CSDL Home IEEE Transactions on Pattern Analysis & Machine Intelligence 2013 vol.35 Issue No.03 - March

Subscribe

Issue No.03 - March (2013 vol.35)

pp: 568-581

D. A. Randell , Sch. of Dentistry, Univ. of Birmingham, Birmingham, UK

G. Landini , Sch. of Dentistry, Univ. of Birmingham, Birmingham, UK

A. Galton , Coll. of Eng., Math. & Phys. Sci., Univ. of Exeter, Exeter, UK

ABSTRACT

Discrete mereotopology (DM) is a first-order spatial logic that fuses together mereology (the theory of parthood relations) and topology to model discrete space. We show how a set of quasitopological functions defined within DM can be mapped to specific operators defined in mathematical morphology (MM) and easily implemented in scientific image processing programs. These functions provide the means to model topological properties of individual regions and spatial relations between them such as contact, overlap, and the relation of part to whole. DM not only extends the expressive power of image processing applications where mathematical morphology is used, but by functioning as a logic it also supplies the formal basis with which to prove the correctness of implemented algorithms as well as providing the computational basis to mechanically reason about segmented digital images using automated reasoning programs. In particular, we show how DM can supply a model-based and algorithmic context to the otherwise blind pixel-based image processing routines still dominating conventional imaging approaches. A number of worked examples drawn from the histological domain are given, including segmentation of cells in culture, identifying basal cell layers from stratified epithelia sections, and cell sorting in blood smears.

INDEX TERMS

Delta modulation, Image segmentation, Mathematical model, Cognition, Imaging, Morphology, representation languages, Life and medical sciences, knowledge representation formalisms and methods, morphological, modeling methodologies

CITATION

D. A. Randell, G. Landini, A. Galton, "Discrete Mereotopology for Spatial Reasoning in Automated Histological Image Analysis",

*IEEE Transactions on Pattern Analysis & Machine Intelligence*, vol.35, no. 3, pp. 568-581, March 2013, doi:10.1109/TPAMI.2012.128REFERENCES

