wavelets

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A BRIEF INTRODUCTION TO WAVELETS AND GABOR FILTER
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Contents

• Introduction
• Fourier Transform
• Wavelet
• Wavelet-Key concepts
• Wavelet transforms
• Discrete wavelet transform
• Gabor wavelet
• Gabor filter
• Applications of gabor filter

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INTRODUCTION

• Signal goes some abrupt changes due to some
  external noises
• Image also has some smooth regions interrupted
  by edges or changes in contrast which result in
  noise

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Fourier transform

• Converting from time to frequency domain
• Signal is represented as a series of sinusoids
• Once the signal is transformed information about
  time is lost and its hard to tell where a
  particular frequency occurs.
• To solve this issue WAVELET concept comes into
  picture

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WAVELET

• Rapidly decaying wave with a zero mean
• A wavelet exist for a finite duration

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(Cont..)

• Examples of wavelets are

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Key Concepts

• SCALING

• SHIFTING

• Process of shrinking or stretching the signal

• Delaying or advancing the signal

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Wavelet transforms

• Two types of wavelet transforms
• Continuous wavelet transform (C.W.T.)
• Discrete wavelet transform (D.W.T.)
• Applications

C.W.T. D.W.T.
-Time and frequency analysis -Filtering of time localized components -De noising images -Compression of images -Representation of images in multiple resolutions
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D.W.T.

• Used to process or represent images with fewer
  coefficients.
• Scaling is done with base 2.

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Introduction to gabor wavelet

• As previously discussed particular wavelet is
  used for particular application
• Gabor wavelet is one among the available wavelets
  used for feature extraction,face recognition in
  image processing
• Gabor wavelet/filter was named after Denis Gabor.

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Gabor Filter

• Linear filter used for edge detection
• Frequency and orientation are similar to human
  visual system
• Used for feature extraction with multiple
  resolutions

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(Cont..)

• Gabor wavelets can be designed for number of
  dilations and rotations of the image
• Practically it consumes more time hence gabor
  filter bank is created with various scales and
  orientations.
• The filters are convolved with the signal
  resulting the gabor space.

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(Cont..)

• A gabor wavelet is the gaussian modulated
  sinusoidal function.
• Set of gabor filters with multiple scales and
  orientations is used for feature extraction of an
  image.
• 2-D gabor filters are give by the equation,

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Applications of gabor filter
Example of a 2D Gabor filter

• Extracting text only regions of the image.
• Feature extraction in face recognition.
• Finger print recognition

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Thank you