On morphological hierarchical representations for image processing and spatial data clustering

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satis ed. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing

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

Holographic Embeddings of Knowledge Graphs

Learning embeddings of entities and relations is an efficient and versatile method to perform machine learning on relational data such as knowledge graphs. In this work, we propose holographic embeddings (HolE) to learn compositional vector space representations of entire knowledge graphs. The proposed method is related to holographic models of associative memory in that it employs circular correlation to create compositional representations. By using correlation as the compositional operator HolE can capture rich interactions but simultaneously remains efficient to compute, easy to train, and scalable to very large datasets. In extensive experiments we show that holographic embeddings are able to outperform state-of-the-art methods for link prediction in knowledge graphs and relational learning benchmark datasets.Comment: To appear in AAAI-1

Lifeworld Analysis

We argue that the analysis of agent/environment interactions should be extended to include the conventions and invariants maintained by agents throughout their activity. We refer to this thicker notion of environment as a lifeworld and present a partial set of formal tools for describing structures of lifeworlds and the ways in which they computationally simplify activity. As one specific example, we apply the tools to the analysis of the Toast system and show how versions of the system with very different control structures in fact implement a common control structure together with different conventions for encoding task state in the positions or states of objects in the environment.Comment: See http://www.jair.org/ for any accompanying file

Inf-structuring Functions: A Unifying Theory of Connections and Connected Operators

International audienceDuring the last decade, several theories have been proposed in order to extend the notion of set connections in mathematical morphology. These new theories were obtained by generalizing the definition to wider spaces (namely complete lattices) and/or by relaxing some hypothesis. Nevertheless, the links among those different theories are not always well understood, and this work aims at defining a unifying theoretical framework. The adopted approach relies on the notion of inf-structuring function which is simply a mapping that associates a set of sub-elements to each element of the space. The developed theory focuses on the properties of the decompositions given by an inf-structuring function rather than in trying to characterize the properties of the set of connected elements as a whole. We establish several sets of inf-structuring function properties that enable to recover the existing notions of connections, hyperconnections, and attribute space connections. Moreover, we also study the case of grey-scale connected operators that are obtained by stacking set connected operators and we show that they can be obtained using specific inf-structuring functions. This work allows us to better understand the existing theories, it facilitates the reuse of existing results among the different theories and it gives a better view on the unexplored areas of the connection theories

Efficient Irregular Wavefront Propagation Algorithms on Hybrid CPU-GPU Machines

In this paper, we address the problem of efficient execution of a computation pattern, referred to here as the irregular wavefront propagation pattern (IWPP), on hybrid systems with multiple CPUs and GPUs. The IWPP is common in several image processing operations. In the IWPP, data elements in the wavefront propagate waves to their neighboring elements on a grid if a propagation condition is satisfied. Elements receiving the propagated waves become part of the wavefront. This pattern results in irregular data accesses and computations. We develop and evaluate strategies for efficient computation and propagation of wavefronts using a multi-level queue structure. This queue structure improves the utilization of fast memories in a GPU and reduces synchronization overheads. We also develop a tile-based parallelization strategy to support execution on multiple CPUs and GPUs. We evaluate our approaches on a state-of-the-art GPU accelerated machine (equipped with 3 GPUs and 2 multicore CPUs) using the IWPP implementations of two widely used image processing operations: morphological reconstruction and euclidean distance transform. Our results show significant performance improvements on GPUs. The use of multiple CPUs and GPUs cooperatively attains speedups of 50x and 85x with respect to single core CPU executions for morphological reconstruction and euclidean distance transform, respectively.Comment: 37 pages, 16 figure

