WP6.2.1 : Affine Manipulation and Image Mapping - PowerPoint PPT Presentation

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WP6.2.1 : Affine Manipulation and Image Mapping

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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 ... – PowerPoint PPT presentation

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Title: WP6.2.1 : Affine Manipulation and Image Mapping


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 manipulation can 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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