research-article

On the search of optimal reconstruction resolution

Authors:

Walter G. KropatschAuthors Info & Claims

Pattern Recognition Letters, Volume 33, Issue 11

Pages 1460 - 1467

https://doi.org/10.1016/j.patrec.2011.10.006

Published: 01 August 2012 Publication History

Abstract

Highlights We search an optimal reconstruction resolution for given non-uniform point sets. We use a statistically-derived topology-controller to find the optimal resolution. The proposed topology-controller is derived from homology-based statistics. We can evaluate of the reconstruction process the need of visual inspection. We show qualitative comparisons and results of the proposed approach. In this paper we present a novel algorithm to optimize the reconstruction from non-uniform point sets. We introduce a statistically-derived topology-controller for selecting the reconstruction resolution of a given non-uniform point set. Deriving information from homology-based statistics, our topology-controller ensures a stable and sound basis for the analysis process. By analyzing our topology-controller, we select an optimal reconstruction resolution which ensures both low reconstruction errors and a topological stability of the underlying signal. Our approach offers a valuable method for the evaluation of the reconstruction process without the need of visual inspection of the reconstructed datasets. By means of qualitative results we show how our proposed topology statistics provides complementary information in the enhancement of existing reconstruction pipelines in visualization.

References

[1]

Beurling-Landau-type theorems for non-uniform sampling in shift invariant spline spaces. J. Fourier Anal. Appl. v6. 93-103.

[2]

Arigovindan, M., Sühling, M., Hunziker, P.R., Unser, M., 2005. Variational image reconstruction from arbitrarily spaced samples: A fast multiresolution spline solution. In: Proc. IEEE Trans. Image Process., vol. 14, pp. 450-460.

Digital Library

[3]

Bajaj, C.L., Pascucci, V., Schikore, D., 1997. The contour spectrum. In: Proc. IEEE Visualizat, pp. 167-174.

Digital Library

[4]

Computing robustness and persistence for images. IEEE Trans. Vis. Comput. Graph. v16 i6. 1251-1260.

Digital Library

[5]

Analyzing and tracking burning structures in lean premixed hydrogen flames. IEEE Trans. Vis. Comput. Graph. v16 i2. 248-260.

Digital Library

[6]

Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree. Comput. Geometry. v43 i1. 42-58.

Digital Library

[7]

Cerri, A., Biasotti, S., Giorgi, D., 2007. k-Dimensional size functions for shape description and comparison. In: Int. Conf. Image Anal. Process., pp. 795-800.

Digital Library

[8]

Gromov-hausdorff stable signatures for shapes using persistence. Comput. Graph. Forum. v28 i5. 1393-1403.

Digital Library

[9]

Splines minimizing rotation-invariant semi-norms in Sobolev spaces. In: Schempp, W., Zeller, K. (Eds.), Multivariate Approx. Theory, Birkhäuser-Verlag. pp. 85-100.

[10]

Topological persistence and simplification. Discrete Comput. Geometry. v28 i4. 511-533.

[11]

Efficient numerical methods in non-uniform sampling theory. Numerische Mathematik. v69. 423-440.

Digital Library

[12]

Fast multi-dimensional scattered data approximation with Neumann boundary conditions. Linear Algebr. Appl. v391. 99-123.

[13]

Gyulassy, A., Natarajan, V., Pascucci, V., Bremer, P.-T., Hamann, B., 2005. Topology-based simplification for feature extraction from 3D scalar fields. In: Proc. IEEE Visualizat., pp. 535-542.

[14]

Enhancing the interactive visualization of procedurally encoded multifield data with ellipsoidal basis functions. Comput. Graph. Forum. v25 i3. 587-596.

[15]

Computational Homology. Applied Mathematical Sciences, 2004.Springer-Verlag.

[16]

Kraus, M., Ertl, T., 2001. Topology-guided downsampling. In: Proc. Vol. Graph., pp. 223-234.

[17]

An Introduction to Morse Theory. American Mathematical Society.

[18]

A topological sampling theorem for robust boundary reconstruction and image segmentation. Discrete Appl. Math. v157 i3. 524-541.

