Computer Laboratory

Technical reports

Surface modelling for 2D imagery

Henrik Lieng

October 2014, 177 pages

This technical report is based on a dissertation submitted June 2014 by the author for the degree of Doctor of Philosophy to the University of Cambridge, Fitzwilliam College.

Some figures in this document are best viewed in colour. If you received a black-and-white copy, please consult the online version if necessary.


Vector graphics provides powerful tools for drawing scalable 2D imagery. With the rise of mobile computers, of different types of displays and image resolutions, vector graphics is receiving an increasing amount of attention. However, vector graphics is not the leading framework for creating and manipulating 2D imagery. The reason for this reluctance of employing vector graphical frameworks is that it is difficult to handle complex behaviour of colour across the 2D domain.

A challenging problem within vector graphics is to define smooth colour functions across the image. In previous work, two approaches exist. The first approach, known as diffusion curves, diffuses colours from a set of input curves and points. The second approach, known as gradient meshes, defines smooth colour functions from control meshes. These two approaches are incompatible: diffusion curves do not support the local behaviour provided by gradient meshes and gradient meshes do not support freeform curves as input. My research aims to narrow the gap between diffusion curves and gradient meshes.

With this aim in mind, I propose solutions to create control meshes from freeform curves. I demonstrate that these control meshes can be used to render a vector primitive similar to diffusion curves using subdivision surfaces. With the use of subdivision surfaces, instead of a diffusion process, colour gradients can be locally controlled using colour gradient curves associated with the input curves.

The advantage of local control is further explored in the setting of vector-centric image processing. I demonstrate that a certain contrast enhancement profile, known as the Cornsweet profile, can be modelled via surfaces in images. This approach does not produce saturation artefacts related with previous filter-based methods. Additionally, I demonstrate various approaches to artistic filtering, where the artist locally models given artistic effects.

Gradient meshes are restricted to rectangular topology of the control meshes. I argue that this restriction hinders the applicability of the approach and its potential to be used with control meshes extracted from freeform curves. To this end, I propose a mesh-based vector primitive that supports arbitrary manifold topology of the control mesh.

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BibTeX record

  author =	 {Lieng, Henrik},
  title = 	 {{Surface modelling for 2D imagery}},
  year = 	 2014,
  month = 	 oct,
  url = 	 {},
  institution =  {University of Cambridge, Computer Laboratory},
  number = 	 {UCAM-CL-TR-862}