A quasi-linear algorithm to compute the tree of shapes of n-D images

International audienceTo compute the morphological self-dual representation of images, namely the tree of shapes, the state-of-the-art algorithms do not have a satisfactory time complexity. Furthermore the proposed algorithms are only effective for 2D images and they are far from being simple to implement. That is really penalizing since a self-dual representation of images is a structure that gives rise to many powerful operators and applications, and that could be very useful for 3D images. In this paper we propose a simple-to-write algorithm to compute the tree of shapes; it works for \nD images and has a quasi-linear complexity when data quantization is low, typically 12~bits or less. To get that result, this paper introduces a novel representation of images that has some amazing properties of continuity, while remaining discrete

A Fast, Memory-Efficient Alpha-Tree Algorithm using Flooding and Tree Size Estimation

The alpha-tree represents an image as hierarchical set of alpha-connected components. Computation of alpha-trees suffers from high computational and memory requirements compared with similar component tree algorithms such as max-tree. Here we introduce a novel alpha-tree algorithm using 1) a flooding algorithm for computational efficiency and 2) tree size estimation (TSE) for memory efficiency. In TSE, an exponential decay model was fitted to normalized tree sizes as a function of the normalized root mean squared deviation (NRMSD) of edge-dissimilarity distributions, and the model was used to estimate the optimum memory allocation size for alpha-tree construction. An experiment on 1256 images shows that our algorithm runs 2.27 times faster than Ouzounis and Soille's thanks to the flooding algorithm, and TSE reduced the average memory allocation of the proposed algorithm by 40.4%, eliminating unused allocated memory by 86.0% with a negligible computational cost

Spherical Fluorescent Particle Segmentation and Tracking in 3D Confocal Microscopy

Spherical fluorescent particle are micrometer-scale spherical beads used in various areas of physics, chemistry or biology as markers associated with local physical media. They are useful for example in fluid dynamics to characterize flows, diffusion coefficients, viscosity or temperature; they are used in cells dynamics to estimate mechanical strain and stress at the micrometer scale. In order to estimate these physical measurements, tracking these particles is necessary. Numerous approaches and existing packages, both open-source and proprietary are available to achieve tracking with a high degree of precision in 2D. However, little such software is available to achieve tracking in 3D. One major difficulty is that 3D confocal microscopy acquisition is not typically fast enough to assume that the beads are stationary during the whole 3D scan. As a result, beads may move between planar scans. Classical approaches to 3D segmentation may yield objects are not spherical. In this article, we propose a 3D bead segmentation that deals with this situation

Extraction of Ancient Map Contents Using Trees of Connected Components

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Extraction of ancient maps content by using trees of connected components

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DEDICAT 6G - Dynamic coverage extension and distributed intelligence for human centric applications with assured security, privacy and trust:From 5G to 6G

5G networks offer unparalleled data rates and features. However these are still far from what a hyperconnected society and industry needs. Future wireless connectivity Beyond 5G (B5G)/6G will require a smart and green platform that is ultra-fast, highly adaptive, and dependable to support innovative, human-centric applications securely. This is the focus of the EU-funded DEDICAT 6G project, the vision and methodology of which is presented in this paper. DEDICAT 6G investigates enablers for dynamic distribution of intelligence to improve task execution time, energy efficiency, and ultimately, reduce end-to-end latency. The project also examines solutions for dynamic coverage extensions utilizing robots, connected vehicles and drones. The scope also comprises methods for security, privacy, and trust assurance including enablers for novel interaction between humans and digital systems exploiting innovative interfaces and devices, like smart glasses. DEDICAT 6G focuses on four representative 6G use cases: Smart Warehousing, Enhanced Experience, Public Safety and Smart Highway. The developed solutions will be demonstrated and tested in these use cases through experiments in laboratory environments, and larger field evaluations utilizing diverse assets and testing facilities. The aim is to derive results that will showcase substantial improvements in terms of intelligent network load balancing and resource allocation, extended coverage, enhanced security, privacy and trust and human-machine applications, </p

Constructing a Braid of Partitions from Hierarchies of Partitions

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A Root-to-Leaf Algorithm Computing the Tree of Shapes of an Image

International audienceWe propose an algorithm computing the tree of shapes of an image, a unified variation of the component trees, proceeding from the root to the leaf shapes in a recursive fashion. It proceeds differently from existing algorithms that start from leaves, which are regional extrema of intensity, and build the intermediate shapes up to the root, which is the whole image. The advantage of the proposed method is a simpler, clearer, and more concise implementation, together with a more favorable running time on natural images. For integer-valued images, the complexity is proportional to the total variation, which is the memory size of the output tree, which makes the algorithm optimal