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Vectorising Photographic Images

A vectorised image is one in which the pixel sample values are represented by the boundaries of level sets which are held in a continuous resolution-independent form. These boundaries are represented in terms of the control points of free-form curves of degree 1 or higher, which may be thought of as vectors in the algebraic sense or chains of vectors in the geometric sense, hence the term vectorisation. Inter-level values are interpolated via a diffusion process the simplest of which allows linear diffusion between levels. An image held as level sets is this itself resolution-independent, although will carry no more detail than that present in the sample set from which it was derived .

A codec has been developed which translates any raster image into vector form with the smallest number of level sets required for reconstruction, and back again into sampled form. The codec is noise-resistant in the sense that images with high noise measures will decode back into images with low noise measures i.e. pixel correlation is normally increased while correlation breaking (at an edge) is preserved. In vector form the image may be manipulated in the same way as any other vector or drawn image without risking the generation of sampling artefacts. Certain image manipulation processes, e.g. histogram re-shaping, image warps, can be carried out far more precisely than with raster images in particular without loss of sampling levels in the case of histogram equalisation.

There is potential for a whole range of improved image sequence manipulation processes, which are difficult or impossible with sampled images including rotoscoping, rotomatting, matte pulling and hole filling. In principle all image manipulation processes can be conducted, usually advantageously in terms of operations on vector formats, including so-called compression processes. These processes are now being investigated with a view to promoting and exploiting the format. Descriptively speaking there are essentially three ways in which raster images might be reduced to a resolution-independent form: as a 3D surface constructed as a locally continuous approximation to the pixel values, as open overlaid brush-strokes which define a combination of pixel values, or as a non-overlapping set of isochromic contours (also known as isophotes) which divide the image space into regions below or above a given colour primary value level set.

The 3D surface approach makes problematic assumptions about pixel correlations, the brush-stroke approach is still a research issue, so the isochromic contour approach was followed. As the term isochromic contour has been applied elsewhere to boundaries of contiguous collections of equal-valued pixels we should emphasise that we treat pixels as being like spot heights in a piecewise continuous landscape and that contours may or may not respect pixel values depending on an estimation of the noise in the samples. Such contours may be derived from any degree of quantisation of the original pixel values although there remains the question of how to interpret the regions between the contours which we have resolve by using diffusion as described in Level Set theory. We now facing a vista of possible avenues for improvements in performance based on new technical development following on from the present approach, including a range of new applications of (the algebraic form of) level set theory, and it is intended to take these approaches in future exploitation.

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Reported by

University of Glasgow
Department of Computing Science 17 Lilybank Gardens
G12 8QQ Glasgow
United Kingdom
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