In the classical approach to high quality shading proposed by Phong, the illumination equation is computed per pixel using an interpolated normal. The normals at the vertices are bi-linearly interpolated over the polygon to obtain a normal per pixel. Correct shading requires normalization of these normals, which is computationally demanding involving a square root. In our research we have shown how this normalization can be eliminated through the use of spherical interpolation and the Chebyshev recurrence formula, reducing the calculation to a few single arithmetic operations per pixel.
Still a substantial setup operation is needed for each scanline. We have studied how also this can be made more efficient, with some limited progress so far. An alternative approach is to do the most of the setup on polygon level and incrementally compute the setup needed per scanline. In particular, we have studied quadratic shading approaches, i.e. fitting second degree surfaces to the polygons. The most successful approach has been through what we have called X-shading, where the setup is calculated by using an efficient approximation for the mid-edge normals. This setup is about four times faster than previously known methods.
In the process of studying shading methods we have also made some contributions to improving bump-mapping and simulation of different kinds of light sources.
The developed methods will be of interest in future generations of computer graphics software and hardware systems, ranging from high end systems to generate realistic movies and 3D games, to handheld devices such as mobile phones with graphics displays.
The objective of this thesis is to develop more general modelling strategies than commonly used today. In particular, the impact of the human factor in the model creation process should be minimised. It is presumed that the human ability of abstraction imposes undesired constraints on the description. In comparison, common approaches are discussed from the viewpoint of generality.
The technique considered introduces appearance space as a common framework to represent both shapes and images. In appearance space, an object is represented by a single point in a high-dimensional vector space. Accordingly, objects subject to variation appear as nonlinear manifolds in appearance space. These manifolds are often characterised by only a few intrinsic dimensions. A model of a class of objects is therefore considered equal to the mathematical description of this manifold.
The presence of nonlinearity motivates the use of artificial auto-associative neural networks in the modelling process. The network extracts nonlinear modes of variation from a number of training examples. The procedure is evaluated on both synthetic and natural data of shapes and images and shows promising results as a general approach to object modelling.
This thesis shows, in two applications, how computerized image analysis can help define and implement these methods. First, by using segmentation to improve visualization of blood-pool contrast enhanced (CE)-MRA, with an additional application in coronary Computerized Tomographic Angiography. We show that, using a limited amount of user interaction and an algorithmic framework borrowed from graph theory and fuzzy logic theory, we can simplify the display of complex 3D structures like vessels. Second, by proposing a methodology to analyze the geometry of arteries in whole-body CE-MRA. The vessel centreline is extracted, and geometrical properties of this 3D curve are measured, to improve interpretation of the angiograms. It represents a more global approach than the conventional evaluation of atherosclerosis, as a first step towards screening for vascular diseases.
We have developed the methods presented in this thesis with clinical practice in mind. However, they have the potential to be useful to other applications of computerized image analysis.
Different algorithms for segmenting individual tree crowns are presented and also compared to each other in order to find their strengths and weaknesses. All segmentation algorithms developed in this thesis focus on preserving the shape of the tree crown. Regions, representing the segmented tree crowns, grow according to certain rules from seed points. One method starts from many regions for each tree crown and searches for the region that fits the tree crown best. The other methods start from a set of seed points, representing the locations of the tree crowns, to create the regions. The segmentation result varies from 73 to 95 % correctly segmented visual tree crowns depending on the type of forest and the method. The former value is for a naturally generated mixed forest and the latter for a non-mixed forest.
The classification method presented uses shape information of the segments and colour information of the corresponding tree crown in order to decide the species. The classification method classifies 77 % of the visual trees correctly in a naturally generated mixed forest, but on a forest stand level the classification is over 90 %.