Image Compression Final

7/31/2019 Image Compression Final

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IMAGE COMPRESSION USINGCONTOURLET WITH SVM

GUIDE : Mr. ARUN VIKAS SINGH

NAVYA R. - 1PI09EC072

NEENA S. HULKOTI 1PI09EC073


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IMAGE

Image is a vivid or graphic description.

It is a 2-D function f(x,y).

x,y are spatial (plane) coordinates.

Amplitude of f(x,y) at any pair of coordinates (x,y) is the intensityor gray level of the image at that point.

Images are stored in various file formats

. gif - Graphics Interchange Format

. jpg -Joint Photographic Experts Group

. tiff - Tagged Image File Format

. png - Portable Network Graphics


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TYPES OF IMAGE

Binary image: Each pixel can takeonly two values either 0 (black) or 1(white).

Greyscale image (8 bit): Each pixelhas a value from 0 (black) to 255(white). The image includes 256shades of grey.

Color image: Each pixel in color image is a threeelement vector and is constructed from threeintensity maps. Each intensity map is projectedthrough a color filter (red, blue, green) to create a

monochrome image.

Color imag

e: Each pixel in color image is a threeelement vector and is constructed from threeintensity maps. Each intensity map is projectedthrough a color filter (red, green, blue) to create a

monochrome image.


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IMAGECOMPRESSION

IMAGEDISPLAY

IMAGERESTORATION

IMAGEACQUISITION

IMAGE ANALYSIS:SEGMENTATION +

RECOGNITION

IMAGE

ENHANCEMENT


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Image Acquisition involves sensing of an image. It also involvespreprocessing, such as scaling. The acquisition of images is referred toas imaging.

Image Enhancement involves highlighting certain features of theacquired image. It enhances the image and is a subjective process basedon human perception.

Image Restoration involves removal of distortion (noise) and restoresa image. It is objective process based on mathematical and probabilisticmodels of image degradation.

Compression is a technique that is used for reducing the storage spacefor saving an image and reducing the bandwidth required fortransmission of image.

Segmentationis the process in which image is converted into smallsegments so that we can extract the more accurate image attributes.

Recognition is a process that assigns a label to an object based on itsdescriptors.


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FOURIER TRANSFORMS

The Fourier transform is a mathematical operation that decomposesa signal into its constituent frequencies.

The Fourier transform decomposes a function into oscillatoryfunctions.

An inverse Fourier transforms data from the frequency domain intothe time domain.

The discrete Fourier transform (DFT) estimates the Fouriertransform of a function from a finite number of its sampled points.


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If f(t) is a nonperiodic signal, the summation of the periodicfunctions, sine and cosine, does not accurately represent the signal

Fourier sine and cosine are not localized in space.

Traditional Fourier methods cannot be used in analyzing physicalsituations where the signal contains discontinuities and sharpspikes.

Disadvantages


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DISCRETE WAVELET TRANSFORM

Wavelets are small waves of varying frequency and limited duration.

They are mathematical functions that cut up data into differentfrequency components. The algorithms process data at different scalesor resolutions.

The individual wavelet functions are localized in space and form thebasis function.

The wavelet series expansion maps a function of a continuous variable

into a sequence of coefficients.

If the function being expanded is itself discrete sample of acontinuous function the resulting coefficients are the discrete wavelettransform (DWT).


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CONTOURLETS

The contourlet transform is a new two-dimensional extension of thewavelet transform using multiscale and directional filter banks.

The contourlet expansion is composed of basis images oriented at

various directions in multiple scales, with flexible aspect ratio.

The main difference between contourlets and other multiscaledirectional systems is that the contourlet transform allows fordifferent and flexible number of directions at each scale, whileachieving nearly critical sampling


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CONTOURLET TRANSFORM

The contourlet transform consists aLP followed by a DFB. LP-laplacian pyramid DFB-directional filter bank

The Laplacian Pyramid (LP) is usedto capture the point discontinuities,and then followed by a DirectionalFilter Bank (DFB) to link the pointdiscontinuities.

In contourlet transform, theLaplacian Pyramid decomposes theimage into sub-bands and then theDirectional Filter Banks analyzeeach detail image

LP DFB


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CONTOURLET DECOMPOSITION


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LAPLACIAN PYRAMID

The LP decomposition at each levelgenerates a down sampled low pass versionof the original and the difference betweenthe original and the prediction, resulting in aband pass image

The Laplacian is then computed as thedifference between the original image andthe low pass filtered image. This process iscontinued to obtain a set of band-passfiltered images. Thus the Laplacian pyramidis a set of band pass filters. By repeatingthese steps several times a sequence ofimages, are obtained.


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DIRECTIONAL FILTER BANK

The directional filter bank is a critically

sampled filter bank that candecompose images into any power oftwos number of directions.


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WAVELETS & CONTOURLETS

Wavelets have square supports that can only capture pointdiscontinuities, whereas contourlets having elongated supports thatcan capture linear segments of contours and thus effectively

represent a smooth contour with fewer coefficients.

2-dimensional wavelets, with tensor-product basis functions lackdirectionality and are only good at catching point discontinuities,but contourlets also capture the geometrical smoothness of the

contours.


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SUPPORT VECTOR MACHINE

SVMs are used for classification,regression, and density estimation.

Typically, the training vectors aremapped to a higher-dimensionalspace using a kernel function, andthe linear separating plane with themaximal margin between classes isfound in this space.

SVM training involves optimizingover a number of parameters.

SVMs can also be applied toregression problems. An input

parameter to a SVM is ainsensitivity zone (tolerance).

The goal of the SVM is to producean output which is within thisinsensitivity zone.


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WAVELET COEFFICIENTS


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CONTOURLET COEFFICIENTS


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ORIGINALCONTOURLET

WITH SVMWAVELET

WITH SVM


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CONTOURLETWITH SVM

PSNR in DBWAVELET

WITH SVMPSNR in DB

31.045321 27.680352

30.879295 25.698467

30.910235 29.868164


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The PSNR (Peak signal-to-noise Ratio) is most commonly used asa measure of quality of reconstruction of lossycompression codecs (e.g., for image compression).

The signal in this case is the original data, and the noise is the error

introduced by compression.

When comparing compression codecs it is used asan approximation to human perception of reconstruction quality,therefore in some cases one reconstruction may appear to be closer tothe original than another, even though it has a lower PSNR (a higher

PSNR would normally indicate that the reconstruction is of higherquality).

QUALITY MEASURE


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REFERENCES

Jonathan Robinson, The Application of Support Vector Machines toCompression of Digital Images, February 2004

Brian Guilfoos, Judy Gardiner, Juan Carlos Chaves, John Nehrbass,Stanley Ahalt, Ashok Krishnamurthy, Jose Unpingco, Alan Chalker,Laura Humphrey, and Siddharth Samsi, Applications in Parallel

MATLAB, Ohio Supercomputer Center, Columbus, OH S. Esakkirajan, T.Veerakumar, V.Senthil Murugan, R.Sudhakar, Image

compression using contourlet transform and multi stage vectorquantization, GVIP Journal,Vol 6,Issue 1, July 2006

Minh N. Do, Martin Vetterli, The Contourlet Transform for Image

Representation, Digital Encoding of Signals, 06.07.2004 Duncan D.-Y. Po and Minh N. Do , Directional Multiscale Modeling

of Images using the Contourlet Transform, IEEE Transactions onImage Processing


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THANK YOU

Image Compression Final

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