specified in image coordinates in one image usually can correspond to an infinite number of ground position coordinates. In most imaging geometries, these ground positions all lie along one imaging
ray. Obviously, the corresponding image coordinates and horizontal ground coordinates will almost
always have different reference points and scales. Furthermore, the shapes of objects will be different in image and horizontal ground coordinates. Straight lines in ground coordinates will
rarely be perfectly straight in image coordinates. Parallel lines in horizontal ground coordinates will usually not be parallel in image coordinates. Similarly, evenly spaced points along a line will
usually not be evenly spaced in image coordinates.
Some of the possible shape differences are indicated in the diagram of Figure 1. Down the center is a cartoon showing a horizontal rectangular feature on the ground with two images of that ground
area. The bottom left square indicates how this feature appears in horizontal ground coordinates. The top-left and top-right squares indicate how this feature could appear in two different images.
This figure assumes that the two images are tilted significantly from vertical, as is typical with convergent stereoscopic images. Of course, many real images would be tilted less, producing less
distortion of the ground rectangle. However, there is usually some significant shape distortion in an image of a ground feature.
Image one Image two
Perspective view of geometry Ground space
Figure 1. Corresponding Ground and Image Shapes
When high accuracy is needed, image exploitation must consider various image sensor or camera non-idealities from a perfect frame or pinhole camera. These non-idealities often include lens
distortion, atmospheric refraction, and earth curvature, all of which tend to change straight lines into slightly curved lines.
2.5. Image Geometry Models
To determine the correct image position of a ground point, an image geometry mathematical model is used. Such an image geometry model relates 3–D ground position coordinates to the
corresponding 2–D image position coordinates. Such an image geometry model is alternately called an image sensor model, sensor model, imaging model, or image mathematical model. The term
“sensor” is often used when the camera is digital; the word “camera” is usually used when the image is captured on film. Of course, film images can be scanned or digitized and are then
“digital”. The data used by such an image geometry model is often called image support data.
An image geometry mathematical model can also be used to determine the correct ground position for an image position, if used with additional data. When a single or monoscopic image is used,
this additional data normally defines the shape and position of the visible ground or object
The Open GIS Abstract Specification Page 3
Volume 16: Image Coordinate Transformation Services 00-116.doc
surface. For example, this additional data is often grid elevation data. Alternately, two or more stereoscopically overlapping images can be used, that show the same ground point viewed from
different directions. In this case, the multiple image geometry mathematical models can be used, with the point coordinates in each image, to determine the corresponding 3–D ground position. A
single IFSAR image can be used to derive the corresponding 3–D ground position, because the gray value represents the distance from the camera to the ground point.
An accurate image geometry model is more complex than a simple polynomial coordinate transformation, between ground coordinates and image coordinates. This document primarily
considers high accuracy image geometry models for general images. Much simpler geometry models are adequate when low accuracy is sufficient, or for images that have been orthorectified.
Also, much simpler geometry models can provide medium horizontal accuracy for rectified or nearly-vertical images, when the imaged ground is relatively flat. Many different high accuracy
image geometry models can be used, as summarized in Topic Volume 7: The Earth Imagery Case [1].
There are multiple possible geometry models for an image, with different properties. For example, a rigorous geometry model can be accurately adjusted, but has high computation requirements. On
the other hand, a non-rigorous or “approximate” geometry model has lesser computation requirements, but cannot be accurately adjusted. Conversion from a rigorous geometry model to a
corresponding approximate geometry model for the same image is then sometimes required. However, conversion from an approximate geometry model to a rigorous geometry model is
usually not possible or practical.
The term “approximate” image geometry model is used here as a synonym for a “non-rigorous” image geometry model. However, many degrees of accuracy are possible when considering the
position errors introduced by the approximation, from large position errors through no detectable position errors. For example, the “Universal Approximate Image Geometry Model” described in
Section 6.5 of Topic 7 can be fitted to almost all rigorous models with no significant position error. Similarly, the “Grid Interpolation Image Geometry Model” described in Section 6.3 of Topic 7 can
approximate a rigorous model with no significant position errors, if enough grid points are used.
An approximate image geometry model has often been called a “real-time” geometry model, and that is the term now used in Topic Volume 7: The Earth Imagery Case [1]. The need for a fast
“real-time” geometry model is decreasing, as computer speeds increase. However, a fast geometry model is still useful in some situations such as generating complex feature graphics overlaid on an
image. On the other hand, an “approximate” image geometry model can be needed or useful for other purposes, such as ignorance or inaccessibility of a rigorous geometry model.
Note: Although Abstract Specification Topic 7 defines both rigorous and “real-time” or approximate image geometry models, Topic 7 currently includes examples of only approximate
image geometry models. It would be useful to add examples of rigorous image geometry models to Topic 7, but no volunteer has yet proposed a description of any rigorous model.
2.6. Multiple Image Versions
