TY - THES AB - Modern computer vision systems heavily rely on statistical machine learning models, which typically require large amounts of labeled data to be learned reliably. Moreover, very recently computer vision research widely adopted techniques for representation learning, which further increase the demand for labeled data. However, for many important practical problems there is relatively small amount of labeled data available, so it is problematic to leverage full potential of the representation learning methods. One way to overcome this obstacle is to invest substantial resources into producing large labelled datasets. Unfortunately, this can be prohibitively expensive in practice. In this thesis we focus on the alternative way of tackling the aforementioned issue. We concentrate on methods, which make use of weakly-labeled or even unlabeled data. Specifically, the first half of the thesis is dedicated to the semantic image segmentation task. We develop a technique, which achieves competitive segmentation performance and only requires annotations in a form of global image-level labels instead of dense segmentation masks. Subsequently, we present a new methodology, which further improves segmentation performance by leveraging tiny additional feedback from a human annotator. By using our methods practitioners can greatly reduce the amount of data annotation effort, which is required to learn modern image segmentation models. In the second half of the thesis we focus on methods for learning from unlabeled visual data. We study a family of autoregressive models for modeling structure of natural images and discuss potential applications of these models. Moreover, we conduct in-depth study of one of these applications, where we develop the state-of-the-art model for the probabilistic image colorization task. AU - Kolesnikov, Alexander ID - 197 SN - 2663-337X TI - Weakly-Supervised Segmentation and Unsupervised Modeling of Natural Images ER - TY - JOUR AB - A central problem of algebraic topology is to understand the homotopy groups πœ‹π‘‘(𝑋) of a topological space X. For the computational version of the problem, it is well known that there is no algorithm to decide whether the fundamental group πœ‹1(𝑋) of a given finite simplicial complex X is trivial. On the other hand, there are several algorithms that, given a finite simplicial complex X that is simply connected (i.e., with πœ‹1(𝑋) trivial), compute the higher homotopy group πœ‹π‘‘(𝑋) for any given 𝑑β‰₯2 . However, these algorithms come with a caveat: They compute the isomorphism type of πœ‹π‘‘(𝑋) , 𝑑β‰₯2 as an abstract finitely generated abelian group given by generators and relations, but they work with very implicit representations of the elements of πœ‹π‘‘(𝑋) . Converting elements of this abstract group into explicit geometric maps from the d-dimensional sphere 𝑆𝑑 to X has been one of the main unsolved problems in the emerging field of computational homotopy theory. Here we present an algorithm that, given a simply connected space X, computes πœ‹π‘‘(𝑋) and represents its elements as simplicial maps from a suitable triangulation of the d-sphere 𝑆𝑑 to X. For fixed d, the algorithm runs in time exponential in size(𝑋) , the number of simplices of X. Moreover, we prove that this is optimal: For every fixed 𝑑β‰₯2 , we construct a family of simply connected spaces X such that for any simplicial map representing a generator of πœ‹π‘‘(𝑋) , the size of the triangulation of 𝑆𝑑 on which the map is defined, is exponential in size(𝑋) . AU - FilakovskΓ½, Marek AU - Franek, Peter AU - Wagner, Uli AU - Zhechev, Stephan Y ID - 6774 IS - 3-4 JF - Journal of Applied and Computational Topology SN - 2367-1726 TI - Computing simplicial representatives of homotopy group elements VL - 2 ER - TY - CONF AB - Synchronous programs are easy to specify because the side effects of an operation are finished by the time the invocation of the operation returns to the caller. Asynchronous programs, on the other hand, are difficult to specify because there are side effects due to pending computation scheduled as a result of the invocation of an operation. They are also difficult to verify because of the large number of possible interleavings of concurrent computation threads. We present synchronization, a new proof rule that simplifies the verification of asynchronous programs by introducing the fiction, for proof purposes, that asynchronous operations complete synchronously. Synchronization summarizes an asynchronous computation as immediate atomic effect. Modular verification is enabled via pending asynchronous calls in atomic summaries, and a complementary proof rule that eliminates pending asynchronous calls when components and their specifications are composed. We evaluate synchronization in the context of a multi-layer refinement verification methodology on a collection of benchmark programs. AU - Kragl, Bernhard AU - Qadeer, Shaz AU - Henzinger, Thomas A ID - 133 SN - 18688969 TI - Synchronizing the asynchronous VL - 118 ER - TY - CONF AB - Given a locally finite X βŠ† ℝd and a radius r β‰₯ 0, the k-fold cover of X and r consists of all points in ℝd that have k or more points of X within distance r. We consider two filtrations - one in scale obtained by fixing k and increasing r, and the other in depth obtained by fixing r and decreasing k - and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in ℝd+1 whose horizontal integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module from Delaunay mosaics that is isomorphic to the persistence module of the multi-covers. AU - Edelsbrunner, Herbert AU - Osang, Georg F ID - 187 TI - The multi-cover persistence of Euclidean balls VL - 99 ER - TY - JOUR AB - We consider families of confocal conics and two pencils of Apollonian circles having the same foci. We will show that these families of curves generate trivial 3-webs and find the exact formulas describing them. AU - Akopyan, Arseniy ID - 692 IS - 1 JF - Geometriae Dedicata TI - 3-Webs generated by confocal conics and circles VL - 194 ER -