Contains and Inside relationships within combinatorial Pyramids

Irregular pyramids are made of a stack of successively reduced graphs embedded in the plane. Such pyramids are used within the segmentation framework to encode a hierarchy of partitions. The different graph models used within the irregular pyramid framework encode different types of relationships between regions. This paper compares different graph models used within the irregular pyramid framework according to a set of relationships between regions. We also define a new algorithm based on a pyramid of combinatorial maps which allows to determine if one region contains the other using only local calculus.Comment: 35 page

Tiled top-down pyramids and segmentation of large histological images

International audienceRecent microscopic imaging systems such as whole slide scanners provide very large (up to 18GB) high resolution images. Such amounts of memory raise major issues that prevent usual image representation models from being used. Moreover, using such high resolution images, global image features, such as tissues, do not clearly appear at full resolution. Such images contain thus different hierarchical information at different resolutions. This paper presents the model of tiled top-down pyramids which provides a framework to handle such images. This model encodes a hierarchy of partitions of large images defined at different resolutions. We also propose a generic construction scheme of such pyramids whose validity is evaluated on an histological image application

Particle hydrodynamics with tessellation techniques

Lagrangian smoothed particle hydrodynamics (SPH) is a well-established approach to model fluids in astrophysical problems, thanks to its geometric flexibility and ability to automatically adjust the spatial resolution to the clumping of matter. However, a number of recent studies have emphasized inaccuracies of SPH in the treatment of fluid instabilities. The origin of these numerical problems can be traced back to spurious surface effects across contact discontinuities, and to SPH's inherent prevention of mixing at the particle level. We here investigate a new fluid particle model where the density estimate is carried out with the help of an auxiliary mesh constructed as the Voronoi tessellation of the simulation particles instead of an adaptive smoothing kernel. This Voronoi-based approach improves the ability of the scheme to represent sharp contact discontinuities. We show that this eliminates spurious surface tension effects present in SPH and that play a role in suppressing certain fluid instabilities. We find that the new `Voronoi Particle Hydrodynamics' described here produces comparable results than SPH in shocks, and better ones in turbulent regimes of pure hydrodynamical simulations. We also discuss formulations of the artificial viscosity needed in this scheme and how judiciously chosen correction forces can be derived in order to maintain a high degree of particle order and hence a regular Voronoi mesh. This is especially helpful in simulating self-gravitating fluids with existing gravity solvers used for N-body simulations.Comment: 26 pages, 24 figures, currentversion is accepted by MNRA

Confocal microscopic image sequence compression using vector quantization and 3D pyramids

The 3D pyramid compressor project at the University of Glasgow has developed a compressor for images obtained from CLSM device. The proposed method using a combination of image pyramid coder and vector quantization techniques has good performance at compressing confocal volume image data. An experiment was conducted on several kinds of CLSM data using the presented compressor compared to other well-known volume data compressors, such as MPEG-1. The results showed that the 3D pyramid compressor gave higher subjective and objective image quality of reconstructed images at the same compression ratio and presented more acceptable results when applying image processing filters on reconstructed images

Hierarchy construction schemes within the Scale set framework

Segmentation algorithms based on an energy minimisation framework often depend on a scale parameter which balances a fit to data and a regularising term. Irregular pyramids are defined as a stack of graphs successively reduced. Within this framework, the scale is often defined implicitly as the height in the pyramid. However, each level of an irregular pyramid can not usually be readily associated to the global optimum of an energy or a global criterion on the base level graph. This last drawback is addressed by the scale set framework designed by Guigues. The methods designed by this author allow to build a hierarchy and to design cuts within this hierarchy which globally minimise an energy. This paper studies the influence of the construction scheme of the initial hierarchy on the resulting optimal cuts. We propose one sequential and one parallel method with two variations within both. Our sequential methods provide partitions near the global optima while parallel methods require less execution times than the sequential method of Guigues even on sequential machines

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

Knowledge Based Measurement Of Enhancing Brain Tissue In Anisotropic Mr Imagery

Medical Image Analysis has emerged as an important field in the computer vision community. In this thesis, two important issues in medical imaging are addressed and a solution for each is derived and synergistically combined as one coherent system. Firstly, a novel approach is proposed for High Resolution Volume (HRV) construction by combining different frequency components at multiple levels, which are separated by using a multi-resolution pyramid structure. Current clinical imaging protocols make use of multiple orthogonal low resolution scans to measure the size of the tumor. The highly anisotropic data result in difficulty and even errors in tumor assessment. In previous approaches, simple interpolation has been used to construct HRVs from multiple low resolution volumes (LRVs), which fail when large inter-plane spacing is present. In our approach, Laplacian pyramids containing band-pass contents are first computed from registered LRVs. The Laplacian images are expanded in their low resolution axes separately and then fused at each level. A Gaussian pyramid is recovered from the fused Laplacian pyramid, where a volume at the bottom level of the Gaussian pyramid is the constructed HRV. The effectiveness of the proposed approach is validated by using simulated images. The method has also been applied to real clinical data and promising experimental results are demonstrated. Secondly, a new knowledge-based framework to automatically quantify the volume of enhancing tissue in brain MR images is proposed. Our approach provides an objective and consistent way to evaluate disease progression and assess the treatment plan. In our approach, enhanced regions are first located by comparing the difference between the aligned set of pre- and post-contrast T1 MR images. Since some normal tissues may also become enhanced by the administration of Gd-DTPA, using the intensity difference alone may not be able to distinguish normal tissue from the tumor. Thus, we propose a new knowledge-based method employing knowledge of anatomical structures from a probabilistic brain atlas and the prior distribution of brain tumor to identify the real enhancing tissue. Our approach has two main advantages. i) The results are invariant to the image contrast change due to the usage of the probabilistic knowledge-based framework. ii) Using the segmented regions instead of independent pixels facilitates an approach that is much less sensitive to small registration errors and image noise. The obtained results are compared to the ground truth for validation and it is shown that the proposed method can achieve accurate and consistent measurements

Atomic Step Organization in Homoepitaxial Growth on GaAs(111)B Substrates

When homoepitaxial growth is performed on exactly oriented (singular) (111) GaAs substrates, while maintaining the √19 x √19 surface reconstruction, the originally flat surface spontaneously evolves vicinal (111) facets that are tilted approximately 2.5° toward the \u3c 211 \u3e azimuthal directions. These facets form pyramid-like structures where the distance between adjacent peaks can be varied from as little as 1 μm to tens of μm. When these surfaces are observed with atomic force microscopy (AFM), we find that they are extremely smooth with the observed tilt resulting from atomic steps which are spaced at approximately 7.5 nm. We have also studied growth on vicinal GaAs(111) substrates. Our results are interpreted as indicating that the 2.5° vicinal (111) surface has a minimum free energy for the √19 x √19 reconstruction (i.e., that 10 nm spacing of \u3c 011 \u3e steps is thermodynamically preferred). Exactly oriented (111) facets are only observed when their facet width is less than a couple of micrometers implying a minimum nucleation size. This is a surprising result since conventional wisdom argues the surfaces with low Miller indexes are preferred. A possible explanation is an anisotropy in the surface in the two degenerate phases of √19 x √19 reconstruction which are rotated ±23° from the unreconstructed surface