Geometric transformations in octrees using shears

Existent algorithms to perform geometric transformations on octrees can be classified in two families: inverse transformation and address computation ones. Those in the inverse transformation family essentially resample the target octree from the source one, and are able to cope with all the affine transformations. Those in the address computation family only deal with translations, but are commonly accepted as faster than the former ones for they do no intersection tests, but directly calculate the transformed address of each black node in the source tree. This work introduces a new translation algorithm that shows to perform better than previous one when very small displacements are involved. This property is particularly useful in applications such as simulation, robotics or computer animation.Postprint (published version

The Representation of symmetric patterns using the quadtree data structure

Hierarchical data structures for image representation have been widely explored in recent years. These data structures are based on the principle of recursive decomposition of an image region. The most commonly mentioned picture data structure for two-dimensional data is referred to as a quadtree . The purpose of this thesis is to investigate the use of a general quadtree scheme as a means of representing symmetric images. Specifically, images are generated according to the rules of selected two-dimensional plane symmetry groups

Representing Images Using the Quadtree Data Structure (Hebrew Consonants and Vowels)

Computing and Information Science

Efficient geographic information systems: Data structures, Boolean operations and concurrency control

Geographic Information Systems (GIS) are crucial to the ability of govern mental agencies and business to record, manage and analyze geographic data efficiently. They provide methods of analysis and simulation on geographic data that were previously infeasible using traditional hardcopy maps. Creation of realistic 3-D sceneries by overlaying satellite imagery over digital elevation models (DEM) was not possible using paper maps. Determination of suitable areas for construction that would have the fewest environmental impacts once required manual tracing of different map sets on mylar sheets; now it can be done in real time by GIS. Geographic information processing has significant space and time require ments. This thesis concentrates on techniques which can make existing GIS more efficient by considering these issues: Data Structure, Boolean Operations on Geographic Data, Concurrency Control. Geographic data span multiple dimensions and consist of geometric shapes such as points, lines, and areas, which cannot be efficiently handled using a traditional one-dimensional data structure. We therefore first survey spatial data structures for geographic data and then show how a spatial data structure called an R-tree can be used to augment the performance of many existing GIS. Boolean operations on geographic data are fundamental to the spatial anal ysis common in geographic data processing. They allow the user to analyze geographic data by using operators such as AND, OR, NOT on geographic ob jects. An example of a boolean operation query would be, Find all regions that have low elevation AND soil type clay. Boolean operations require signif icant time to process. We present a generalized solution that could significantly improve the time performance of evaluating complex boolean operation queries. Concurrency control on spatial data structures for geographic data processing is becoming more critical as the size and resolution of geographic databases increase. We present algorithms to enable concurrent access to R-tree spatial data structures so that efficient sharing of geographic data can occur in a multi user GIS environment

Lazy Image Processing: An Investigation into Applications of Lazy Functional Languages to Image Processing

The suitability of lazy functional languages for image processing applications is investigated by writing several image processing algorithms. The evaluation is done from an application programmer's point of view and the criteria include ease of writing and reading, and efficiency. Lazy functional languages are claimed to have the advantages that they are easy to write and read, as well as efficient. This is partly because these languages have mechanisms to improve modularity, such as higher-order functions. Also, they have the feature that no subexpression is evaluated until its value is required. Hence, unnecessary operations are automatically eliminated, and therefore programs can be executed efficiently. In image processing the amount of data handled is generally so large that much programming effort is typically spent in tasks such as managing memory and routine sequencing operations in order to improve efficiency. Therefore, lazy functional languages should be a good tool to write image processing applications. However, little practical or experimental evidence on this subject has been reported, since image processing has mostly been written in imperative languages. The discussion starts from the implementation of simple algorithms such as pointwise and local operations. It is shown that a large number of algorithms can be composed from a small number of higher-order functions. Then geometric transformations are implemented, for which lazy functional languages are considered to be particularly suitable. As for representations of images, lists and hierarchical data structures including binary trees and quadtrees are implemented. Through the discussion, it is demonstrated that the laziness of the languages improves modularity and efficiency. In particular, no pixel calculation is involved unless the user explicitly requests pixels, and consecutive transformations are straightforward and involve no quantisation errors. The other items discussed include: a method to combine pixel images and images expressed as continuous functions. Some benchmarks are also presented

Quadtree algorithms for image processing

The issue of constructing a computer-searchable image encoding algorithm for complex images and the effect of this encoded image on algorithms for image processing are considered. A regular decomposition of image (picture) area into successively smaller bounded homogeneous quadrants is defined. This hierarchical search is logarithmic, and the resulting picture representation is shown to enable rapid access of the image data to facilitate geometric image processing applications (i.e. scaling, rotation), and efficient storage. The approach is known as quadtree (Q-Tree) encoding. The applications in this thesis are primarily to grayscale pixel images as opposed to simple binary images