No Arabic abstract
In the segmentation of fine-scale structures from natural and biomedical images, per-pixel accuracy is not the only metric of concern. Topological correctness, such as vessel connectivity and membrane closure, is crucial for downstream analysis tasks. In this paper, we propose a new approach to train deep image segmentation networks for better topological accuracy. In particular, leveraging the power of discrete Morse theory (DMT), we identify global structures, including 1D skeletons and 2D patches, which are important for topological accuracy. Trained with a novel loss based on these global structures, the network performance is significantly improved especially near topologically challenging locations (such as weak spots of connections and membranes). On diverse datasets, our method achieves superior performance on both the DICE score and topological metrics.
In this paper, we study Formans discrete Morse theory in the context of weighted homology. We develop weight
Establishing correspondences between two images requires both local and global spatial context. Given putative correspondences of feature points in two views, in this paper, we propose Order-Aware Network, which infers the probabilities of correspondences being inliers and regresses the relative pose encoded by the essential matrix. Specifically, this proposed network is built hierarchically and comprises three novel operations. First, to capture the local context of sparse correspondences, the network clusters unordered input correspondences by learning a soft assignment matrix. These clusters are in a canonical order and invariant to input permutations. Next, the clusters are spatially correlated to form the global context of correspondences. After that, the context-encoded clusters are recovered back to the original size through a proposed upsampling operator. We intensively experiment on both outdoor and indoor datasets. The accuracy of the two-view geometry and correspondences are significantly improved over the state-of-the-arts. Code will be available at https://github.com/zjhthu/OANet.git.
Semantic segmentation (SS) is an important perception manner for self-driving cars and robotics, which classifies each pixel into a pre-determined class. The widely-used cross entropy (CE) loss-based deep networks has achieved significant progress w.r.t. the mean Intersection-over Union (mIoU). However, the cross entropy loss can not take the different importance of each class in an self-driving system into account. For example, pedestrians in the image should be much more important than the surrounding buildings when make a decisions in the driving, so their segmentation results are expected to be as accurate as possible. In this paper, we propose to incorporate the importance-aware inter-class correlation in a Wasserstein training framework by configuring its ground distance matrix. The ground distance matrix can be pre-defined following a priori in a specific task, and the previous importance-ignored methods can be the particular cases. From an optimization perspective, we also extend our ground metric to a linear, convex or concave increasing function $w.r.t.$ pre-defined ground distance. We evaluate our method on CamVid and Cityscapes datasets with different backbones (SegNet, ENet, FCN and Deeplab) in a plug and play fashion. In our extenssive experiments, Wasserstein loss demonstrates superior segmentation performance on the predefined critical classes for safe-driving.
We prove the Lefschetz hyperplane section theorem using a simpler machinery by making the observation that we can compose the Lefschetz Pencil with a Real Morse function to get a map from the variety to $mathbb{R}$ which is close to being a Real Morse function. The proof uses a new method unlike the conventional one which uses vanishing cycles, thimbles and monodromy. We prove the genus formula for plane curves using Morse theory, Lefschetz pencil and Bezouts theorem. And then we prove the Riemann Hurwitz formula for ramified maps between curves by employing techniques from deformation theory. Lastly, we prove the Lefschetz Hyperplane Section Theorem solely using Real Morse Theory and exact sequences.
In this work, we introduce the new scene understanding task of Part-aware Panoptic Segmentation (PPS), which aims to understand a scene at multiple levels of abstraction, and unifies the tasks of scene parsing and part parsing. For this novel task, we provide consistent annotations on two commonly used datasets: Cityscapes and Pascal VOC. Moreover, we present a single metric to evaluate PPS, called Part-aware Panoptic Quality (PartPQ). For this new task, using the metric and annotations, we set multiple baselines by merging results of existing state-of-the-art methods for panoptic segmentation and part segmentation. Finally, we conduct several experiments that evaluate the importance of the different levels of abstraction in this single task.