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5 - Kernel Operators

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

You need boundaries … Even in our material creations, boundaries mark the most beautiful of places, between the ocean and the shore, between the mountains and the plains, where the canyon meets the river

– Wm. Paul Young

Introduction

In this chapter, linear operations on images are investigated. The derivative, probably the most common linear operator, is considered first. That discussion is extended into edge detection, the result of applying derivative kernels on images. A variety of methods for accomplishing this objective are considered.

  • • (Section 5.2)We first define what makes a linear operator and explain the kernel operator, or sum of products, which is the type of linear operator that will appear most frequently in this book.

  • • (Section 5.3) We show in this section how to use vector representation of images to convert kernel operators to the matrix multiplication form in order to facilitate some analytical study.

  • • (Section 5.4) We focus on the discussion of derivatives, since it is probably the most common kernel operator used in Computer Vision applications. We discuss how to find the derivative kernel operators through the definition of derivatives, by function fitting, using vector representation of images, and taking derivatives of special blurring kernels.

  • • (Section 5.5) Applying derivative operators on images would result in edge images. We describe in this section the different types of edges and a popular edge detector, the Canny edge detector.

  • • (Section 5.6) The concept of scale space is explained and how the scale space is associated with the detection of edges at different scales.

  • • (Section 5.7) In Chapter 1, we briefly described the biological vision. Here, we revisit this issue and ask the question how human beings perform lower-level vision, i.e., edge detection. We introduce the Gabor filter, which is believed to well characterize the functionality of receptive fields in the visual cortex.

  • • (Section 5.8) We wrap up this chapter by performing an experimental study on the various types of derivative kernels in terms of their ability in detecting edges (both angle and magnitude) of different orientations.

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    Fundamentals of Computer Vision , pp. 51 - 91
    Publisher: Cambridge University Press
    Print publication year: 2017

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    References

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    • Kernel Operators
    • 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/10.1017/9781316882641.009
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    • Kernel Operators
    • 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/10.1017/9781316882641.009
    Available formats
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    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.

    • Kernel Operators
    • 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/10.1017/9781316882641.009
    Available formats
    ×