Machine Hyperconsciousness

Individual animal consciousness appears limited to a single giant component of interacting cognitive modules, instantiating a shifting, highly tunable, Global Workspace. Human institutions, by contrast, can support several, often many, such giant components simultaneously, although they generally function far more slowly than the minds of the individuals who compose them. Machines having multiple global workspaces -- hyperconscious machines -- should, however, be able to operate at the few hundred milliseconds characteistic of individual consciousness. Such multitasking -- machine or institutional -- while clearly limiting the phenomenon of inattentional blindness, does not eliminate it, and introduces characteristic failure modes involving the distortion of information sent between global workspaces. This suggests that machines explicitly designed along these principles, while highly efficient at certain sets of tasks, remain subject to canonical and idiosyncratic failure patterns analogous to, but more complicated than, those explored in Wallace (2006a). By contrast, institutions, facing similar challenges, are usually deeply embedded in a highly stabilizing cultural matrix of law, custom, and tradition which has evolved over many centuries. Parallel development of analogous engineering strategies, directed toward ensuring an 'ethical' device, would seem requisite to the sucessful application of any form of hyperconscious machine technology

Structuring a Wayfinder\u27s Dynamic and Uncertain Environment

Wayfinders typically travel in dynamic environments where barriers and requirements change over time. In many cases, uncertainty exists about the future state of this changing environment. Current geographic information systems lack tools to assist wayfinders in understanding the travel possibilities and path selection options in these dynamic and uncertain settings. The goal of this research is a better understanding of the impact of dynamic and uncertain environments on wayfinding travel possibilities. An integrated spatio-temporal framework, populated with barriers and requirements, models wayfinding scenarios by generating four travel possibility partitions based on the wayfinder\u27s maximum travel speed. Using these partitions, wayfinders select paths to meet scenario requirements. When uncertainty exists, wayfinders often cannot discern the future state of barriers and requirements. The model to address indiscemibility employs a threevalued logic to indicate accessible space, inaccessible space, and possibly inaccessible space. Uncertain scenarios generate up to fifteen distinct travel possibility categories. These fifteen categories generalize into three-valued travel possible partitions based on where travel can occur and where travel is successful. Path selection in these often-complex environments is explored through a specific uncertain scenario that includes a well-defined initial requirement and the possibility of an additional requirement somewhere beforehand. Observations from initial path selection tests with this scenario provide the motivation for the hypothesis that paths arriving as soon as possible to well-defined requirements also maximize the probability of success in meeting possible additional requirements. The hypothesis evaluation occurs within a prototype Travel Possibility Calculator application that employs a set of metrics to test path accessibility in various linear and planar scenarios. The results did not support the hypothesis, but showed instead that path accessibility to possible additional requirements is greatly influenced by the spatio-temporal characteristics of the scenario\u27s barriers

Antiextensive connected operators for image and sequence processing

This paper deals with a class of morphological operators called connected operators. These operators filter the signal by merging its flat zones. As a result, they do not create any new contours and are very attractive for filtering tasks where the contour information has to be preserved. This paper shows that connected operators work implicitly on a structured representation of the image made of flat zones. The max-tree is proposed as a suitable and efficient structure to deal with the processing steps involved in antiextensive connected operators. A formal definition of the various processing steps involved in the operator is proposed and, as a result, several lines of generalization are developed. First, the notion of connectivity and its definition are analyzed. Several modifications of the traditional approach are presented. They lead to connected operators that are able to deal with texture. They also allow the definition of connected operators with less leakage than the classical ones. Second, a set of simplification criteria are proposed and discussed. They lead to simplicity-, entropy-, and motion-oriented operators. The problem of using a nonincreasing criterion is analyzed. Its solution is formulated as an optimization problem that can be very efficiently solved by a Viterbi (1979) algorithm. Finally, several implementation issues are discussed showing that these operators can be very efficiently implemented.Peer ReviewedPostprint (published version

Efficient component-hypertree construction based on hierarchy of partitions

The component-hypertree is a data structure that generalizes the concept of component-tree to multiple (increasing) neighborhoods. However, construction of a component-hypertree is costly because it needs to process a high number of neighbors. In this article, we review some choices of neighborhoods for efficient component-hypertree computation. We also explore a new strategy to obtain neighboring elements based on hierarchy of partitions, leading to a more efficient algorithm with the counterpart of a slight decrease of precision on the distance of merged nodes