- Homomorphic filtering
Homomorphic filtering is a generalized technique for signal and image processing, involving a nonlinear mapping to a different domain in which linear filter techniques are applied, followed by mapping back to the original domain. This concept was developed in the 1960s by
Thomas Stockham ,Alan V. Oppenheim , andRonald W. Schafer atMIT .Image enhancement
Homomorphic filter is sometimes used for
image enhancement . It simultaneously normalizes the brightness across an image and increases contrast. Here homomorphic filtering is used to removemultiplicative noise . Illumination and reflectance are not separable, but their approximate locations in the frequency domain may be located. Since illumination and reflectance combine multiplicatively, the components are made additive by taking thelogarithm of the image intensity, so that these multiplicative components of the image can be separated linearly in the frequency domain. Illumination variations can be thought of as a multiplicative noise, and can be reduced by filtering in the log domain.To make the illumination of an image more even, the high-frequency components are increased and low-frequency components are decreased, because the high-frequency components are assumed to represent mostly the reflectance in the scene (the amount of light reflected off the object in the scene), whereas the low-frequency components are assumed to represent mostly the illumination in the scene. That is,
high-pass filter ing is used to suppress low frequencies and amplify high frequencies, in the log-intensity domain. [cite book | url = http://books.google.com/books?id=sNEodegXy2MC&pg=PT1120&dq=%22homomorphic+filtering%22+stockham+oppenheim&as_brr=3&ei=sfriRo3QJqPIowLzvYXuAw&sig=Ut69Hq1Xnr8J_lTAclOxXZ295vI#PPT1120,M1 | title = Digital signal processing handbook | author = Douglas B. Williams and Vijay Madisetti | publisher = CRC Press | year = 1999 | isbn = 0849321352 ]Audio and speech analysis
Homomorphic filtering is used in the log-spectral domain to separate filter effects from excitation effects, for example in the computation of the
cepstrum as a sound representation; enhancements in the log spectral domain can improve sound intelligibility, for example inhearing aids . [cite book | title = Readings in Speech Recognition | author = Alex Waibel and Kai-Fu Lee | isbn = 1558601244 | year = 1990 | publisher = Morgan Kaufmann | url = http://books.google.com/books?id=IJoOLVYD8KQC&pg=PA64&dq=%22homomorphic+filtering%22+stockham+oppenheim&as_brr=3&ei=sfriRo3QJqPIowLzvYXuAw&sig=UMPo33j2ppYSISVSgJXrM6-eP90 ]References
External links
* [http://www.cs.sfu.ca/~stella/papers/blairthesis/main/node35.html Overview of homomorphic filtering]
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