A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

The Spine of the Cosmic Web

We present the SpineWeb framework for the topological analysis of the Cosmic Web and the identification of its walls, filaments and cluster nodes. Based on the watershed segmentation of the cosmic density field, the SpineWeb method invokes the local adjacency properties of the boundaries between the watershed basins to trace the critical points in the density field and the separatrices defined by them. The separatrices are classified into walls and the spine, the network of filaments and nodes in the matter distribution. Testing the method with a heuristic Voronoi model yields outstanding results. Following the discussion of the test results, we apply the SpineWeb method to a set of cosmological N-body simulations. The latter illustrates the potential for studying the structure and dynamics of the Cosmic Web.Comment: Accepted for publication HIGH-RES version: http://skysrv.pha.jhu.edu/~miguel/SpineWeb

Voids in cosmological simulations over cosmic time

We study evolution of voids in cosmological simulations using a new method for tracing voids over cosmic time. The method is based on tracking watershed basins (contiguous regions around density minima) of well developed voids at low redshift, on a regular grid of density field. It enables us to construct a robust and continuous mapping between voids at different redshifts, from initial conditions to the present time. We discuss how the new approach eliminates strong spurious effects of numerical origin when voids evolution is traced by matching voids between successive snapshots (by analogy to halo merger trees). We apply the new method to a cosmological simulation of a standard LambdaCDM cosmological model and study evolution of basic properties of typical voids (with effective radii between 6Mpc/h and 20Mpc/h at redshift z=0) such as volumes, shapes, matter density distributions and relative alignments. The final voids at low redshifts appear to retain a significant part of the configuration acquired in initial conditions. Shapes of voids evolve in a collective way which barely modifies the overall distribution of the axial ratios. The evolution appears to have a weak impact on mutual alignments of voids implying that the present state is in large part set up by the primordial density field. We present evolution of dark matter density profiles computed on iso-density surfaces which comply with the actual shapes of voids. Unlike spherical density profiles, this approach enables us to demonstrate development of theoretically predicted bucket-like shape of the final density profiles indicating a wide flat core and a sharp transition to high-density void walls.Comment: 13 pages, 13 figures; accepted for publication in MNRA

Identification of Individual Glandular Regions Using LCWT and Machine Learning Techniques

A new approach for the segmentation of gland units in histological images is proposed with the aim of contributing to the improvement of the prostate cancer diagnosis. Clustering methods on several colour spaces are applied to each sample in order to generate a binary mask of the different tissue components. From the mask of lumen candidates, the Locally Constrained Watershed Transform (LCWT) is applied as a novel gland segmentation technique never before used in this type of images. 500 random gland candidates, both benign and pathological, are selected to evaluate the LCWT technique providing results of Dice coefficient of 0.85. Several shape and textural descriptors in combination with contextual features and a fractal analysis are applied, in a novel way, on different colour spaces achieving a total of 297 features to discern between artefacts and true glands. The most relevant features are then selected by an exhaustive statistical analysis in terms of independence between variables and dependence with the class. 3.200 artefacts, 3.195 benign glands and 3.000 pathological glands are obtained, from a data set of 1468 images at 10x magnification. A careful strategy of data partition is implemented to robustly address the classification problem between artefacts and glands. Both linear and non-linear approaches are considered using machine learning techniques based on Support Vector Machines (SVM) and feedforward neural networks achieving values of sensitivity, specificity and accuracy of 0.92, 0.97 and 0.95, respectivelyThis work has been funded by the Ministry of Economy, Industry and Competitiveness under the SICAP project (DPI2016-77869-C2-1-R). The work of Adri´an Colomer has been supported by the Spanish FPI Grant BES-2014-067889. We gratefully acknowledge the support of NVIDIA Corporation with the donation of the Titan Xp GPU used for this researchGarcía-Pardo, JG.; Colomer, A.; Naranjo Ornedo, V.; Peñaranda, F.; Sales, MÁ. (2018). Identification of Individual Glandular Regions Using LCWT and Machine Learning Techniques. En Intelligent Data Engineering and Automated Learning – IDEAL 2018. Springer. 642-650. https://doi.org/10.1007/978-3-030-03493-1_67S642650Gleason, D.F.: Histologic grading and clinical staging of prostatic carcinoma. In: Urologic Pathology (1977)Naik, S., Doyle, S., Feldman, M., Tomaszewski, J., Madabhushi, A.: Gland segmentation and computerized gleason grading of prostate histology by integrating low-, high-level and domain specific information. In: MIAAB Workshop, pp. 1–8 (2007)Nguyen, K., Sabata, B., Jain, A.K.: Prostate cancer grading: gland segmentation and structural features. Pattern Recogn. Lett. 33(7), 951–961 (2012)Kwak, J.T., Hewitt, S.M.: Multiview boosting digital pathology analysis of prostate cancer. Comput. Methods Programs Biomed. 142, 91–99 (2017)Ren, J., Sadimin, E., Foran, D.J., Qi, X.: Computer aided analysis of prostate histopathology images to support a refined gleason grading system. In: SPIE Medical Imaging, International Society for Optics and Photonics, p. 101331V (2017)Soille, P.: Morphological Image Analysis: Principles and Applications. Springer, Berlin (2013)Nguyen, K., Sarkar, A., Jain, A.K.: Structure and context in prostatic gland segmentation and classification. In: Ayache, N., Delingette, H., Golland, P., Mori, K. (eds.) MICCAI 2012. LNCS, vol. 7510, pp. 115–123. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33415-3_15Beare, R.: A locally constrained watershed transform. IEEE Trans. Pattern Anal. Mach. Intell. 28(7), 1063–1074 (2006)Gertych, A., et al.: Machine learning approaches to analyze histological images of tissues from radical prostatectomies. Comput. Med. Imaging Graph. 46, 197–208 (2015)Ojala, T., Pietikainen, M., Maenpaa, T.: Multiresolution gray-scale and rotation invariant texture classification with local binary patterns. IEEE Trans. Pattern Anal. Mach. Intell. 24(7), 971–987 (2002)Guo, Z., Zhang, L., Zhang, D.: A completed modeling of local binary pattern operator for texture classification. IEEE Trans. Image Process. 19(6), 1657–1663 (2010)Huang, P., Lee, C.: Automatic classification for pathological prostate images based on fractal analysis. IEEE Trans. Med. Imaging 28(7), 1037–1050 (2009)Ruifrok, A.C., Johnston, D.A., et al.: Quantification of histochemical staining by color deconvolution. Anal. Quant. Cytol. Histol. 23(4), 291–299 (2001

