Quadtrees based method

This technique, based on the use of the quadtree data structure, was suggested by Ibbs and Stevens (1988) and Stevens et a l (1988). There is no reference in the literature to the complete structure of this method, only an introductory work was found which consisted mainly of an indication of which type of quadtree to adopt for representing the vector data.

Quadtrees have many relevant advantages over other methods of data representation. A set of functions can be applied to quadtrees to perform various operations that include intersection, union and windowing (Gahegan and Hogg,

1986). According to Waugh (1986) it is undoubtedly true that quadtrees are excellent for certain types of manipulation but it should also be added that they are unsuitable for certain types of manipulation and the cost of creating them may far outweigh the advantages of the manipulative capability they provide. The largest problem associated with quadtrees appear to be that the tree representation is not translation invariant, two regions of the same shape and size may have quite different quadtrees.

Chapter 7. Map to image matching

consequently shape analysis and pattern recognition are not straightforward (Burroughs 1986).

Quadtree structures have been extensively used to store and access raster data. The term quadtree is used to describe a class of hierarchical data structures whose common property is that they are based on the principle of recursive decomposition of space. Quadtrees can be differentiated by the type of data they are used to represent, the principle guiding the decomposition process and the resolution. The representation chosen for a specific task will be heavily influenced by the type of operation to be performed on the data. Gargantini (1982) proposed a data structure to represent quadtrees which is known as a linear quadtree. Mason (1987) developed a particular quadtree representation (compact pointerless representation) based on the quadtree presented by Gargantini. The point quadtree as a multidimensional generalisation of a binary search tree was described by Bentley (1975). According to Samet and Webber (1985) among the quadtree-based data structures the point region (PR) quadtree forms a better base than the point quadtree for the development of a practical algorithm to process cartographic data in an interactive environment. The PM quadtree is the quadtree developed for storing polygonal maps and it can be seen as an adaption of the PR quadtree. PM3 quadtrees use the same decomposition rule as the PR quadtree but store considerably more information in the terminal nodes. Samet and Webber (1985) showed how to perform point location, dynamic line insertion, and overlay two polygonal maps that are represented by PM quadtrees. The quadtree used by Ibbs (1988) is a modification of the PM3 quadtree which is a variant of the region quadtree. Ibbs and Stevens et al. (1988) reported on the implementation of QUADIFF (a study on quadtrees developed by Laser -Scan) and some of the advantages of storing vector data within a quadtree organisation:

1. The data are stored in floating point format, at their original precision . This is without approximation and means that manipulations will produce well-defined results.

2. The quadtree structure can be regarded as a spatial index into the vector data. Propagation of feature-oriented information up the tree from the leaves allows spatially-oriented searches to be performed in an efficient manner.

3. Quadtrees are well-understood, and established algorithms may be used to manipulate data stored in this form.

4. Storing vector data in a quadtree form means that interactions with other data in quadtree form, for example raster data, are simplified.

No assumptions are made on the quadtree used to represent image data. This should not constitute a problem since the quadtree is a structure that was primarily developed as a more compact representation of raster data. Therefore, appropriate quadtree algorithms to deal with image data are considered to be better understood than the quadtree representation of map data. According to Ibbs (1988) there is no great problem in relating the quadtree developed by Laser-Scan for map data to a quadtree of an image. To interact with other data (whether raster or vector), there is a need to ensure that, at some level, the relevant quadtrees share a quad-square size and shape - for raster this would be the pixel itself. There is no particular need to ensure that the origins of the data are the same, methods are available to cope with logical operations on unregistered trees (Samet and Webber, 1985). There have not been any results published on the application of this method as a map-image matching technique. Shneider (1981) presented work on several algorithms to manipulate data stored in this form which include intersection, which can be a useful tool for map to image matching.

7.2.2 Relational m atching

Haala and Vosselman (1992) used the relational matching method developed by Shapiro and Haralick (1981). In order to get comparable representation of the image and the landmark, structural descriptions have to be extracted from both data formats. They describe the selected image and map objects in terms of geometric primitives (points, lines and regions) and their relations. To get an expressive description, objects containing sufficient structure such as roads, rivers and cornfields were used. The structural description of the landmarks may be obtained by digitising maps or from a geographic information system.

The relational image descriptions used were extracted from colour images due to the fact that without the use of colour (or multi-spectral) images, a reliable extraction of roads and rivers is hardly possible (Haala and Vosselman, 1992).

Chapter 7. Map to image matching

The data structure described by Haralick (1980) can naturally and efficiently contain the vector format and the raster format data. In this relational matching technique no distinction will be made between the sources of the data structures to be matched. The matching of spatial data structures is a problem of finding homomorphisms from one spatial data to another. If there is a homomorphism from one structure to a part of another then there is a base for considering the two structures as being similar and comparing them further.

Haala and Vosselman (1992) concluded that landmarks can be located by matching relational descriptions of landmarks and images. The procedure is considered very robust with respect to spurious and missing image features, e.g. resulting from occlusions or additional image detail, and to geometric distortions. The search time needed to find a match is hard to predict. It is mainly dependent on the number of image and model features to be matched, the quality of the image description and the uniqueness of the control feature attributes. Differences between the description of the landmark model and the image, which make it necessary to use wildcard assignments also have a great influence on the size of the tree search. This technique does not require approximate values for the orientation. However, if approximate values are available (such as scale rotation or position of the landmark), they are very useful for reducing the search space. This study by Haala and Vosselman (1992), was focused on the recognition of the landmark in the image and did not include further developments to include it into an absolute orientation process.

Intensive research has been carried out on relational descriptions and relational matching, for more details on the subject see Haralick (1980), Shapiro and Haralick (1978, 1980, 1981), Haralick and Shapiro (1979, 1980), Shapiro (1979, 1980) and Vosselman (1992).