Institute of Industrial Science, University of Tokyo
7221, Roppongi, MinatoKu Tokyo 106, Japan
Tel: (81)334026231 Fax: (81)334792762
Email:[email protected]
Abstract
As a wide variety of satellite images with different resolutions become available and various types of geographic information is being accumulated, it is rather common among users to integrate those data for their application s. To conduct consistent and efficient processing of a wide range of geographic information, it is essential to develop data models for geographic information together with efficient operation method. However, we have no sufficient sets of data models and operations for handling image data as geographic or spatial data. This insufficiency leads to the generation of artifacts or the degradation of image data quality in overlying image data or transferring it to different coordinate systems by resampling. This study reveals possible degradation in the overlay and resampling operations, and makes comparison of data models and operations in term of computational load and its degradation. The results implies a possible future image data model.
1.Introduction
As a great variety of image data become available due to the launch of many remote sensing satellites, techniques of extracting necessary information by integrating these data are increasingly important. And as the development of GIS data and remote sensing image data are becoming very common. GIS is now an indispensable system as a platform of integrating information. For GIS, accurate and consistent processing are achieved by representing geographic information using data models and data handling.
So, what kinds of models should be used for imaged data? Image data is intuitively handled as raster data because in practice it is a two dimensional array of pixels which correspond with a certain unit area on the ground surface. But image data may not be raster data exactly all the time since the shape of each pixel neither be square nor rectangular due to viewing angle effects and topographic distortions. This means that we need to devise a new model to represent foot print more accurately, and a set of operations to handle them efficiently.
The objective of this study is to propose and make comparison of image data models together with operations consistent with those models. The performance of those models is evaluated in terms of computational complexity and size of the models. The shape of foot prints may be different, appending on the types of sensors. We paid attention here only to optical sensors whose foot prints are either square or rectangular.
2.Image data models
2.1 Necessity of image data model
Conventionally, pixel position is represented by its central points, while the shape of the pixel is only ambiguously represented by resolution. The shape of the pixel on the ground (foot print) is not represented explicitly. This kind of representation of image data is not sufficient for mapping foot print. We need to represent the foot print more clearly and explicitly. The ambiguity of the foot print representation cause several serious problems in "resampling" process. Resampling is an operation of projecting an image data onto grid cells defined on a given two dimensional coordinate system (Fig.1). Usually, for the implementation of the resampling, centre position of each grid cell is transferred to the image plane, and pixel value at the transferred location is given with interpolation. In many cases, since the size of the grid cells are set to be almost the same with that of the pixel, each pixel of the image data is mapped to a single grid cell.
Fig.1 Resampling
Fig.2 summarizes the possible errors, which may occur in the resampling process. Error percentage denotes the ratio of unoverlapped portion to the original footprint. Fig.3 shows that the error percentage are strongly affected by the relative size of grid cells, rotation angles between the image coordinate systems (line and pixel directions) and the gridcell is as large as the pixel, maximum error could be 90%. This kind of errors also affect severely to the quality of product, when we overlay high resolution image data on low resolution image data which are resampled to the same coordinate system of the high resolution image data. This problem comes from the same source a the shape of footprints of pixels are not properly represented and no sufficient algorithms for operating those data models are developed. By applying smaller grid cells, of course, this problem can be solved with a conventional resampling algorithm. In those cases, however, computational load of the resampling would be proportional to the numbers of grid cells, which means the load may become quite heavy if "high quality resampling" is required. As will see later, a data model which represent explicitly the footprint boundary can mitigate the increase of computational load rather effectively.
Fig.2 Degradation of Image data in Resampling.
Fig.3 Average Percentage of the Unoverlapping area by the rotation angle* and grid size.
See* Fig.2
2.2 Proposal of image data model
1) Fundamental configuration of image data model
The image data model consists of 2dimensional pixel model and additional footprint boundary models.
2) 2dimensional pixel model
2dimensional model have two components; one is 2doimensional array of pixel values and mapping function which relate the image coordinate values with the ground coordinate values. The mapping function is denoted by f(i,j) , {(i,j) = (line# and pixel#)} for transferring the image coordinate values to the corresponding ground values. The model also has an inverse function f1(x,y,z) , {(x,y,z): ground coordinate values}. These functions are usually non linear function due to the topographic distortions and so on. The boundary of footprint is indirectly or implicitly represented as the boundary of square a rectangle pixel on the image plane. Although operation algorithms consistent with model are not sufficient by provided, this model is conventionally used.
3) Footprint boundary models
The footprint boundary models represent the shape or the boundary of pixel on the ground surfaces clearly. This model is not used independently, but is always used as additional models to the basic 2dimensional pixel model. We propose two types of model as follows, under this category.
 Grid line model
This model represents the line boundary and the pixel boundary of footprint the parallel straight lines with regular intervals on the 2dimensional plane. This model has a directional vector, distance of each boundary, and the origin of the initial line and pixel boundary as parameter.  Line segment model
This model approximates the shape of the footprint (the boundary of line and pixel) by line segments. To represent this model, we should make a table of coordinate values of segment end points (ground coordinate values). Operations based on this model can be conducted efficiently by generating an interim file as follows.Ymn £y*We assume each line segment is denoted by a series of end points with coordinate values as (Xpij,Ypij), (XLij,YLij), (XL**,YL**) denotes the boundary of pixels, while (XL**, YL**) is boundary of line, where I is boundary # (pixel#, line#), and j is the serial # of ends points of line segments. In Fig.4 the image data has pixel boundaries (P0,P1,P2,…..) and line boundaries (L0,L1,L2,…). The location of P0 is represented by (Xpoj, Ypoj), {j=0,1,2…..M}.
Fig.4 Line segment model
We will show how the intersection of the line (y=y*) between the boundary of pixel (Pm) can be computed. First, find n satisfying the following inequalities. And, the solution of the following equations (Xm(y=y*), y*) is the point of intersection.
Xm(y=y*)= y*ymn
——————
Ym(n+1)ymn.(xm(n+1)xm)+ xmn We will compute all x coordinate values of intersection points between the pixel boundaries and y=y* where (y*=a0, a1, a2,…: sorted y coordinates of end of all pixel boundaries descending order) , with the above method. The same procedure is applied to compute all x coordinate values of intersection points with all line boundaries. With this process , we can generate the interim file shown as Table .1. When m is the number of pixel boundaries, n is line boundaries, and the total number of end points is M and N respectively for all the pixel boundaries and all the line boundaries, the maximum computational load is O (M=n+m=N).
3.The operation methods of the image data model
At this section, we list the operations necessary for the integrated use of multiresolution image data with vector data, examine the computational load of the operations and the possible data quality degradation by resampling and overlaying.
Table 1. Intrim file for Line Segment Model
Line#
Y

0  1  2  … 
b 0  X 0 0  X 0 1  X 0 2  
b 1  X 1 0  X 1 1  
b 2  X 2 0  
:  
pixel#
Y

0  1  2  … 
a 0  X 0 0  X 0 1  X 0 2  
a 1  X 1 0  X 1 1  
a 2  X 2 0  
: 
3.1 Transformation to raster data (Resampling) 1) Two dimensional pixel model 2) Footprint boundary model
3.2 Overlaying with vector data 
