Plateau Problem in the Watershed Transform

The watershed transform is one of best known and widely used methods for image segmentation in mathematical morphology. Since the definition, deriving from geology and nature observation is quite intuitive and straightforward to implement; many fast and powerful algorithms for watershed transform have already been presented. However, there still occur problems when one wishes to achieve a precise solution on blurred or noised image. The same range of problems is faced when a plateau occurs in the image. In this paper several methods for plateau reduction are discussed and some novel ideas proposed. All algorithms are performed on a set of both natural and synthetic images

Large-Scale Clustering of Cosmic Voids

We study the clustering of voids using $N$-body simulations and simple theoretical models. The excursion-set formalism describes fairly well the abundance of voids identified with the watershed algorithm, although the void formation threshold required is quite different from the spherical collapse value. The void cross bias $b_{\rm c}$ is measured and its large-scale value is found to be consistent with the peak background split results. A simple fitting formula for $b_{\rm c}$ is found. We model the void auto-power spectrum taking into account the void biasing and exclusion effect. A good fit to the simulation data is obtained for voids with radii $\gtrsim$ 30 Mpc/$h$, especially when the void biasing model is extended to 1-loop order. However, the best-fit bias parameters do not agree well with the peak-background split results. Being able to fit the void auto-power spectrum is particularly important not only because it is the direct observable in galaxy surveys, but also our method enables us to treat the bias parameters as nuisance parameters, which are sensitive to the techniques used to identify voids.Comment: 20 pages, 14 figures, minor changes to match published versio

Implementation and complexity of the watershed-from-markers algorithm computed as a minimal cost forest

The watershed algorithm belongs to classical algorithms in mathematical morphology. Lotufo et al. published a principle of the watershed computation by means of an Image Foresting Transform (IFT), which computes a shortest path forest from given markers. The algorithm itself was described for a 2D case (image) without a detailed discussion of its computation and memory demands for real datasets. As IFT cleverly solves the problem of plateaus and as it gives precise results when thin objects have to be segmented, it is obvious to use this algorithm for 3D datasets taking in mind the minimizing of a higher memory consumption for the 3D case without loosing low asymptotical time complexity of O(m+C) (and also the real computation speed). The main goal of this paper is an implementation of the IFT algorithm with a priority queue with buckets and careful tuning of this implementation to reach as minimal memory consumption as possible. The paper presents five possible modifications and methods of implementation of the IFT algorithm. All presented implementations keep the time complexity of the standard priority queue with buckets but the best one minimizes the costly memory allocation and needs only 19-45% of memory for typical 3D medical imaging datasets. Memory saving was reached by an IFT algorithm simplification, which stores more elements in temporary structures but these elements are simpler and thus need less memory. The best presented modification allows segmentation of large 3D medical datasets (up to 512x512x680 voxels) with 12-or 16-bits per voxel on currently available PC based workstations.Comment: v1: 10 pages, 6 figures, 7 tables EUROGRAPHICS conference, Manchester, UK, 2001. v2: 12 pages, reformated for letter, corrected IFT to "Image Foresting Tranform

Investigation of the Statistical and Spatial Distributions of Mercury Contaminated Fish, Surface Waters and Soils in Arkansas

Mercury (Hg) contamination of fish is a widespread problem throughout much of the United States and the world (Louisiana WWW page, 1997). Levels ofHg in fish suffic1ent to exceed the FDA action level of 1 mg kg-1 have been found in many water bodies, including some in Arkansas and Louisiana. As a result of the serious public health ramifications for developing fetuses and for people that subsist on native fish, fish consumption advisories due to Hg contamination have been issued in 29 states. Contamination of surface water bodies by Hg results from deforestation, forest fires, fossil fuels, mining, natural emissions and commercial emissions (Armstrong, 1994). In addition, Hg has a high affinity for organic matter in soil and sediments, and therefore, long-term storage of Hg is an environmental problem. An excellent review of the integration and synthesis of recent work on Hg pollution is given in several papers edited by Watras and Huckabee (1994). The general consensus of the reports in this document seems to be that increases in Hg levels can be attributed to one or more of several mechanisms including atmospheric deposition, acidification of soils and lakes by sulfur deposition followed by an increased sulfate reduction, and transport from other source areas

