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3D coordinates

Using 3D Coordinates

A rectifier like ASRix is, like a photograph, a 2 dimensional concept. We are taking a 2D image and transforming it in a 2D plane to come up with another 2D image that better represents a 2D surface of an object.

ASRix supports 3 dimensional coordinates for three reasons:

  1. In many situations the measurements we have of a surface are in 3D, usually coming
  2. from a total station or similar survey instrument.
  3. By knowing the location of the image in 3D space we can make a 2.5D photo mosaic
  4. using AutoCAD
  5. By having the image tied to the location of the artifact in 3D space the images (both
  6. source and rectified) along with their point file become a document that can be used to monitor change.
In order to use 3D coordinates in a 2D application a conversion must take place where each 3D point is mapped onto a plane. In ASRix that plane is defined by you, by selecting three of the points you are using for rectification as the axes of a 2D coordinate system.

You will most often select which points you want to use in the Mapping Points window, though they can be also be changed in the Pixel Mapping dialogue box with the Status variable though this option is best reserved for experienced users because you can't see what is happening.

In a 3D project (or in a 2D project where Axes have been specifically enabled) you will see, to the left of the point numbers in the Mapping Points window three letters indicating the points to be used for the Origin, Horizontal axis and Vertical axis of the coordinate system you want for the rectified image. By default the first three points are assigned the O H V (in that order) but you can change this by clicking one of these letters, to turn it off, and then selecting one of the other points by clicking in the space to its left.

If a point's status is changed the values in the Points Window under 2D-X, 2D-Y and Z-deviation will change to reflect the new coordinate system and if not all of the axis points have been defined these columns will be blank.

On a perfectly flat surface with perfect measurements the Z-deviation values would all be zero but, of course this will never be the case with real measurements. Still they should be close to zero and any point that has a much value too far from zero (either positive or negative) will cause erroneous results and should be examined.

The only reasons for a large deviation are

1. a faulty measurement
2. a measurement to a point not on the plane defined by your O H V.

Your only protection from either is redundancy so it is a good idea to have a few more than the minimum 4 points for each surface or be prepared to return to the site.

The sample image cube is a good place to experiment with the 3D aspect of ASRix.

This example shows 6 points, one of which (# 06) is not on the same plane as the others. You can follow this example by loading the cube image from the Samples and using the Alternate Point File feature to load the .PTS file cube-3d6.PTS

The Points Window below shows the World Coordinate and 2D mapping values for this point file. Note the Z-deviation value for point 06. This is clearly an error and will cause a significant distortion when rectified. The solution in this case is to disable and eventually delete this point. However, if the point not on the plane happens to be one of the axis points it becomes much more difficult to track down.

Of course in real life the error would not be so great and the numbers not so round so you would have to examine the deviation values more carefully.

If one of the points deviates substantially from the plane the point should either be re-measured or deleted but if several points deviate from the rectification plane the problem is probably with one of the points defining the coordinate system. The Points Window below shows what will happen if point 06 becomes one of the axis points.

Point 06 itself, because it helps define the rectification plane, shows a Z-deviation value of 0.000, as do the other axis points, but the other points all show significant deviation.

In this case the solution is to change the O H Vs one at a time and watch the Z-deviation for the case that shows the minimum deviation for the most points.

When manipulating these points it is important to remember that the definition of the coordinate system is also responsible for the orientation of the rectified image. The Origin will be near the lower left corner, the Horizontal axis point will be to the right of that and the Vertical axis will be above the line between the other two. Therefore switching O and H will give a vertically mirrored image and switching O and V will mirror it horizontally and image rotation will be affected if your points are not parallel to your desired base line. These parameters can all be adjusted using the rotation options in the output parameters dialogue box or by establishing a base line by pressing Ctrl or using the right click menu in the Rectified Image Window.

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Generated by: CART
(Thu Sep 20 17:56:24 2007 )