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IMAGE FUSION COMPARISON IMPROVEMENT OF IMAGE FUSION USING WAVELETS Abhinay reddy T

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IMAGE FUSION COMPARISON IMPROVEMENT OF IMAGE FUSION USING WAVELETS Abhinay reddy T Powered By Docstoc
					COMPARISON & IMPROVEMENT
  OF IMAGE FUSION USING
        WAVELETS

    Abhinay reddy.T     (06651A0402)
    Amarendhar.G        (06651A0403)
     Anvesh choudary.N (06651A0408)
    Praveen kumar.Y     (06651A0465)
INTRODUCTION
 In computer vision, Multisensor Image Fusion is the
  process of combining relevant information from two or
  more images into a single image.
 The resulting image will be more informative than any of
  the input images.
 In remote sensing applications, the increasing
  availability of space borne sensors gives a motivation for
  different image fusion algorithms.
 Several situations in image processing require high
  spatial and high spectral resolution in a single image.
STANDARD IMAGE FUSION METHODS
   Image fusion methods can be broadly classified into two
          1. Spatial domain fusion
          2. Transform domain fusion.
   The fusion methods such as averaging, Brovey method,
    principal component analysis (PCA) and IHS based methods
    fall under spatial domain approaches.
   The disadvantage of spatial domain approaches is that they
    produce spatial distortion in the fused image. Spectral
    distortion becomes a negative factor while we go for further
    processing, such as classification problem, of the fused
    image.
   The spatial distortion can be very well handled by transform
    domain approaches on image fusion.
CONT……

 The  multiresolution analysis has become a very
  useful tool for analyzing remote sensing images.
 The discrete wavelet transform has become a very
  useful tool for fusion.
 Some other fusion methods are also there, such as
  Laplacian pyramid based, Curvelet transform based
  etc.
 These methods show a better performance in spatial
  and spectral quality of the fused image compared to
  other spatial methods of fusion.
APPLICATIONS
   Image Classification
   Aerial and Satellite imaging
   Medical imaging
   Robot vision
   Concealed weapon detection
   Multi-focus image fusion
   Digital camera application
   Concealed weapon detection
   Battle field monitoring
PRINCIPAL COMPONENT ANALYSIS
 The PCA involves a mathematical procedure that
  transforms a number of correlated variables into a
  number of uncorrelated variables called principal
  components.
 It computes a compact and optimal description of the
  data set.
 The PCA is also called as Karhunen-Loève transform or
  the Hotelling transform.
 The PCA does not have a fixed set of basis vectors like
  FFT, DCT and wavelet etc. and its basis vectors depend
  on the data set.
IMAGE FUSION BY PCA




Figure: Information flow diagram in image fusion scheme employing
  PCA.
IMAGE FUSION BY SIMPLE AVERAGE
   This technique is a basic and straightforward technique
    and fusion could be achieved by simple averaging
    corresponding pixels in each input image as:
IMAGE FUSION BY WAVELET TRANSFORMS




   Information flow diagram in image fusion by wavelets
FOURIER ANALYSIS
 Signal analysts already have at their disposal an
  impressive arsenal of tools. Perhaps the most well known
  of these is Fourier analysis, which breaks down a signal
  into constituent sinusoids of different frequencies.
 Another way to think of Fourier analysis is as a
  mathematical technique for transforming our view of the
  signal from time-based to frequency-based
FOURIER ANALYSIS (CONT)
FOURIER ANALYSIS (CONT)

  Fourier analysis has a serious drawback.
  In transforming to the frequency domain, time information
   is lost
  When looking at a Fourier transform of a signal, it is
   impossible to tell when a particular event took place.
  If the signal properties do not change much over time that is,
   if it is what is called a stationary signal—this drawback isn’t
   very important.
  However, most interesting signals contain numerous non
   stationary or transitory characteristics: drift, trends, abrupt
   changes, and beginnings and ends of events.
  These characteristics are often the most important part of the
   signal, and Fourier analysis is not suited to detecting them.
SHORT-TIME FOURIER ANALYSIS


   In an effort to correct this deficiency, Dennis Gabor
    (1946) adapted the Fourier transform to analyze only a
    small section of the signal at a time—a technique called
    windowing the signal.

   Gabor’s adaptation, called the Short-Time Fourier
    Transform (STFT), which maps a signal into a two-
    dimensional function of time and frequency.
SHORT-TIME FOURIER ANALYSIS(CONT)
WAVELET ANALYSIS


    Wavelet analysis allows the use of long time intervals where
     we want more precise low-frequency information, and
     shorter regions where we want high-frequency information
WAVELET ANALYSIS(CONT)
WHAT IS WAVELET ANALYSIS
   A wavelet is a waveform of effectively limited duration
    that has an average value of zero.

   Compare wavelets with sine waves, which are the basis
    of Fourier analysis.