A Cosmic Watershed: the WVF Void Detection Technique

On megaparsec scales the Universe is permeated by an intricate filigree of clusters, filaments, sheets and voids, the Cosmic Web. For the understanding of its dynamical and hierarchical history it is crucial to identify objectively its complex morphological components. One of the most characteristic aspects is that of the dominant underdense Voids, the product of a hierarchical process driven by the collapse of minor voids in addition to the merging of large ones. In this study we present an objective void finder technique which involves a minimum of assumptions about the scale, structure and shape of voids. Our void finding method, the Watershed Void Finder (WVF), is based upon the Watershed Transform, a well-known technique for the segmentation of images. Importantly, the technique has the potential to trace the existing manifestations of a void hierarchy. The basic watershed transform is augmented by a variety of correction procedures to remove spurious structure resulting from sampling noise. This study contains a detailed description of the WVF. We demonstrate how it is able to trace and identify, relatively parameter free, voids and their surrounding (filamentary and planar) boundaries. We test the technique on a set of Kinematic Voronoi models, heuristic spatial models for a cellular distribution of matter. Comparison of the WVF segmentations of low noise and high noise Voronoi models with the quantitatively known spatial characteristics of the intrinsic Voronoi tessellation shows that the size and shape of the voids are succesfully retrieved. WVF manages to even reproduce the full void size distribution function.Comment: 24 pages, 15 figures, MNRAS accepted, for full resolution, see http://www.astro.rug.nl/~weygaert/tim1publication/watershed.pd

Correcting curvature-density effects in the Hamilton-Jacobi skeleton

The Hainilton-Jacobi approach has proven to be a powerful and elegant method for extracting the skeleton of two-dimensional (2-D) shapes. The approach is based on the observation that the normalized flux associated with the inward evolution of the object boundary at nonskeletal points tends to zero as the size of the integration area tends to zero, while the flux is negative at the locations of skeletal points. Nonetheless, the error in calculating the flux on the image lattice is both limited by the pixel resolution and also proportional to the curvature of the boundary evolution front and, hence, unbounded near endpoints. This makes the exact location of endpoints difficult and renders the performance of the skeleton extraction algorithm dependent on a threshold parameter. This problem can be overcome by using interpolation techniques to calculate the flux with subpixel precision. However, here, we develop a method for 2-D skeleton extraction that circumvents the problem by eliminating the curvature contribution to the error. This is done by taking into account variations of density due to boundary curvature. This yields a skeletonization algorithm that gives both better localization and less susceptibility to boundary noise and parameter choice than the Hamilton-Jacobi method

Information extraction from sensor networks using the Watershed transform algorithm

Wireless sensor networks are an effective tool to provide fine resolution monitoring of the physical environment. Sensors generate continuous streams of data, which leads to several computational challenges. As sensor nodes become increasingly active devices, with more processing and communication resources, various methods of distributed data processing and sharing become feasible. The challenge is to extract information from the gathered sensory data with a specified level of accuracy in a timely and power-efficient approach. This paper presents a new solution to distributed information extraction that makes use of the morphological Watershed algorithm. The Watershed algorithm dynamically groups sensor nodes into homogeneous network segments with respect to their topological relationships and their sensing-states. This setting allows network programmers to manipulate groups of spatially distributed data streams instead of individual nodes. This is achieved by using network segments as programming abstractions on which various query processes can be executed. Aiming at this purpose, we present a reformulation of the global Watershed algorithm. The modified Watershed algorithm is fully asynchronous, where sensor nodes can autonomously process their local data in parallel and in collaboration with neighbouring nodes. Experimental evaluation shows that the presented solution is able to considerably reduce query resolution cost without scarifying the quality of the returned results. When compared to similar purpose schemes, such as “Logical Neighborhood”, the proposed approach reduces the total query resolution overhead by up to 57.5%, reduces the number of nodes involved in query resolution by up to 59%, and reduces the setup convergence time by up to 65.1%

Stream network analysis and geomorphic flood plain mapping from orbital and suborbital remote sensing imagery application to flood hazard studies in central Texas

The author has identified the following significant results. Development of a quantitative hydrogeomorphic approach to flood hazard evaluation was hindered by (1) problems of resolution and definition of the morphometric parameters which have hydrologic significance, and (2) mechanical difficulties in creating the necessary volume of data for meaningful analysis. Measures of network resolution such as drainage density and basin Shreve magnitude indicated that large scale topographic maps offered greater resolution than small scale suborbital imagery and orbital imagery. The disparity in network resolution capabilities between orbital and suborbital imagery formats depends on factors such as rock type, vegetation, and land use. The problem of morphometric data analysis was approached by developing a computer-assisted method for network analysis. The system allows rapid identification of network properties which can then be related to measures of flood response