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Design for Embedded Image Processing on FPGAs, 2nd Edition
book

Design for Embedded Image Processing on FPGAs, 2nd Edition

by Donald G. Bailey
August 2023
Intermediate to advanced content levelIntermediate to advanced
496 pages
23h 47m
English
Wiley
Content preview from Design for Embedded Image Processing on FPGAs, 2nd Edition

11Linear Transforms

Linear transformation extends and generalises local linear filtering of Eq. (9.4) by removing the restriction of the window. Each output value is a linear combination of all of the input pixel values:

This enables linear transforms to separate different components of an image, for example separating signal from interference or noise.

Direct implementation of Eq. (11.1) is very expensive. For an upper N times upper N input image, each output value requires upper N squared multiplications and additions. Therefore, an upper N times upper N output requires upper N Superscript 4 operations. Many useful transforms are separable in that they can be decomposed into separate, independent, one‐dimensional transforms on the rows and columns. In this case, Eq. (11.1) simplifies to

(11.2)upper Q left-bracket u comma v right-bracket equals sigma-summation Underscript y Endscripts w left-bracket v comma y right-bracket left-parenthesis sigma-summation Underscript x Endscripts w left-bracket u comma x right-bracket upper I left-bracket x comma y right-bracket right-parenthesis comma

reducing the number of operations to 2 upper N cubed. Separable transforms ...

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Publisher Resources

ISBN: 9781119819790Purchase Link