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Visual Contrast Preserving Representation of High Dynamic Range Mathematical Functions

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Numerical Methods for Differential Equations, Optimization, and Technological Problems

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 27))

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Abstract

When Gaussian distributed inputs, representing model parameters with some measurement error, are mapped through certain mechanical vibration models, the corresponding output probability distribution exhibits an approximately logarithmic data value distribution (in the histogram sense) with a high dynamic range (HDR). We look at applying tone mapping techniques from HDR photography to produce a low dynamic range, visual contrast preserving representation of such high dynamic range mathematical functions—thus enabling HDR plotting. This makes it possible to visualize HDR functions, displaying their structure in a clear manner on standard low dynamic range media such as computer screens and print. The advantages over simple logarithmic scaling are the visual contrast preservation and data adaptivity. Comparing to histogram equalization, the present approach has the advantage of not exaggerating small contrasts. Three methods are suggested and demonstrated on two mechanical vibration problems: transverse waves in a classical vibrating string, and the dynamic out-of-plane behaviour of an axially travelling panel submerged in axial potential flow.

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Notes

  1. 1.

    SAVU, Sample-based Analysis and Visualization of Uncertainty: https://yousource.it.jyu.fi/savu/codes/ Link cited 13 Jan 2012.

  2. 2.

    Strictly speaking, in the case of data-adaptive histogram remappers, if some of the histogram bins are empty, there may be a flat region in the mapping function. In this case the mapping is not globally one-to-one. However, since such regions contain no samples in the data, for the existing data it is one-to-one.

  3. 3.

    Files hdr*.m in https://yousource.it.jyu.fi/savu/codes/. Link cited 13 Jan 2012.

  4. 4.

    Similar ideas were explored ten years earlier in a medical imaging context by [38]; however, we use [28] since it explicitly provides an algorithm.

  5. 5.

    According to [18], root-taking is a popular naïve approach.

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Authors and Affiliations

  1. Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (Agora), 40014, Jyväskylä, Finland

    Juha Jeronen

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  1. Juha Jeronen
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Correspondence to Juha Jeronen .

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Editors and Affiliations

  1. Mathematical Information Technology, University of Jyväskylä, Mattilanniemi 2, Jyväskylä, 40100, Finland

    Sergey Repin

  2. Mathematical Information Technology, University of Jyväskylä, Mattilanniemi 2, Jyväskylä, 40100, Finland

    Timo Tiihonen

  3. Mathematical Information Technology, University of Jyväskylä, Mattilanniemi 2, Jyväskylä, 40100, Finland

    Tero Tuovinen

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Jeronen, J. (2013). Visual Contrast Preserving Representation of High Dynamic Range Mathematical Functions. In: Repin, S., Tiihonen, T., Tuovinen, T. (eds) Numerical Methods for Differential Equations, Optimization, and Technological Problems. Computational Methods in Applied Sciences, vol 27. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5288-7_23

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  • DOI: https://doi.org/10.1007/978-94-007-5288-7_23

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