Fractal compression

Fractal compression is a lossy compression method for digital images, based on fractals. The method is best suited for textures and natural images, relying on the fact that parts of an image resemble other parts of the same image. Fractal algorithms convert these parts into mathematical data called "fractal codes" which are used to recreate the encoded image. Fractal image representation may be described mathematically as an iterated function system. We begin with the representation of a binary image, where the image may be thought of as a subset of R 2. An IFS is a set of contraction mappings ƒ1...ƒN, f i: R 2 → R 2. According to these mapping functions, the IFS describes a two-dimensional set S as the fixed point of the Hutchinson operator H = ⋃ i = 1 N f i, A ⊂ R 2; that is, H is an operator mapping sets to sets, S is the unique set satisfying H = S. The idea is to construct the IFS such; the set S can be recovered from the IFS by fixed point iteration: for any nonempty compact initial set A0, the iteration Ak+1 = H converges to S.

The set S is self-similar because H = S implies that S is a union of mapped copies of itself: S = f 1 ∪ f 2 ∪ ⋯ ∪ f N So we see the IFS is a fractal representation of S. IFS representation can be extended to a grayscale image by considering the image's graph as a subset of R 3. For a grayscale image u, consider the set S =. Similar to the binary case, S is described by an IFS using a set of contraction mappings ƒ1...ƒN, but in R 3, f i: R 3 → R 3. A challenging problem of ongoing research in fractal image representation is how to choose the ƒ1...ƒN such that its fixed point approximates the input image, how to do this efficiently. A simple approach for doing so is the following partitioned iterated function system: Partition the image domain into range blocks Ri of size s×s. For each Ri, search the image to find a block Di of size 2s×2s, similar to Ri. Select the mapping functions such that H = Ri for each i. In the second step, it is important to find a similar block so that the IFS represents the input image, so a sufficient number of candidate blocks for Di need to be considered.

On the other hand, a large search considering many blocks is computationally costly. This bottleneck of searching for similar blocks is why PIFS fractal encoding is much slower than for example DCT and wavelet based image representation; the initial square partitioning and brute-force search algorithm presented by Jacquin provides a starting point for further research and extensions in many possible directions -- different ways of partitioning the image into range blocks of various sizes and shapes. Other researchers attempt to find algorithms to automatically encode an arbitrary image as RIFS or global IFS, rather than PIFS. Fractal image compression has many similarities to vector quantization image compression. With fractal compression, encoding is computationally expensive because of the search used to find the self-similarities. Decoding, however, is quite fast. While this asymmetry has so far made it impractical for real time applications, when video is archived for distribution from disk storage or file downloads fractal compression becomes more competitive.

At common compression ratios, up to about 50:1, Fractal compression provides similar results to DCT-based algorithms such as JPEG. At high compression ratios fractal compression may offer superior quality. For satellite imagery, ratios of over 170:1 have been achieved with acceptable results. Fractal video compression ratios of 25:1–244:1 have been achieved in reasonable compression times. Compression efficiency increases with higher image complexity and color depth, compared to simple grayscale images. An inherent feature of fractal compression is that images become resolution independent after being converted to fractal code; this is because the iterated function systems in the compressed file scale indefinitely. This indefinite scaling property of a fractal is known as "fractal scaling"; the resolution independence of a fractal-encoded image can be used to increase the display resolution of an image. This process is known as "fractal interpolation". In fractal interpolation, an image is encoded into fractal codes via fractal compression, subsequently decompress

Mark Anstice

Mark Anstice is a Scottish explorer, adventurous documentary reality television film maker and writer. He is best known for appearing in the Travel Channel's series Mark & Olly: Living with the Tribes with Oliver Steeds. After school, Anstice travelled extensively throughout Asia. In London he joined the 5th Royal Inniskilling Dragoon Guards of the British Army. Anstice spent six years in the guards with operational commitments in the Middle East, Central America and Bosnia, leaving the service in 1995 as a Captain. In 2000, Mark travelled along with his friend Bruce Parry for 77 days to climb Puncak Mandala in the Indonesian part of New Guinea; this is the third highest mountain of Australasia, but is little known and climbed. During the expedition, the team had first contact with some members of the Korowai tribe. In the course of the expedition, the adventure documentary, Extreme Lives: Cannibals and Crampons. was co-directed and written along with Bruce Parry. The film won both Kendal Mountain Film Festival.

Mark subsequently wrote the book First Contact, published by Eye Books. Which was published in 2004. Chronicling the expedition to Mount Mandela. In 2005, Mark took part in the recreation of the Terra Nova Expedition of Robert Falcon Scott and the Amundsen's South Pole expedition of Roald Amundsen as part of the BBC Blizzard: Race to the Pole documentary; the documentary reconstructed the 2500 km expedition using the same equipment and clothing as the original two teams, placing the setting in Greenland as dogs were no longer allowed in Antarctica. Between 2006-2008 he co-presented, with Olly Steeds, three 8-part series for Travel Channel in each of which the duo went to live with a remote, jungle-dwelling tribe for three months. In 2009, amidst growing resentment at the way their experiences were edited for the viewing audience, public controversy surrounding the edit of the third series Steeds left the team and the show was axed. Anstice went on to make ` Secrets of The Tribes', in West Africa.

Mark Anstice runs the charity Fertile Roots Foundation. Extreme Lives: Cannibals and Crampons First Contact – a BBC Anthropology series presentation surrounding the ethics of "First Contact" experiences staged by tour operators Blizzard: Race To The Pole Mark & Olly: Living with the Tribes Worlds Lost Tribes: The New Adventures of Mark and Olly Secrets of the Tribes Anstice is married to Ayelen, Argentinian

Christine Crawley, Baroness Crawley

Christine Mary Crawley, Baroness Crawley FRSA is a British politician for the Labour Party. Crawley was educated at the Notre Dame High School School in Plymouth before going to Digby Stuart College to train as a teacher. After graduation she began teaching children aged between 9 and 15, ran the local youth theatre, her work to gain funding for the youth theatre brought her into contact with local politicians, she became involved in politics, joining the Labour Party. Soon after joining the party she became secretary of the local branch, Social Secretary for the local Women's Branch, she was elected as a District Councillor for the South Oxfordshire District Council, at a time when the Labour Party was a minority party on the council. In 1983, she ran for a seat in the House of Commons but was not elected, instead spending a year working on local issues before she was elected as a Member of the European Parliament for the Birmingham East constituency); as an MEP Crawley was active on the Committee on Women's Rights and Gender Equality and helped push their Maternity Leave Directive through, becoming Chair of that committee in 1989.

She stepped down as an MEP in 1999, is now a member of the West Midlands Regional Assembly and a sponsor of the National Women's Network. She was Chair of the Women's National Commission between 1999 and 2001, in 1998 was created Baroness Crawley, of Edgbaston in the County of West Midlands. Between 2002 and 2008 she served as a Party Whip in the House of Lords, she is a member of Labour Friends of Israel. In 2013, Baroness Crawley was awarded an Honorary Doctorate of Health from Plymouth University Profile at New Statesman "Baroness Christine M. Crawley". European Parliament. Retrieved 28 May 2013