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

Modelling mammographic microcalcification clusters using persistent mereotopology

AbstractIn mammographic imaging, the presence of microcalcifications, small deposits of calcium in the breast, is a primary indicator of breast cancer. However, not all microcalcifications are malignant and their distribution within the breast can be used to indicate whether clusters of microcalcifications are benign or malignant. Computer-aided diagnosis (CAD) systems can be employed to help classify such microcalcification clusters. In this paper a novel method for classifying microcalcification clusters is presented by representing discrete mereotopological relations between the individual microcalcifications over a range of scales in the form of a mereotopological barcode. This barcode based representation is able to model complex relations between multiple regions and the results on mammographic microcalcification data shows the effectiveness of this approach. Classification accuracies of 95% and 80% are achieved on the MIAS and DDSM datasets, respectively. These results are comparable to existing state-of-the art methods. This work also demonstrates that mereotopological barcodes could be used to help trained clinicians in their diagnosis by providing a clinical interpretation of barcodes that represent both benign and malignant cases

The Logic of Discrete Qualitative Relations

We consider a modal logic based on mathematical morphology which allows the expression of mereotopological relations between subgraphs. A specific form of topological closure between graphs is expressible in this logic, both as a combination of the negation ¬ and its dual , and as modality, using the stable relation Q, which describes the incidence structure of the graph. This allows to define qualitative spatial relations between discrete regions, and to compare them with earlier works in mereotopology, both in the discrete and in the continuous space

The Logic of Discrete Qualitative Relations

We consider a modal logic based on mathematical morphology which allows the expression of mereotopological relations between subgraphs. A specific form of topological closure between graphs is expressible in this logic, both as a combination of the negation ¬ and its dual , and as modality, using the stable relation Q, which describes the incidence structure of the graph. This allows to define qualitative spatial relations between discrete regions, and to compare them with earlier works in mereotopology, both in the discrete and in the continuous space

Ontological Levels in Histological Imaging

Paper presented at the 9th edition of the Formal Ontology in Information Systems conference, FOIS 2016, July 6–9, 2016, Annecy, FranceThis is the author accepted manuscript. The final version is available from IOS Press via the DOI in this record.In this paper we present an ontological perspective on ongoing work in histological and histopathological imaging involving the quantitative and algorithmic analysis of digitised images of cells and tissues. We present the derivation of consistent histological models from initially captured images of prepared tissue samples as a progression through a number of ontological levels, each populated by its distinctive classes of entities related in systematic ways to entities at other levels. We see this work as contributing to ongoing efforts to provide a consistent and widely accepted suite of ontological resources such as those currently constituting the OBO Foundry, and where possible we draw links between our work and existing ontologies within that suite.This research is supported by EPSRC through funding under grant EP/M023869/1 “Novel context-based segmentation algorithms for intelligent microscopy”

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

Topological Foundations of Cognitive Science

A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki

Subatomic quantification (Volume 6)

The goal of this book is to explore the relationship between the cognitive notion of parthood and various grammatical devices expressing this concept in natural language. The monograph aims to investigate syntactic constructions and lexical categories, e.g., partitives, whole-adjectives, and multipliers, encoding different kinds of part-whole structures both in Slavic and non-Slavic languages. It is envisioned to inspire radical rethinking of the ontology of models accounting for nominal semantics. Specifically, it provides novel evidence for a mereotopological approach to meaning, i.e., a theory of wholes that captures not only parthood but also topological relations holding between parts. This evidence comes from the phenomenon of subatomic quantification, i.e., quantification over parts of referents of concrete count nouns

AN AUTOMATED COMPUTER-AIDED DETECTION (CADe) AND DIAGNOSIS (CADx) SYSTEM FOR BREAST MICROCALCIFICATIONS IN MAMMOGRAMS

ABSTRACTAn automated computer aided diagnosis system has been proposed for detection of microcalcification (MC) clusters in mammograms. The proposed system is a whole system including suspicious regions identification, MCs detection, false positive reduction and benign/malign classification. For classification of suspicious microcalcification regions, a multilayer perceptron (MLP) neural network was used with grey level co-occurrence matrix (GLCM) and statistical features.  Then to decrease the false positive classification ratio, we used cascade correlation neural network (CCNN) with grey level run length matrix (GLRLM) features. In the last step, hybrid form of discriminant analysis and support vector machine (SVM) methods were used with GLRLM features for benign/malign classification of detected MC clusters. The open access Mammographic Image Analysis Society (MIAS) database was used for the study. Experimental results show that the proposed algorithm obtained 86% sensitivity, 98.3% specificity and 1.163 FPpI rates for detection an for diagnosis of breast cancer, the obtained sensitivity and specificity values are 100% and 100% respectively. Despite the vision difficulty of MC clusters, the novel system provides very satisfactory results. Furthermore, the developed system is fully automatic whole system which gives outputs as percentages and transformed assessment categories. Keywords: Mammograms, Breast cancer, Computer aided diagnosis, Cascade correlation neural network (CCNN), Grey level co-occurrence matrix (GLCM), Grey level run length matrix (GLRLM).