In recent years there has been a resurgence of interest in our community in the shape analysis of 3D objects represented by surface meshes, their voxelized interiors, or surface point clouds. In part, this interest has been stimulated by the increased availability of RGBD cameras, and by applications of computer vision to autonomous driving, medical imaging, and robotics. In these settings, spectral coordinates have shown promise for shape representation due to their ability to incorporate both local and global shape properties in a manner that is qualitatively invariant to isometric transformations. Yet, surprisingly, such coordinates have thus far typically considered only local surface positional or derivative information. In the present article, we propose to equip spectral coordinates with medial (object width) information, so as to enrich them. The key idea is to couple surface points that share a medial ball, via the weights of the adjacency matrix. We develop a spectral feature using this idea, and the algorithms to compute it. The incorporation of object width and medial coupling has direct benefits, as illustrated by our experiments on object classification, object part segmentation, and surface point correspondence.

Humans are excellent at perceiving illusory outlines. We are readily able to complete contours, shapes, scenes, and even unseen objects when provided with images that contain broken fragments of a connected appearance. In vision science, this ability is largely explained by perceptual grouping: a foundational set of processes in human vision that describes how separated elements can be grouped. In this paper, we revisit an algorithm called Stochastic Completion Fields (SCFs) that mechanizes a set of such processes -- good continuity, closure, and proximity -- through contour completion. This paper implements a modernized model of the SCF algorithm, and uses it in an image editing framework where we propose novel methods to complete fragmented contours. We show how the SCF algorithm plausibly mimics results in human perception. We use the SCF completed contours as guides for inpainting, and show that our guides improve the performance of state-of-the-art models. Additionally, we show that the SCF aids in finding edges in high-noise environments. Overall, our described algorithms resemble an important mechanism in the human visual system, and offer a novel framework that modern computer vision models can benefit from.

Traditionally, the needs of vulnerable populations have been addressed by a plethora of public and private agencies that rely on donations of money, goods and services which they distribute based on their perception of what is needed and where. This approach, however, lacks a comprehensive understanding of the demand side as well as the ability to coordinate between various suppliers of goods and services, identify latent supply and predict future demand. To help address these issues, we have developed a knowledge-based platform that harnesses advances in several AI fields for efficient and effective provisioning of goods and services.

The design of ontologies for new commonsense domains continues to pose challenges, particularly in cases where multiple potential axiomatizations satisfy the requirements for the ontology. One approach is to specify the requirements with respect to the intended semantics of the terminology; from a mathematical perspective the requirements may be characterized by the class of structures(referred to as the required models) which capturethe intended semantics. This approach leads to a natural notion of the correctness as a relationship between the models of the axiomatization of the ontology and the required models for the ontology. In this paper, we consider three possible generalizations of the notion of the correctness of an ontology in the case in which the ontology and the required models have different signatures.We show that these notions of correctness lead to different approaches for ontology evaluation and discuss the benefits and drawbacks of each approach.

The representation of dates and their relationship to time and duration has long been recognized as an important problem in commonsense reasoning. However, existing date ontologies, such as OWL-Time and Date-Time Foundation Vocabulary from the Object Modeling Group, take either over-simplistic or convoluted approaches to defining the key semantics for dates. We show that such approaches are inadequate and provide an improved solution: a first-order Date Ontology that is an extension of the Process Specification Language and an existing duration ontology. Rather than treat dates as a class of timepoints, we axiomatize dates as a class of complex activities which have multiple periodic occurrences. We consider two modules of the Date Ontology, and characterize the models of the Date Ontology up to elementary equivalence.

Estimating the distance from a current partial-order plan to the goal state of the plan task is a challenging problem, with past research achieving only limited success. In an effort to understand the reasons for this situation, we investigate the computational complexity of the partial-order plan viability problem. We define several boundaries between the tractable and intractable subclasses of the problem, from which we identify several constraints that contribute to the computational intractability of the problem. These results bring new insights into the design and the development of future  partial-order planning heuristics.

We present an ontology consisting of a theory of spatial dimension and a theory of dimension-independent mereological and topological relations in space. Though both are fairly weak axiomatizations, their interplay suffices to define various mereotopological relations and to make any necessary dimension constraints explicit. We show that models of the INCH Calculus and the Region-Connection Calculus (RCC) can be obtained from extensions of the proposed ontology.

A semantics-preserving exchange of information between two software applications requires mappings between logically equivalent concepts in the ontology of each application. The challenge of semantic integration is therefore equivalent to the problem of generating such mappings, determining that they are correct, and providing a vehicle for executing the mappings, thus translating terms from one ontology into another. This article presents an approach toward this goal using techniques that exploit the model-theoretic structures underlying ontologies. With these as inputs, semiautomated and automated components may be used to create mappings between ontologies and perform translations.

A semantics-preserving exchange of information between two software applications requires mappings between logically equivalent concepts in the ontology of each application. The challenge of semantic integration is therefore equivalent to the problem of generating such mappings, determining that they are correct, and providing a vehicle for executing the mappings, thus translating terms from one ontology into another. This article presents an approach toward this goal using techniques that exploit the model-theoretic structures underlying ontologies. With these as inputs, semiautomated and automated components may be used to create mappings between ontologies and perform translations.

The PROCESS SPECIFICATION language (PSL) has been designed to facilitate correct and complete exchange of process information among manufacturing systems, such as scheduling, process modeling, process planning, production planning, simulation, project management, work flow, and business-process reengineering. We give an overview of the theories within the PSL ontology, discuss some of the design principles for the ontology, and finish with examples of process specifications that are based on the ontology.