Isosurfaces: Geometry, Topology, and Algorithms R. Wenger. A.K. Peters/CRC Press, 2013. "Isosurfaces: Geometry, Topology, and Algorithms" is the book I wrote on isosurfaces. Topics include the Marching Cubes algorithm and variants, dual contouring algorithms, multilinear interpolation, multiresolution isosurface extraction, isosurfaces in four dimensions, interval volumes, and contour trees. The book also describes data structures for faster isosurface extraction as well as methods for selecting significant isovalues. For more information, including the table of contents, see: http://www.crcpress.com/product/isbn/9781466570979 Chapter 2, Sections 13: A sample preview of the text. 
Constructing Isosurfaces with Sharp Edges and Corners using Cube Merging A, Bhattacharya and R. Wenger. Computer Graphics Forum, 32, 2013, 1120. A number of papers present algorithms to construct isosurfaces with sharp edges and corners from hermite data, i.e. the exact surface normals at the exact intersection of the surface and grid edges. We discuss some fundamental problems with the previous algorithms and describe a new approach, based on merging grid cubes near sharp edges, that produces significantly better results. Our algorithm requires only gradients at the grid vertices, not at each surfaceedge intersection point. We also give a method for measuring the correctness of the resulting sharp edges and corners in the isosurface. Paper (pdf format) Related tech report: Experimental Results on MergeSharp (pdf format) 

On the Fractal Dimension of Isosurfaces M. Khoury and R. Wenger. IEEE Transactions on Visualization and Computer Graphics, 16, 2010, 11981205. The fractal dimension of an isosurface represents the growth in the isosurface as the number of grid cubes increases. We define and discuss the fractal isosurface dimension, present statistics on the average fractal dimension of 60 publicly available benchmark data sets, show the fractal dimension is highly correlated with topological noise in the benchmark data sets, and present a formula predicting the fractal dimension as a function of noise. Paper(pdf format)  
A Randomized O(m log m) Time Algorithm for Computing Reeb Graphs of Arbitrary Simplicial Complexes W. Harvey, Y. Wang. and R. Wenger. Proc. of the ACM Symposium on Computational Geometry (SOCG) 2010. We present the first subquadratic algorithm to compute the Reeb graph for a function on an arbitrary simplicial complex K. Our algorithm is randomized with an expected running time O(m log n) where m is the size of the 2skeleton of K and n is the number of vertices. Our algorithm is very simple to implement. Paper(pdf format) 

Isotopic
Reconstruction of Surfaces with Boundaries T. K. Dey, K. Li., E. A. Ramos, and R. Wenger. Proc. Sympos. Geom. Processing.(SGP09), special issue of Computer Graphics Forum, Vol. 28, No. 5 (2009), 13711382. [Webpage] [Software] We present an algorithm for the reconstruction of a surface with boundaries (including a nonorientable one) in three dimensions from a sufficiently dense sample. It is guaranteed that the output is isotopic to the unknown sampled surface. No previously known algorithm guarantees isotopic or homeomorphic reconstruction of surfaces with boundaries. Our algorithm is surprisingly simple. It `peels' slivers greedily from an alphacomplex of a sample of the surface. No other postprocessing is necessary. We provide several experimental results from an implementation of our basic algorithm and also a modified version of it. Paper (pdf format) 

Quality Isosurface Mesh Generation Using an Extended Marching Cubes Lookup TableSundaresan Raman and Rephael Wenger.Computer Graphics Forum, 27, 2008, 791798. Abstract: The Marching Cubes Algorithm may return degenerate, zero area isosurface triangles, and often returns isosurface triangles with small areas, edges or angles. We show how to avoid both problems using an extended Marching Cubes lookup table. As opposed to the conventional Marching Cubes lookup table, the extended lookup table differentiates scalar values equal to the isovalue from scalar values greater than the isovalue. The lookup table has 3^{8} = 6561 entries, based on three possible labels, '' or '=' or '+', of each cube vertex. We present an algorithm based on this lookup table which returns an isosurface close to the Marching Cubes isosurface, but without any degenerate triangles or any small areas, edges or angles. Paper (pdf format) 

Isosurface Construction in Any Dimension Using Convex HullsPraveen Bhaniramka, Rephael Wenger and Roger Crawfis IEEE Trans. on Visualization and Computer Graphics, 10, 2004, 353400. Abstract: We present an algorithm for constructing isosurfaces in any dimension. The input to the algorithm is a set of scalar values in a ddimensional regular grid of (topological) hypercubes. The output is a set of (d1)dimensional simplices forming a piecewise linear approximation to the isosurface. The algorithm constructs the isosurface piecewise within each hypercube in the grid using the convex hull of an appropriate set of points. We prove that our algorithm correctly produces a triangulation of a (d1)manifold with boundary. In dimensions three and four, lookup tables with 2^{8} and 2^{16} entries, respectively, can be used to speed the algorithm’s running time. In three dimensions this gives the popular Marching Cubes algorithm. We discuss applications of four dimensional isosurface construction to time varying isosurfaces, interval volumes and morphing. Paper (pdf format) 

Stability of Critical Points with Interval PersistenceTamal K. Dey and Rephael WengerDiscrete and Computational Geometry, 38, 2007, 479512. Abstract: Scalar functions defined on a topological space W are at the core of many applications such as shape matching, visualization and physical simulations. Topological persistence is an approach to characterizing these functions. It measures how long topological structures in the sublevel sets {x in W: f(x) <= c} persist as c changes. Recently it was shown that the critical values defining a topological structure with relatively large persistence remain almost unaffected by small perturbations. This result suggests that topological persistence is a good measure for matching and comparing scalar functions. We extend these results to critical points in the domain by redefining persistence and critical points and replacing sublevel sets {x in W: f(x) <= c} with interval sets {x in W: a <= f(x) < b}. With these modifications we establish a stability result for critical points. This result is strengthened for maxima that can be used for matching two scalar functions. Paper (pdf format) 

Contour Area Filtering of 2Dimensional Electrophoresis ImagesRamakrishnanKazhiyurMannar, Dominic J Smiraglia, Christoph Plass and Rephael Wenger Medical Image Analysis, 10, 2006, 353365. Abstract: We describe an algorithm, Contour Area Filtering, for separating background from foreground in gray scale images. The algorithm is based on the area contained within gray scale contour lines. It can be viewed as a form of local thresholding, or as a seed growing algorithm, or as a type of watershed segmentation. The most important feature of the algorithm is that it uses object area to determine the segmentation. Thus it is relatively impervious to brightness and contrast variations across an image or between different images. Contour Area Filtering was designed specifically for image analysis of 2D electrophoresis gels, although it can be applied to other gray scale images... Paper (pdf format) 

Restriction Landmark Genomic Scanning (RLGS) spot identification by second generation virtual RLGS in multiple genomes with multiple enzyme combinationsAuthors: Dominic Smiraglia, Ramakrishnan KazhiyurMannar, Christopher Oakes, YueZhong Wu, Ping Liang, Tahmina Ansari, Jian Su, Laura Rush, Laura Smith, Li Yu, Chunhui Liu, Zunyan Dai, ShihShih Chen, ShuHuei Wang, Joseph Costello, Ilya Ioshikhes, David Dawson, Jason Hong, Michael Teitell, Angela Szafranek, Marta Camoriano, Fei Song, Rosemary Elliott, William Held, Jacquetta Trasler, Christoph Plass and Rephael Wenger BMC Genomics, 8:446, November 2007 Abstract 

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