Fractal Image Compression

Image Compression Techniques

Group MemberMd Meraj AlamMd.Minhaj AlamINSTITUTE OF SCIENCE & TECHNOLOGYOverviewIntroductionFractal Image CompressionMathematical BackgroundMathematical representationWorkEncodingDecodingResolution Independent decodingExamplesPossible Improvements IntroductionMost physical processes in nature yield Fractal structures. FIC exploit self-similarity in images of natural scenes like clouds, hills, trees, bushes and textures for compression.FIC (Fractal Image Compression ) technique represents images in terms of fractal codes or iterated function systems that can be used to generate the image.

Fractal Image CompressionDifferent type of compression scheme exploringTakes advantage of similarities within an imageAdvanced detail interpolationHigh theoretical compression ratesFast decompression timesMathematical BackgroundStarted with Michael Barnsley, and refined by A. JacquinTry and find a set of transforms that map an image itself.The key is the Collage TheoremStates that if the error difference between the target image and the transformation of that image is less than a certain value the transforms are an equivalent representation of the image.Mathematical representationContractive Mappings are Transforms on points in Metric spaces such that the distance between the Transformed points is less than that between original points.The contractive Mappings used in FIC are Affine Transformations such as :Fi(x,y,z) = (ai*x + bi*y +ei, ci*x + di*y + fi, si*z + oi).si controls the contrast and oi the brightness.

Work-EncodingTake a starting image and divide it into small, non-overlapping, square blocks, typically called parent blocks.Divide each parent block into 4 each blocks, or child blocks. Compare each child block against a subset of all possible overlapping blocks of parent block size.Need to reduce the size of the parent to allow the comparison to work.Calculate a grayscale transform to match intensity levels between large block and child block precisely. Typically an affine transform is used (w*x = a*x + b) to match grayscale levels.

7Draw Pictures on a board here. Work EncodingUpper left corner child block, very similar to upper right parent block.Compute affine transform.Store location of parent block (or transform block), affine transform components, and related child block into a file.Repeat for each child block.Lots of comparisons can calculations.256x256 original image16x16 sized parent blocks241*241 = 58,081 block comparisons

Work- DecodingRead in child block and trans form block position, transform, and size information.Use any blank starting image of same size as original imageFor each child block apply stored transforms against specified transform blockOverwrite child block pixel values with transform block pixel valuesRepeat until acceptable image quality is reached.Resolution Independent decoding (RID)Original Image:

Fractal decoded image and ordinary zoom using image magic at 2x.

Fractal decoded image and ordinary zoomed image using image magic at 4x.

Fractal decoded image and ordinary zoomed image using image magic at 8x:

ExamplesOriginal Image

Starting Image for Decoding

Work DecodingFirst Iteration

Second Iteration

Work - DecodingFifth Iteration

Tenth Iteration

Possible ImprovementsGreatest weakness is time for encodingPossible speed upsOrder transform blocks into domains based off of average intensity and varianceOnly search through blocks with similar structuresReduce number of child blocksQuality and Compression Improvements through

Quad trees or HV TreesRotations of Transform Blocks during comparisonImproved grayscale transformsThank You