Public participation in watershed management:international practices for inclusiveness

This paper outlines a number of examples from around the world of participatory processes for watershed decision-making, and discusses how they work, why they are important, their social and ecological potential, and the practical details of how to start, expand and develop them. Because of longstanding power differentials in all societies along gender, class and ethnic lines, equitable public participation requires the recognition that different members of society have different kinds of relationships with the environment in general, and with water in particular. From a range of political perspectives, inclusive participatory governance processes have many benefits. The author has recently completed a 5 year project linking universities and NGOs in Brazil and Canada to develop methods of broadening public engagement in local watershed management committees, with a special focus on gender and marginalized communities. The innovative environmental education and multi-lingual international public engagement practices of the Centre for Socio-Environmental Knowledge and Care of the La Plata Basin (which spans Brazil, Argentina, Uruguay, Paraguay and Bolivia) are also discussed in this paper.This research was supported by the International Development Research Centr

A Cosmic Watershed: the WVF Void Detection Technique

On megaparsec scales the Universe is permeated by an intricate filigree of clusters, filaments, sheets and voids, the Cosmic Web. For the understanding of its dynamical and hierarchical history it is crucial to identify objectively its complex morphological components. One of the most characteristic aspects is that of the dominant underdense Voids, the product of a hierarchical process driven by the collapse of minor voids in addition to the merging of large ones. In this study we present an objective void finder technique which involves a minimum of assumptions about the scale, structure and shape of voids. Our void finding method, the Watershed Void Finder (WVF), is based upon the Watershed Transform, a well-known technique for the segmentation of images. Importantly, the technique has the potential to trace the existing manifestations of a void hierarchy. The basic watershed transform is augmented by a variety of correction procedures to remove spurious structure resulting from sampling noise. This study contains a detailed description of the WVF. We demonstrate how it is able to trace and identify, relatively parameter free, voids and their surrounding (filamentary and planar) boundaries. We test the technique on a set of Kinematic Voronoi models, heuristic spatial models for a cellular distribution of matter. Comparison of the WVF segmentations of low noise and high noise Voronoi models with the quantitatively known spatial characteristics of the intrinsic Voronoi tessellation shows that the size and shape of the voids are succesfully retrieved. WVF manages to even reproduce the full void size distribution function.Comment: 24 pages, 15 figures, MNRAS accepted, for full resolution, see http://www.astro.rug.nl/~weygaert/tim1publication/watershed.pd