Topic
Adjacency list
About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.
Papers published on a yearly basis
Papers
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TL;DR: 2DSLSDP can well preserve not only the adjacency similarity structure, but also the diversity of data points, which is important for the classification, as well as the effectiveness of the proposed method.
39 citations
TL;DR: A new linear integer programming formulation of adjacency constraints for the area restriction model is presented, which are small in number and are a strong model for the adjacence probl...
Abstract: We present a new linear integer programming formulation of adjacency constraints for the area restriction model. These constraints are small in number and are a strong model for the adjacency problem. We describe constraint development, including strengthening and lifting, to improve the basic formulation. The model does not prohibit all adjacency violations, but computations show they are few in number. Using example forests ranging from 750 to more than 6000 polygons, optimization problems were solved and good solutions obtained in very short computational time.
39 citations
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TL;DR: This work proposes a novel formulation that allows to jointly recover the geometry of a 3D object as a set of primitives as well as their latent hierarchical structure without part-level supervision, and recovers the higher level structural decomposition of various objects in the form of a binary tree ofPrimitives.
Abstract: Humans perceive the 3D world as a set of distinct objects that are characterized by various low-level (geometry, reflectance) and high-level (connectivity, adjacency, symmetry) properties. Recent methods based on convolutional neural networks (CNNs) demonstrated impressive progress in 3D reconstruction, even when using a single 2D image as input. However, the majority of these methods focuses on recovering the local 3D geometry of an object without considering its part-based decomposition or relations between parts. We address this challenging problem by proposing a novel formulation that allows to jointly recover the geometry of a 3D object as a set of primitives as well as their latent hierarchical structure without part-level supervision. Our model recovers the higher level structural decomposition of various objects in the form of a binary tree of primitives, where simple parts are represented with fewer primitives and more complex parts are modeled with more components. Our experiments on the ShapeNet and D-FAUST datasets demonstrate that considering the organization of parts indeed facilitates reasoning about 3D geometry.
39 citations
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TL;DR: The chordal-TSSOS hierarchy that is proposed is a new sparse moment-SOS framework based on term-sparsity and chordal extension, which is a two-level hierarchy of semidefinite programming relaxations for solving polynomial optimization problems (POPs).
Abstract: This work is a follow-up and a complement to arXiv:1912.08899 [math.OC] for solving polynomial optimization problems (POPs). The chordal-TSSOS hierarchy that we propose is a new sparse moment-SOS framework based on term-sparsity and chordal extension. By exploiting term-sparsity of the input polynomials we obtain a two-level hierarchy of semidefinite programming relaxations. The novelty and distinguishing feature of such relaxations is to obtain quasi block-diagonal matrices obtained in an iterative procedure that performs chordal extension of certain adjacency graphs. The graphs are related to the terms arising in the original data and not to the links between variables. Various numerical examples demonstrate the efficiency and the scalability of this new hierarchy for both unconstrained and constrained POPs. The two hierarchies are complementary. While the former TSSOS arXiv:1912.08899 [math.OC] has a theoretical convergence guarantee, the chordal-TSSOS has superior performance but lacks this theoretical guarantee.
38 citations
TL;DR: This paper investigates two constraints for the connected operator class, and leads to a new approach to the class of filters by reconstruction of flat non-binary (gray-level) operators.
Abstract: This paper investigates two constraints for the connected operator class. For binary images, connected operators are those that treat grains and pores of the input in an all or nothing way, and therefore they do not introduce discontinuities. The first constraint, called connected-component (c.c.) locality, constrains the part of the input that can be used for computing the output of each grain and pore. The second, called adjacency stability, establishes an adjacency constraint between connected components of the input set and those of the output set. Among increasing operators, usual morphological filters can satisfy both requirements. On the other hand, some (non-idempotent) morphological operators such as the median cannot have the adjacency stability property. When these two requirements are applied to connected and idempotent morphological operators, we are lead to a new approach to the class of filters by reconstruction. The important case of translation invariant operators and the relationships between translation invariance and connectivity are studied in detail. Concepts are developed within the binary (or set) framework; however, conclusions apply as well to flat non-binary (gray-level) operators.
38 citations