Adjacency list

About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.

Fuzzy adjacency between image objects

Abstract: The notion of adjacency has a strong interest for image processing and pattern recognition, since it denotes an important relationship between objects or regions in an image, widely used as a feature in model-based pattern recognition. A crisp definition of adjacency often leads to low robustness in the presence of noise, imprecision, or segmentation errors. We propose two approaches to cope with spatial imprecision in image processing applications, both based on the framework of fuzzy sets. These approaches lead to two completely different classes of definitions of a degree of adjacency. In the first approach, we introduce imprecision as a property of the adjacency relation, and consider adjacency between two (crisp) objects to be a matter of degree. We represent adjacency by a fuzzy relation whose value depends on the distance between the objects. In the second approach, we introduce imprecision (in particular spatial imprecision) as a property of the objects, and consider objects to be fuzzy subsets of the image space. We then represent adjacency by a relation between fuzzy sets. This approach is, in our opinion, more powerful and general. We propose several ways for extending adjacency to fuzzy sets, either by using α-cuts, or by using a formal translation of binary equations into fuzzy ones. Since set equations are more easily translated into fuzzy terms, we shall privilege set representations of adjacency, particularly in the framework of fuzzy mathematical morphology. Finally, we give some hints on how to compare degrees of adjacency, typically for applications in model-based pattern recognition.

3D Dynamic Scene Graphs: Actionable Spatial Perception with Places, Objects, and Humans.

Abstract: We present a unified representation for actionable spatial perception: 3D Dynamic Scene Graphs. Scene graphs are directed graphs where nodes represent entities in the scene (e.g. objects, walls, rooms), and edges represent relations (e.g. inclusion, adjacency) among nodes. Dynamic scene graphs (DSGs) extend this notion to represent dynamic scenes with moving agents (e.g. humans, robots), and to include actionable information that supports planning and decision-making (e.g. spatio-temporal relations, topology at different levels of abstraction). Our second contribution is to provide the first fully automatic Spatial PerceptIon eNgine(SPIN) to build a DSG from visual-inertial data. We integrate state-of-the-art techniques for object and human detection and pose estimation, and we describe how to robustly infer object, robot, and human nodes in crowded scenes. To the best of our knowledge, this is the first paper that reconciles visual-inertial SLAM and dense human mesh tracking. Moreover, we provide algorithms to obtain hierarchical representations of indoor environments (e.g. places, structures, rooms) and their relations. Our third contribution is to demonstrate the proposed spatial perception engine in a photo-realistic Unity-based simulator, where we assess its robustness and expressiveness. Finally, we discuss the implications of our proposal on modern robotics applications. 3D Dynamic Scene Graphs can have a profound impact on planning and decision-making, human-robot interaction, long-term autonomy, and scene prediction. A video abstract is available at this https URL

Learning Unsupervised Hierarchical Part Decomposition of 3D Objects From a Single RGB Image

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.

B-matching for spectral clustering

Abstract: We propose preprocessing spectral clustering with b-matching to remove spurious edges in the adjacency graph prior to clustering. B-matching is a generalization of traditional maximum weight matching and is solvable in polynomial time. Instead of a permutation matrix, it produces a binary matrix with rows and columns summing to a positive integer b. The b-matching procedure prunes graph edges such that the in-degree and out-degree of each node is b, producing a more balanced variant of k-nearest-neighbor. The combinatorial algorithm optimally solves for the maximum weight subgraph and makes subsequent spectral clustering more stable and accurate. Experiments on standard datasets, visualizations, and video data support the use of b-matching to prune graphs prior to spectral clustering.