Image Compression Using Affine Fractal Interpolation on Rectangular Lattices

Abstract

Two methods for representing discrete image data on rectangular lattices using fractal surfaces are proposed. They offer the advantage of a more general fractal modeling compared to previous one-dimensional fractal interpolation techniques resulting in higher compression ratios. Theory, implementation and analytical study of the proposed methods are also presented.

Some properties of fractal interpolation functions on Sierpinski gasket

“…The following property is the well-known " 1 5 -2 5 rule" of harmonic functions. (1,2,3). Then h(q ij ) = 2 5 h(q i ) + 2 5 h(q j ) + 1 5 h(q k ).…”

Image Authentication Based on Fractal Features

“…The first fractal image coding method 15 partitions an image into square blocks, and improves the performance by the adaptive quadtree partitioning. To make it more consistent with the image content, the arbitrary shape partitioning is reported, 16,17 which satisfies the natural image's properties. Secondly, domain block searching is in close relation with the matching efficiency.…”

“…[25][26][27] Fractal image coding is based on the construction of iterated function systems (IFS). 15,17,18 The IFS is a set of contractive transformations, among which, each contractive transformation corresponds to an image block. For example, in the typical implementation, the image is partitioned into non-overlapped range blocks, R i , and overlapping domain blocks, D i .…”

“…This property has been used to compress images, named fractal image coding. [15][16][17][18] In fractal image coding, the transformation mapping one image region to another region is named fractal transformation that is controlled by some parameters. Generally, for different images, the fractal transformations are different, which distinguish an image from another image.…”

Fractal Dimension Based Shot Transition Detection in Sport Videos

“…Textural segmentation, classification, shape analysis are applicable research areas of FD in satellite, medical and natural images [12,13]. Image zooming [14], video coding [15] and compression [16,17] are other research topics where FD is used as a feature. Reference [18] is one of the few studies where FD is used for scene analysis purpose.…”