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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.

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image fusion, wavelet transform, image registration, input images, fusion techniques, fusion algorithms, fusion rules, source images, image processing, wavelet coefﬁcients, Data Fusion

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posted: | 8/8/2010 |

language: | English |

pages: | 39 |

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