   Sinusoids do not have limited duration — they extend
    from minus to plus infinity. And where sinusoids are
    smooth and predictable, wavelets tend to be irregular and
    asymmetric.
CONT…
THE CONTINUOUS WAVELET TRANSFORM

Similarly, the continuous wavelet transform (CWT) is
 defined as the sum over all time of the signal multiplied
 by scaled, shifted versions of the wavelet function


   The result of the CWT are many wavelet coefficients C,
    which are a function of scale and position.
CONTINUOUS WAVELET TRANSFORM(CONT)
FIVE EASY STEPS TO A CONTINUOUS
WAVELET TRANSFORM
  1.   Take a wavelet and compare it to a section at the start
       of the original signal.
  2.   Calculate a number, C, that represents how closely
       correlated the wavelet is with this section of the
       signal. The higher C is, the more the similarity
CONT…
3. Shift the wavelet to the right and repeat steps 1 and 2
   until you’ve covered the whole signal.
CONT…
4. Scale (stretch) the wavelet and repeat steps 1
  through 3.




5. Repeat steps 1 through 4 for all scales.
DISCRETE WAVELET TRANSFORM

  The wavelet transform (WT) has gained widespread
   acceptance in signal processing and image compression.
  Because of their inherent multi-resolution nature, wavelet-
   coding schemes are especially suitable for applications where
   scalability and tolerable degradation are important
  Recently the JPEG committee has released its new image
   coding standard, JPEG-2000, which has been based upon
   DWT.
DISCRETE WAVELET TRANSFORM

  Wavelet transform decomposes a signal into a set of basis
   functions.
  These basis functions are called wavelets
  Wavelets are obtained from a single prototype wavelet y(t)
   called mother wavelet by dilations and shifting:

                          1     t b
        
             a ,b (t )     (      )          (1)
                           a      a
     where a is the scaling parameter and b is the shifting
      parameter
DISCRETE WAVELET TRANSFORM
   Theory of WT
      The wavelet transform is computed separately for
       different segments of the time-domain signal at
       different frequencies.
      Multi-resolution analysis: analyzes the signal at
       different frequencies giving different resolutions
      MRA is designed to give good time resolution and
       poor frequency resolution at high frequencies and
       good frequency resolution and poor time resolution at
       low frequencies
      Good for signal having high frequency components
       for short durations and low frequency components for
       long duration.e.g. images and video frames
DISCRETE WAVELET TRANSFORM

    The 1-D wavelet transform is given by :
DISCRETE WAVELET TRANSFORM

    The inverse 1-D wavelet transform is given by:
DISCRETE WAVELET TRANSFORM
 Discrete wavelet transform (DWT), which transforms a
  discrete time signal to a discrete wavelet representation.
 It converts an input series x0, x1, ..xm, into one high-pass
  wavelet coefficient series and one low-pass wavelet
  coefficient series (of length n/2 each) given by:
DISCRETE WAVELET TRANSFORM
 where sm(Z) and tm(Z) are called wavelet filters, K is the
  length of the filter, and i=0, ..., [n/2]-1.
 In practice, such transformation will be applied
  recursively on the low-pass series until the desired
  number of iterations is reached.
MULTI STEP DECOMPOSITION AND
RECONSTRUCTION
WAVELET DECOMPOSITION
  Images are treated as two dimensional signals, they
  change horizontally and vertically, thus 2D wavelet
  analysis must be used for images.
 2D wavelet analysis uses the same ’mother wavelets’ but
  requires an extra step at every level of decomposition.
 The 1D analysis filtered out the high frequency
  information from the low frequency information at every
  level of decomposition; so only two sub signals were
  produced at each level.
WAVELET DECOMPOSITION
(CONT…)
  In 2D, the images are considered to be matrices with N
  rows and M columns.
 At every level of decomposition the horizontal data is
  filtered, then the approximation and details produced
  from this are filtered on columns.
WAVELET DECOMPOSITION OF 2-D
IMAGE
   2-D DWT for Image
CONT…
CONT…
   2-D DWT for Image
IMAGE FUSION (CONT..)

  In wavelet image fusion scheme, the source images I1 (x,y)
   and I2 (x,y), are decomposed into approximation and
   detailed coefficients at required level using DWT.
  The approximation and detailed coefficients of both images
   are combined using fusion rule Φ.
  The fused image (If (x, y)) could be obtained by taking the
   inverse discrete wavelet transform (IDWT).
ENTROPY

  Entropy is a statistical measure of randomness that can be
   used to characterize the texture of the input image.
  Entropy is defined as -sum (p.*log2 (p)) where p contains the
   histogram counts returned from imhist.
  By default, entropy uses two bins for logical arrays and 256
   bins for uint8, uint16, or double arrays.
  Image can be a multidimensional image.
  If Image have more than two dimensions, the entropy
   function treats it as a multidimensional grayscale image and
   not as an RGB image.
CONCLUSIONS

  Pixel-level image fusion using wavelet transform and
   principal component analysis are implemented in PC
   MATLAB.
  Different image fusion performance metrics with and
   without reference image have been evaluated.
  The simple averaging fusion algorithm shows degraded
   performance.
  Image fusion using wavelets with higher level of
   decomposition shows better performance when compared to
   PCA based method.
  Some further investigation is needed to resolve this issue.