Efficiently Storing Well-Composed Polyhedral Complexes Computed Over 3D Binary Images

A 3D binary image I can be naturally represented by a combinatorial-algebraic structure called cubical complex and denoted by Q(I ), whose basic building blocks are vertices, edges, square faces and cubes. In Gonzalez-Diaz et al. (Discret Appl Math 183:59–77, 2015), we presented a method to “locally repair” Q(I ) to obtain a polyhedral complex P(I ) (whose basic building blocks are vertices, edges, specific polygons and polyhedra), homotopy equivalent to Q(I ), satisfying that its boundary surface is a 2D manifold. P(I ) is called a well-composed polyhedral complex over the picture I . Besides, we developed a new codification system for P(I ), encoding geometric information of the cells of P(I ) under the form of a 3D grayscale image, and the boundary face relations of the cells of P(I ) under the form of a set of structuring elements. In this paper, we build upon (Gonzalez-Diaz et al. 2015) and prove that, to retrieve topological and geometric information of P(I ), it is enough to store just one 3D point per polyhedron and hence neither grayscale image nor set of structuring elements are needed. From this “minimal” codification of P(I ), we finally present a method to compute the 2-cells in the boundary surface of P(I ).Ministerio de Economía y Competitividad MTM2015-67072-

Sufficient conditions for topological invariance of 2D images under rigid transformations

International audienceIn ℝ^2, rigid transformations are topology-preserving operations. However, this property is generally no longer true when considering digital images instead of continuous ones, due to digitization effects. In this article, we investigate this issue by studying discrete rigid transformations (DRTs) on ℤ^2. More precisely, we define conditions under which digital images preserve their topological properties under any arbitrary DRTs. Based on the recently introduced notion of DRT graph and the classical notion of simple point, we first identify a family of local patterns that authorize topological invariance under DRTs. These patterns are then involved in a local analysis process that guarantees topological invariance of whole digital images in linear time

A topological sampling theorem for Robust boundary reconstruction and image segmentation

AbstractExisting theories on shape digitization impose strong constraints on admissible shapes, and require error-free data. Consequently, these theories are not applicable to most real-world situations. In this paper, we propose a new approach that overcomes many of these limitations. It assumes that segmentation algorithms represent the detected boundary by a set of points whose deviation from the true contours is bounded. Given these error bounds, we reconstruct boundary connectivity by means of Delaunay triangulation and α-shapes. We prove that this procedure is guaranteed to result in topologically correct image segmentations under certain realistic conditions. Experiments on real and synthetic images demonstrate the good performance of the new method and confirm the predictions of our theory

Guidance for benthic habitat mapping: an aerial photographic approach

This document, Guidance for Benthic Habitat Mapping: An Aerial Photographic Approach, describes proven technology that can be applied in an operational manner by state-level scientists and resource managers. This information is based on the experience gained by NOAA Coastal Services Center staff and state-level cooperators in the production of a series of benthic habitat data sets in Delaware, Florida, Maine, Massachusetts, New York, Rhode Island, the Virgin Islands, and Washington, as well as during Center-sponsored workshops on coral remote sensing and seagrass and aquatic habitat assessment. (PDF contains 39 pages) The original benthic habitat document, NOAA Coastal Change Analysis Program (C-CAP): Guidance for Regional Implementation (Dobson et al.), was published by the Department of Commerce in 1995. That document summarized procedures that were to be used by scientists throughout the United States to develop consistent and reliable coastal land cover and benthic habitat information. Advances in technology and new methodologies for generating these data created the need for this updated report, which builds upon the foundation of its predecessor

3D Well-composed Polyhedral Complexes

A binary three-dimensional (3D) image $I$ is well-composed if the boundary surface of its continuous analog is a 2D manifold. Since 3D images are not often well-composed, there are several voxel-based methods ("repairing" algorithms) for turning them into well-composed ones but these methods either do not guarantee the topological equivalence between the original image and its corresponding well-composed one or involve sub-sampling the whole image. In this paper, we present a method to locally "repair" the cubical complex $Q(I)$ (embedded in $\mathbb{R}^3$) associated to $I$ to obtain a polyhedral complex $P(I)$ homotopy equivalent to $Q(I)$ such that the boundary of every connected component of $P(I)$ is a 2D manifold. The reparation is performed via a new codification system for $P(I)$ under the form of a 3D grayscale image that allows an efficient access to cells and their faces

Archival time-based media : topologies of preservation and access

textThe analog time-based media of film, videotape, grooved sound recordings and audiotape have emerged as a growing area of concern for cultural institutions. Collectively, these media constitute a rich body of historical evidence and intangible cultural heritage whose varied physical and technological components incur a wide range of preservation needs. The current moment is also one where digitally-enabled technologies for migrating and sharing time-based media appear to hold infinite promise, even as the most vulnerable elements of the historical record embodied in moving images and recorded sound threaten to disappear. This study investigates the preservation of analog time-based media as it exists in local repositories. The study was formed in response to the needs of a specific collection of analog audio open reels containing music recorded at Houston's Andrus Studios dating from the 1960s and early 1970s, and to the task of finding an appropriate repository to acquire the collection. Physical, technological and intellectual aspects of time-based media are articulated in the literature review, study criteria and semi-structured interview questions employed for the study. The findings form a topology of preservation and access activities that exist in local repositories and that contribute to the sustainability of acquiring substantial collections of obsolete time-based media such as the Andrus Studios collection.Informatio