Digital Library

[19]

Morse Theory. Princeton University Press.

[20]

Elements of Algebraic Topology. 1984. Addison-Wesley, Redwook City, California.

[21]

Natarajan, V., Pascucci, V., 2005. Volumetric data analysis using Morse-Smale complexes. In: Proc. Shape Model. Int., pp. 322-327.

Digital Library

[22]

Scattered data modeling. IEEE Comput. Graph. Appl. v13. 60-70.

Digital Library

[23]

Ohtake, Y., Belyaev, A.G., Seidel, H.-P., 2004. 3D scattered data approximation with adaptive compactly supported radial basis functions. In: Proc. Int. Conf. Shape Model. Appl., pp. 31-39.

Digital Library

[24]

Schlatter, P., 2001. Direct numerical simulation of laminar-turbulent transition in boundary layer subject to free-stream turbulence. Master's thesis, Royal Institute of Technology, Stockholm.

[25]

Silver, D., Wang, X., 1998. Tracking scalar features in unstructured datasets. In: Proc. IEEE Visualizat., pp. 79-86.

Digital Library

[26]

Topological equivalence between a 3d object and the reconstruction of its digital image. IEEE Trans. Pattern Anal. Mach. Intell. v29 i1. 126-140.

Digital Library

[27]

Takahashi, S., Nielson, G.M., Takeshima, Y., Fujishiro, I., 2004. Topological volume skeletonization using adaptive tetrahedralization. In: Proc. Geometric Modell. Process., pp. 227-236.

Digital Library

[28]

Interpolation revisited. IEEE Trans. Med. Imaging. v19 i7. 739-758.

[29]

Efficient reconstruction from non-uniform point sets. The Visual Computer, 2008.Springer, Berlin/ Heidelberg.

[30]

Vuçini, E., Möller, T., Gröller, M.E., 2009. On visualization and reconstruction from non-uniform point sets using b-splines. In: Proceedings of Eurographics/ IEEE-VGTC Symposium on Visualization, vol. 28, pp. 1007-1014.

Digital Library

[31]

Topology-controlled volume rendering. IEEE Trans. Vis. Comput. Graph. v13 i2. 330-341.

Digital Library

[32]

Weber, G.H., Bremer, P.-T., Day, M.S., Bell, J.B., Pascucci, V., 2009. Feature tracking using reeb graphs. In: Proc. Topol.-based Methods Visualizat.

Cited By

El-Rushaidat DYeh RTricoche X(2021)Accurate parallel reconstruction of unstructured datasets on rectilinear gridsJournal of Visualization10.1007/s12650-020-00740-024:4(787-806)Online publication date: 1-Aug-2021
https://dl.acm.org/doi/10.1007/s12650-020-00740-0
Vuçini E(2012)Enhancing the reconstruction from non-uniform point sets using persistence informationProceedings of the 4th international conference on Computational Topology in Image Context10.1007/978-3-642-30238-1_4(30-38)Online publication date: 28-May-2012
https://dl.acm.org/doi/10.1007/978-3-642-30238-1_4

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Published In

cover image Pattern Recognition Letters

Pattern Recognition Letters Volume 33, Issue 11

August, 2012

73 pages

ISSN:0167-8655

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Copyright © Elsevier B.V.

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Elsevier Science Inc.

United States

Publication History

Published: 01 August 2012

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Cited By

El-Rushaidat DYeh RTricoche X(2021)Accurate parallel reconstruction of unstructured datasets on rectilinear gridsJournal of Visualization10.1007/s12650-020-00740-024:4(787-806)Online publication date: 1-Aug-2021
https://dl.acm.org/doi/10.1007/s12650-020-00740-0
Vuçini E(2012)Enhancing the reconstruction from non-uniform point sets using persistence informationProceedings of the 4th international conference on Computational Topology in Image Context10.1007/978-3-642-30238-1_4(30-38)Online publication date: 28-May-2012
https://dl.acm.org/doi/10.1007/978-3-642-30238-1_4

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