Applications of Image Analysis in Orientation Space

At the heart of many problem-solving techniques lies the reduction of the problem into smaller sub-problems. Image analysis is no exception, and it is therefore not surprising that a lot of attention has been given to the detection of the fundamental building blocks of images: lines and edges. These building blocks, or primitives, can be characterised by a fairly small number of features: contrast, scale, orientation and phase. These building blocks and their features form the basis for the description of slightly more complex structures and descriptors. Examples are corners, T-junctions, wavelets 1 (structures) and curvature (feature). The distinction between primitives and complex structures is not always completely clear and may depend on the techniques used to extract them. The technique described in this paper for example, is based on linear filtering theory. Within that framework it is convenient to consider wavelets as primitives, alongside lines and edges. We will show a number of problems which we can solve on the basis of these primitives and, in particular, making use of one of their features: orientation. We will argue below that to cope with moderately complex structures, a special representation for orientation is required: orientation space. But first we must establish what exactly we mean by orientation: