Distributed Connected Component Filtering and Analysis in 2-D and 3-D Tera-Scale Data Sets

Connected filters and multi-scale tools are region-based operators acting on the connected components of an image. Component trees are image representations to efficiently perform these operations as they represent the inclusion relationship of the connected components hierarchically. This paper presents disccofan (DIStributed Connected COmponent Filtering and ANalysis), a new method that extends the previous 2-D implementation of the Distributed Component Forests (DCFs) to handle 3-D processing and higher dynamic range data sets. disccofan combines shared and distributed memory techniques to efficiently compute component trees, user-defined attributes filters, and multi-scale analysis. Compared to similar methods, disccofan is faster and scales better on low and moderate dynamic range images, and is the only method with a speed-up larger than 1 on a realistic, astronomical floating-point data set. It achieves a speed-up of 11.20 using 48 processes to compute the DCF of a 162 Gigapixels, single-precision floating-point 3-D data set, while reducing the memory used by a factor of 22. This approach is suitable to perform attribute filtering and multi-scale analysis on very large 2-D and 3-D data sets, up to single-precision floating-point value

Connected operators based on region-tree pruning strategies

This paper discusses region-based representations useful to create connected operators. The filtering approach involves three steps: 1) a region tree representation of the input image is constructed; 2) the simplification is obtained by pruning the tree; and 3) and output image is constructed from the pruned tree. The paper focuses in particular on the pruning strategies that can be used depending of the increasing of the simplification criteria.Peer ReviewedPostprint (published version

Auto-dual connected operators based on iterative merging algorithms

This paper proposes a new set of connected operators that are autodual. Classical connected operators are analyzed within the framework of merging algorithms. The discussion highlights three basic notions: merging order , merging criterion and region model. As a result a general merging algorithm is proposed. It can be used to create new connected operators and in particular autodual operators. Implementation issues are also discussed.Peer ReviewedPostprint (published version

Analytical solution of thermal magnetization on memory stabilizer structures

We return to the question of how the choice of stabilizer generators affects the preservation of information on structures whose degenerate ground state encodes a classical redundancy code. Controlled-not gates are used to transform the stabilizer Hamiltonian into a Hamiltonian consisting of uncoupled single spins and/or pairs of spins. This transformation allows us to obtain an analytical partition function and derive closed form equations for the relative magnetization and susceptibility. These equations are in agreement with the numerical results presented in [arXiv:0907.0394v1] for finite size systems. Analytical solutions show that there is no finite critical temperature, Tc=0, for all of the memory structures in the thermodynamic limit. This is in contrast to the previously predicted finite critical temperatures based on extrapolation. The mismatch is a result of the infinite system being a poor approximation even for astronomically large finite size systems, where spontaneous magnetization still arises below an apparent finite critical temperature. We extend our analysis to the canonical stabilizer Hamiltonian. Interestingly, Hamiltonians with two-body interactions have a higher apparent critical temperature than the many-body Hamiltonian.Comment: 13 pages, 7 figures, analytical solutions of problems studied numerically in arXiv:0907.0394v1 [quant-ph

Morphological operators for very low bit rate video coding

This paper deals with the use of some morphological tools for video coding at very low bit rates. Rather than describing a complete coding algorithm, the purpose of this paper is to focus on morphological connected operators and segmentation tools that have proved to be attractive for compression.Peer ReviewedPostprint (published version

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

Pattern tree-based XOLAP rollup operator for XML complex hierarchies

With the rise of XML as a standard for representing business data, XML data warehousing appears as a suitable solution for decision-support applications. In this context, it is necessary to allow OLAP analyses on XML data cubes. Thus, XQuery extensions are needed. To define a formal framework and allow much-needed performance optimizations on analytical queries expressed in XQuery, defining an algebra is desirable. However, XML-OLAP (XOLAP) algebras from the literature still largely rely on the relational model. Hence, we propose in this paper a rollup operator based on a pattern tree in order to handle multidimensional XML data expressed within complex hierarchies

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