Verifying
the Solution

In general, there will be several sets of corresponding control points; the task is not to just calculate the inversion -- it is also necessary to select the correct one. As a first stage those answers which are not physically possible can be eliminated. For example if the triple being used is not visible in the transformed model. This test could be achieved using complete hidden line removal but to avoid the computational expense a simpler test may be applied to see if any of the planes adjoining the central point of a point triple formed by two coterminating lines are visible. If this is not the case the solution is not considered any further. Similarly an extra condition which can be imposed is that the overall size of the object, which can be estimated from the projection of its bounding box, must fall within limits. For example it might be known that the object being sought is not twice the size of the image or just a few pixels across. The overall method has no problems in dealing with these cases but such a condition can usually be imposed. The next stage, if these tests are passed, is to carry out the transformation on the model and compare the predicted scene with the two dimensional image data. At the simplest level this is a counting of the number of coincidences which occur between the predicted and actual points.

As an alternative a Hough transform could be applied to the hypothetical transformations. Each time a transform is estimated a set of six values are produced characterising the transformation. These values can be collected and the value which occurs most often should correspond to highest number matches and hence the true location of the object. For, whenever any triple within the object is matched to its true triple in the object, roughly the same set of parameters should result. After each estimation of a transform, a counter is incremented for a set of parameters and also a record stored of the triple to triple pairing and the parameters produced. After accumulation, the Hough space is examined and the few largest clusters chosen to see what triples contributed -- those matching are then checked to remove inconsistencies.

Figure 8 shows the complete processing of an image to recognise and locate the object.


[ Solving for perspective inversion | References ]

Comments to: Sarah Price at ICBL.