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Building Spatial Databases – Theory / LOD algorithms

Learners guide


The LOD algorithms are for fast access and display for large digital images and elevation models. LOD algorithm is a group of similar methods. In this unit only the Gauss pyramid will be described.


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LOD algorithms

Displaying and handling of remote sensed images, aerial images or digital elevation models is a great challenge for any geographical information software. Let us take a case where a large area is displayed by high resolution images: a huge amount of data must be handled and displayed, whereas the resolution of monitors is much smaller than the data set. It is not reasonable to display that huge are with original resolution (even by using TIN model), namely rarefication must be done over the data set.

Algorithms simplifying images and relief models are commonly called level of detail (LOD) algorithms. Basically, two variations exists for LOD: static and continuous. As for static, different detailed variations of a model have been made in advance, and these pre-made variations are changed depending on what level of details is needed for the actual purpose of use (e.g. altering zooming). It has been widely applied for remote sensed images and raster images with height data.

However, static LOD cannot be applied on terrain models. Terrain models are usually large and therefore it is common to view a portion of it at low zoom level. The level of detail cannot be altered at the same time. Continuous level of detail (CLOD) algorithms are the solution for this kind of problems. Basically, they split up the model into pieces depending on the current viewpoint (or different, predefined metrics), and the model is re-analyzed to see what can be simplified.

LOD algorithms are constantly changing the resolution of each component. The main question is how to pre-determine the level of detail or quality of a certain portion of an image. Many solutions exist to avoid various types and extent of errors; they only differ in the way of usage, which way is more convenient.

Gauss pyramid

One of the best-known and mostly used static LOD algorithm is the Gauss pyramid. Relatively large images can be displayed quickly with it. The computation speedup has been achieved by pre-generating images in different resolution levels and displaying the requested resolution when needed. It is a very simple method.

Figure 78. Gauss pyramid with different resolution levels. Image sizes are decreased by the power of two; for example, the original image size is 512*512, but after the first level its size is 256*256, and so on.

The algorithm works as follows. Take a high resolution image. Apply a smoothening filter on the original image with half of the upper-bound frequency value, then rarefy the image, namely resample the image with the double of the sampling distance. Continue the process on the resulted image as described in the first steps (Figure 78).

The calculation of a Gauss pyramid in practice is the following. Denote the image on l-1 level gl-1. The pixels on level l are calculated by:

which is a convolution. Figure 79 describes (for one-dimension) how to calculate the pixel value for a rarefied image from a larger resolution image one level below it.

Figure 79. Calculation of a Gauss pyramid (one-dimensional illustration).

Most GIS software are using this method for the first time when the user opens an image; the software always asks to create a Gauss pyramid or not. By choosing this option for the first time the display of the image may take a while, however for latter times it will not take any time at all to open. Not only the opening but also zooming will be much faster.

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