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WP6.2.1 : Affine Manipulation and Image Mapping

WP6.2.1 : Affine Manipulation and Image Mapping. A key aim of the work on representation and image manipulation - Pixel independent representing images (IP image) that assuming the image sequence is a continuous function

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WP6.2.1 : Affine Manipulation and Image Mapping

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  1. WP6.2.1 : Affine Manipulation and Image Mapping A key aim of the work on representation and image manipulation -Pixel independent representing images (IP image) that assuming the image sequence is a continuous function -IP image uses a superposition of polynomial functions at different scales -IP image functions have 3 real variables restricted to the range 0..1 for x and y and 0..t for time -Image manipulation is delay evaluated

  2. IP Image Representation A Racine IP I  is resolution independent, which can be represented as Monadic manipulation can be represented as HM = MApply(M, Hs) Where Hs is the source image and Hd the destination image and M is a monadic operator. Dyadic manipulationcan be represented as HD = DApply(D, Hs1, Hs2)  Where Hs1 Hs2 are the source images and Hd the destination image and D is a dyadic operation.

  3. Functions on IP Image We treat IP images as functions. Manipulations on IP images are regarding a composition of functions. The evaluation of an image is defined in terms of the evaluation of its composed functions: The evaluation is defined either on a point in space/time or over a set of points in space/time. It is evident that if such compositions are to be stored in a file and can be subsequently loaded and evaluated, then the process of defining the manipulation API is indirect.

  4. Delayed Image Evaluation * Non-destructive manipulation. * Non-linear, dynamic manipulation. * Reusability An edit session creates a composed set of image pyramids in heap 1, and these are then written to disk. They can be transmitted between sites on magnetic store and then restored to a second heap, from which they are rendered.We are pursuing a delayed evaluation approach pioneered by Friedman (Friedman 1976). The image evaluation will be delayed until it is required

  5. Manipulation Functions We use a byte-code representation of the image manipulation expressions. Expressions are made up of nodes, each of which has a byte code header followed by one or more data fields. • Combinators Combinators combine functions by performing composition, reduction, fork, currying and generalised matrix product. • Functions over points We will need functions over points in several contexts. Images themselves can be viewed as functions. • Primitive operators We assume that the basic operations of arithmetic are defined over functions and that in addition we have a matrix product operation to allow affine transforms.

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