Grounding spatial relations in natural language by fuzzy representation for human-robot interaction

Additional file 1. Fourier coefficient decomposition for the first guess of the Newton’s method

Topological augmentation: A step forward for qualitative partition reasoning

The current state of the art for partition based qualitative spatial reasoning systems such as the 9-intersection, 9+-intersection, direction relation matrix, and peripheral direction relations is that of the binary set intersection — either empty or non-empty — conveying the intersection (or lack thereof) of an object in the sets deriving the partition. While such representations are sufficient for topological components of objects, these representations are not sufficient for various tasks in qualitative spatial reasoning (composition, representation transfer, converse, etc.) regarding partitions as tiles. Topological augmentation expands the current binary status quo into a system of assigning topological relations between objects and tiles. A case study is presented in the form of the direction relation matrix, demonstrating that an increased vocabulary has benefits for spatial information systems, providing localized context within a qualitative embedding

Dual Logic Concepts based on Mathematical Morphology in Stratified Institutions: Applications to Spatial Reasoning

Several logical operators are defined as dual pairs, in different types of logics. Such dual pairs of operators also occur in other algebraic theories, such as mathematical morphology. Based on this observation, this paper proposes to define, at the abstract level of institutions, a pair of abstract dual and logical operators as morphological erosion and dilation. Standard quantifiers and modalities are then derived from these two abstract logical operators. These operators are studied both on sets of states and sets of models. To cope with the lack of explicit set of states in institutions, the proposed abstract logical dual operators are defined in an extension of institutions, the stratified institutions, which take into account the notion of open sentences, the satisfaction of which is parametrized by sets of states. A hint on the potential interest of the proposed framework for spatial reasoning is also provided.Comment: 36 page

Novel applications of discrete mereotopology to mathematical morphology

This paper shows how the Discrete Mereotopology notions of adjacency and neighbourhood between regions can be exploited through Mathematical Morphology to accept or reject changes resulting from traditional morphological operations such as closing and opening. This leads to a set of six morphological operations (here referred to generically as minimal opening and minimal closing ) where minimal changes fulfil specific spatial constraints. We also present an algorithm to compute the RCC5D and RCC8D relation sets across multiple regions resulting in a performance improvement of over three orders of magnitude over our previously published algorithm for Discrete Mereotopology

Mereotopological Correction of Segmentation Errors in Histological Imaging

In this paper we describe mereotopological methods to programmatically correct image segmentation errors, in particular those that fail to fulfil expected spatial relations in digitised histological scenes. The proposed approach exploits a spatial logic called discrete mereotopology to integrate a number of qualitative spatial reasoning and constraint satisfaction methods into imaging procedures. Eight mereotopological relations defined on binary region pairs are represented as nodes in a set of 20 directed graphs, where the node-to-node graph edges encode the possible transitions between the spatial relations after set-theoretic and discrete topological operations on the regions are applied. The graphs allow one to identify sequences of operations that applied to regions of a given relation, and enables one to resegment an image that fails to conform to a valid histological model into one that does. Examples of the methods are presented using images of H&E-stained human carcinoma cell line cultures

Visuospatial abilities in normal and pathological aging: cognitive processes and neuroimaging correlates

The field of spatial cognition has been evolving rapidly over the last few years, driven by convergence of results from both basic and clinical research. Spatial ability is involved in many cognitive tasks typically performed in everyday life, so it is important to accurately define and assess spatial ability in the context of everyday life. Recent studies also suggest that spatial abilities decline with normal aging, but it is not yet clear which spatial components decline during normal age-related cognitive decline, which are preserved, and at what point the spatial deficits become severe enough to suggest MCI or another degenerative disease. The main goal of my research projects, developed in three studies, was to investigate different components of spatial ability in a population of healthy older people, in individuals affected by mild cognitive impairment, and in autopsy-verified patients with dementia, in order to (a) develop new, more ecological instruments for the assessment of spatial abilities, (b) verify whether the assessment of spatial abilities may help in discriminating between MCI and controls and be used as a marker of the onset of AD, and (c) be used in differential diagnosis between Alzheimer's Disease and Dementia with Lewy bodies. In Study 1, results confirm the a priori hypothesis, ascertaining the reliability of these new spatial tests in measuring different components of spatial abilities: object memory, simultaneous spatial memory and sequential spatial memory. In the second study, the discriminant analyses revealed an elevated discriminative power of the new spatial battery in identifying MCI. Neuroimaging findings showed that MCI patients present a higher level of cortical atrophy in memory-related regions and a different pattern of brain correlation between visuospatial abilities and grey matter values compared with healthy elderly controls. Finally, results of Study 3 suggest that disproportionately severe visuospatial deficits, which are known to be prevalent in DLB patients, also extend to visuoperceptual abilities that do not involve construction or motor manipulation. This deficit reflects primarily Lewy Body pathology and is not related to the degree of concomitant AD pathology. All of this evidence supports the main idea that visuospatial evaluation should have a greater role in normal and pathological aging, in understanding the daily life abilities of healthy older people, in completing the diagnostic process of MCI, and also helping in the differential diagnosis between different types of dementia