5.6 Edge Orientation Coherence 
The basic notion governing edge orientation coherence ap- 
proaches is that neighbouring pixels positioned on an edge will 
approximately show equal orientation (cf. Gregson, 1993). 
Therefore one may examine the gradient directions of the 
pixels. This can be done along the following line: 
1. Compute the mean and the variance of the directions 
of the gradients in a local neighbourhood (e.g. a 3 x 3 
window) of which the magnitude is above a predefined 
threshold; 
2. Decide whether the orientations of all gradients point 
sufficiently well into the same direction on basis of the 
computed variance and an a priori variance measure 
derived from the edge orientation bias introduced by 
the detector and a noise estimate, using and F-test. 
3. If the computed variance indicates that all orientations 
are the same, assign to the central pixel the mean of 
the directions of the gradients. 
It is possible to refine the above process, by removing the 
outliers step by step and by examining whether the remain- 
ing orientations point in the same direction and are spatial 
connected in such a way that they form likely an edge. 
6 Discussion 
V The apparently simple problem of locating edges in an 
image has proved to be very difficult and is still poorly under- 
stood. There probably exists virtually no mathematical ap- 
proach or trick that has been remained untouched to tackle 
the boundary delineation problem, which is an indication of 
its intricacy. Optimal methods based on thorough theoret- 
ical considerations reveal to produce poor results on aerial 
and satellite images, due to the fact that the underlying as- 
sumptions about the data are often violated. In particular 
the design of many of the (optimal) edge detection schemes 
are based on assumptions, which are unrealistic for images of 
non-restricted scenes, including: (1) the image contains only 
ideal step edges embedded in zero-mean Gaussian distributed 
noise, (2) the image may be described as an analytical func- 
tion, (3) the only intensity changes are locally straight step 
edges, (4) intensity varies linearly in the direction perpendic- 
ular to the edge, (5) edges are broadly spaced, and (6) abrupt 
intensity changes in the image correspond to meaningful ob- 
ject boundaries in the scene. One of the main reasons for fail- 
ing is that local edge detectors can not discriminate among 
the many types of features that may be present in the image. 
Even in noisy and texture areas, high responses will occur. 
V The above weaknesses of edge detection schemes com- 
bined with the fact that the boundary delineation problem 
is task-domain dependent results in the inevitable conclusion 
that the exploration of specific geometric object information 
is indispensable to arrive at reliable boundary outlinings. This 
conclusion introduces questions like: how to obtain adequate 
descriptions of specific geometric constraints?, and how to 
match these constraints with the image function? 
V. The main reasons why so many edge detection schemes 
could emerge, are: (1) the broad variety of mathematical 
principles and tricks that can be used to base an edge detector 
on, and (2) existing techniques are often not suited for the 
particular task the researcher has at hand, forcing to search 
for other methods resulting in a new approach. 
440 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
V/ It is remarkable that the performance of the many local 
edge detectors, whether they are based on heuristic grounds 
or on rigorous mathematical considerations, does not exhibit 
expressive differences. The choice of the type of preprocess- 
ing (smoothing) and the type of postprocessing, in particular 
context incorporation, reveals to be actually more important 
for the final result than the choice of a particular local edge 
detector. 
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