-cut/max-flow) algorithms are used to solve a variety of problems in computer vision and thus significant effort has been put into developing fast min-cut/max-flow algorithms. This makes it difficult to choose an optimal algorithm for a given problem -especially for parallel algorithms, which have not been thoroughly compared. In this paper, we review the state-of-the-art min-cut/max-flow algorithms for unstructured graphs in computer vision. We evaluate run time performance and memory use of various implementations of both serial and parallel algorithms on a set of graph cut problems. Our results show that the Hochbaum pseudoflow algorithm is the fastest serial algorithm closely followed by the Excesses Incremental Breadth First Search algorithm, while the Boykov-Kolmogorov algorithm is the most memory efficient. The best parallel algorithm is the adaptive bottom-up merging approach by Liu and Sun. Additionally, we show significant variations in performance between different implementations the same algorithms highlighting the importance of low-level implementation details. Finally, we note that existing parallel min-cut/max-flow algorithms can significantly outperform serial algorithms on large problems but suffers from added overhead on small to medium problems. Implementations of all algorithms are available at: github.com/patmjen/maxflow algorithms.

Shape priors have long been known to be effective when reconstructing 3D shapes from noisy or incomplete data. When using a deep-learning based shape representation, this often involves learning a latent representation, which can be either in the form of a single global vector or of multiple local ones. The latter allows more flexibility but is prone to overfitting. In this paper, we advocate a hybrid approach representing shapes in terms of 3D meshes with a separate latent vector at each vertex. During training the latent vectors are constrained to have the same value, which avoids overfitting. For inference, the latent vectors are updated independently while imposing spatial regularization constraints. We show that this gives us both flexibility and generalization capabilities, which we demonstrate on several medical image processing tasks. * Equal supervision.Preprint. Under review.

We introduce a parallel version of the Quadratic Pseudo-Boolean Optimization (QPBO) algorithm for solving binary optimization tasks, such as image segmentation. The original QPBO implementation by Kolmogorov and Rother relies on the Boykov-Kolmogorov (BK) maxflow/mincut algorithm and performs well for many image analysis tasks. However, the serial nature of their QPBO algorithm results in poor utilization of modern hardware. By redesigning the QPBO algorithm to work with parallel maxflow/mincut algorithms, we significantly reduce solve time of large optimization tasks. We compare our parallel QPBO implementation to other state-of-the-art solvers and benchmark them on two large segmentation tasks and a substantial set of small segmentation tasks. The results show that our parallel QPBO algorithm is over 20 times faster than the serial QPBO algorithm on the large tasks and over three times faster for the majority of the small tasks. Although we focus on image segmentation, our algorithm is generic and can be used for any QPBO problem. Our implementation and experimental results are available at

Minimum cut/maximum flow (min-cut/max-flow) algorithms solve a variety of problems in computer vision and thus significant effort has been put into developing fast min-cut/max-flow algorithms. As a result, it is difficult to choose an ideal algorithm for a given problem. Furthermore, parallel algorithms have not been thoroughly compared. In this paper, we evaluate the state-of-the-art serial and parallel min-cut/max-flow algorithms on the largest set of computer vision problems yet. We focus on generic algorithms, i.e., for unstructured graphs, but also compare with the specialized GridCut implementation. When applicable, GridCut performs best. Otherwise, the two pseudoflow algorithms, Hochbaum pseudoflow and excesses incremental breadth first search, achieves the overall best performance. The most memory efficient implementation tested is the Boykov-Kolmogorov algorithm. Amongst generic parallel algorithms, we find the bottom-up merging approach by Liu and Sun to be best, but no method is dominant. Of the generic parallel methods, only the parallel preflow push-relabel algorithm is able to efficiently scale with many processors across problem sizes, and no generic parallel method consistently outperforms serial algorithms. Finally, we provide and evaluate strategies for algorithm selection to obtain good expected performance. We make our dataset and implementations publicly available for further research.