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6 - Noise Removal

from Part II - Preprocessing

Published online by Cambridge University Press:  25 October 2017

Wesley E. Snyder  and
Hairong Qi
Wesley E. Snyder
Affiliation:
North Carolina State University
Hairong Qi
Affiliation:
University of Tennessee
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Summary

To change and to change for the better are two different things.

– German proverb.

Introduction

In a photosensitive device such as a phototransistor or charge-coupled device, an incidence of a photon of light may (probabilistically) generate an electronic charge. The number of charges produced should be proportional to the photons per second striking the device. However, the presence of heat (anything above absolute zero) will also randomly produce charges, and therefore signal. Such a signal is called dark current because it is a signal that is produced by a camera, even in the dark. Dark current is one of several phenomena that result in random fluctuations to the output of a camera that we call noise. The nature of noise is closely related to the type of sensor. For example, devices that count emissions of radioactive particles are corrupted by a noise that has a Poisson distribution rather than the Gaussian noise of dark current.

In this chapter, techniques are developed that remove noise and degradations so that features can be derived more cleanly for segmentation. We will introduce each topic in one dimension, to allow the student to better understand the process, and then extend that concept to two dimensions. This is covered in the following sections:

  • • (Section 6.2) The noise in the image can be reduced simply by smoothing. However, the smoothing process also blurs the edges. This section introduces the subject of reducing the noise while at the same time preserving edges, i.e., edge-preserving smoothing.

  • • (Section 6.3) An intuitive idea in designing edge-preserving smoothing is that smoothing should be associated with a weight according to the local image data where it is applied. And the weight should be large if two pixels are close spatially and have similar photometric values. Otherwise, the weight should be small. The bilateral filter is an algorithm that realizes this ad hoc “good idea.”

  • • (Section 6.4) Diffusion is described here to pose the denoising problem as the solution to a partial differential equation (PDE). The challenge is how to find a PDE that causes blurring except at edges.

  • • (Section 6.5) The Maximum A Posteriori probability (MAP) algorithm is discussed to show how to formulate noise removal as a minimization problem. Here, the challenge is to find an objective function whose minimum is the desired result.

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    Information
    Fundamentals of Computer Vision , pp. 92 - 118
    Publisher: Cambridge University Press
    Print publication year: 2017

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    References

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    • Noise Removal
    • Wesley E. Snyder, North Carolina State University, Hairong Qi, University of Tennessee
    • Book: Fundamentals of Computer Vision
    • Online publication: 25 October 2017
    • Chapter DOI: https://doi.org/10.1017/9781316882641.010
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    • Noise Removal
    • Wesley E. Snyder, North Carolina State University, Hairong Qi, University of Tennessee
    • Book: Fundamentals of Computer Vision
    • Online publication: 25 October 2017
    • Chapter DOI: https://doi.org/10.1017/9781316882641.010
    Available formats
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    Save book to Google Drive

    To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

    • Noise Removal
    • Wesley E. Snyder, North Carolina State University, Hairong Qi, University of Tennessee
    • Book: Fundamentals of Computer Vision
    • Online publication: 25 October 2017
    • Chapter DOI: https://doi.org/10.1017/9781316882641.010
    Available formats
    ×