- [1] A. Galton, "The Mereotopology of Discrete Space,"
Proc. Spatial Information Theory: Cognitive and Computational Foundations of Geographic Science, pp. 251-266, 1999.- [2] A. Galton, "The Mereotopology of Discrete Space," manuscript extending the COSIT-99I paper of the same name, unpublished.
- [3] A.G. Cohn and J. Renz, "Qualitative Spatial Reasoning,"
Handbook of Knowledge Representation, F. van Harmelen, V. Lifschitz, and B. Porter, eds., Elsevier, 2007.- [4] D.A. Randell, Z. Cui, and A.G. Cohn, "A Spatial Logic Based on Regions and Connection,"
Proc. Third Int'l Conf. Knowledge Representation and Reasoning, pp. 165-176, 1992.- [5] G. Landini, "Quantitative Analysis of the Epithelial Lining Architecture in Radicular Cysts and Odontogenic Keratocysts,"
Head and Face Medicine, vol. 2, no. 4, pp. 1-9, 2006.- [6] G. Landini and I.E. Othman, "Estimation of Tissue Layer Level by Sequential Morphological Reconstruction,"
J. Microscopy, vol. 209, no. 2, pp. 118-125, 2003.- [7] G. Landini and I.E. Othman, "Architectural Analysis of Oral Cancer, Dysplastic and Normal Epithelia,"
Cytometry A, vol. 61, pp. 45-55, 2004.- [8] G. Landini and D.A. Randell, "Morphological Analysis of Tissue Microarchitecture,"
Proc. Workshop Shape and Size in Medicine, Biotechnology and Materials Science, Apr. 2008.- [9] G. Landini and D.A. Randell, "The Complexity of Cellular neighborhoods,"
Proc. Fifth Int'l Symp. Fractals in Biology and Medicine, pp. 129-158, 2008.- [10] S. Li and M. Ying, "Generalized Region Connection Calculus,"
Artificial Intelligence, vol. 160, nos. 1/2, pp. 1-34, 2004.- [11] M. Aiello and B. Ottens, "The Mathematical MorphoLogical View on Reasoning about Space,"
Proc. Int'l Joint Conf. Artificial Intelligence, pp. 205-211, 2007.- [12] I. Bloch, "Spatial Reasoning under Imprecision Using Fuzzy Set Theory, Formal Logics and Mathematical Morphology,"
Int'l J. Approximate Reasoning, vol. 41, pp. 77-95, 2006.- [13] I. Bloch, "Mathematical Morphology,"
Handbook of Spatial Logics, M. Aiello, I. Pratt-Hartmann, and J. van Benthem, eds., pp. 53 and 80-81, Springer, 2007.- [14] J. Inglada and J. Michel, "Qualitative Spatial Reasoning for High-Resolution Remote Sensing Image Analysis,"
IEEE Trans. Geoscience and Remote Sensing, vol. 47, no. 2, pp. 599-612, Feb. 2009.- [15] S. Li and M. Ying, "Region Connection Calculus: Its Models and Composition Table,"
Artificial Intelligence, vol. 145, pp. 121-146, 2003.- [16] N. Maillot, M. Thonnat, and A. Boucher, "Towards Ontology-Based Cognitive Vision,"
Machine Vision and Applications, vol. 16, no. 1, pp. 33-40, 2004.- [17] J. Serra,
Image Analysis and Mathematical Morphology, vol. 1, Academic Press, 1982 (Image Analysis and Mathematical Morphology, vol. 2: Theoretical AdvancesI by Jean Serra, 1988). - [18] D.A. Randell and G. Landini, "Discrete Mereotopology in Automated Histological Image Analysis,"
Proc. Second ImageJ User and Developer Conf., pp. 151-156, 2008.- [19] W.S. Rasband, "ImageJ," U.S. Nat'l Inst. of Health, http://imagej.nih.govij/, 1997-2012.
- [20] Z. Cui, A.G. Cohn, and D.A. Randell, "Qualitative Simulation Based on a Logic of Space and Time,"
Proc. 10th Nat'l Conf. Artificial Intelligence, pp. 679-684, 1992.- [21] D. Papadias and V. Delis, "Relation-Based Similarity,"
Proc. Fifth ACM Workshop Advances in Geographic Information Systems, 1997.- [22] H.T. Bruns and M.J. Egenhofer, "Similarity of Spatial Scenes,"
Proc. Seventh Symp. Spatial Data Handling, pp. 31-42, 1996.- [23] D.A. Randell and M. Witkowski, "Tracking Regions Using Conceptual Neighborhoods,"
Proc. 16th European Conf. Artificial Intelligence, pp. 63-71, 2004.- [24] D.A. Randell and M. Witkowski, "Using Occlusion Calculi to Interpret Digital Images,"
Proc. 17th European Conf. Artificial Intelligence, pp. 432-436, 2006.- [25] E. Čech,
Topological Spaces. Wiley, 1966, (revised ed. by Z. Frolík and M. Katětov). - [26] A. Galton, "A Generalized Topological View of Motion in Discrete Space,"
Theoretical Computer Science, vol. 305, pp. 111-134, 2003.- [27] C. Freksa, "Temporal Reasoning Based on Semi-Intervals,"
Artificial Intelligence, vol. 54, pp. 199-227, 1992.- [28] A. Galton, "Towards a Qualitative Theory of Movement,"
Proc. Int'l Conf. Spatial Information Theory, pp. 377-396, 1995.- [29] C. Weidenbach, D. Dimova, A. Fietzke, R. Kumar, M. Suda, and P. Wischnewski, "SPASS Version 3.5,"
Proc. 22nd Int'l Conf. Automated Deduction, pp. 140-145, 2009.- [30] J.M.S Prewitt and M.L. Mendelsohn, "The Analysis of Cell Images,"
Annals New York Academy of Sciences, vol. 128, pp. 1035-1053, 1966. |