1. November 2005 IP-Racine FP6 Integrated Project 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. November 2005 IP-Racine FP6 Integrated Project IP Image Representation A Racine IP I is resolution independent, which can be represented as Monadic manipulation can be represented as H M = MApply(M, H s ) Where H s is the source image and H d the destination image and M is a monadic operator. Dyadic manipulation can be represented as H D = DApply(D, H s1, H s2 ) Where H s1 H s2 are the source images and H d the destination image and D is a dyadic operation.

3. November 2005 IP-Racine FP6 Integrated Project 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. November 2005 IP-Racine FP6 Integrated Project Delayed Image Evaluation 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 * Non-destructive manipulation. * Non-linear, dynamic manipulation. * Reusability

5. November 2005 IP-Racine FP6 Integrated Project Manipulation Functions Combinators combine functions by performing composition, reduction, fork, currying and generalised matrix product. Functions over points Primitive operators We will need functions over points in several contexts. Images themselves can be viewed as functions. 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. 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