frequency phenomena and their interferences have been
removed. Subsequently, these features are traced back to the
finer levels, where their precise spatial positions are
determined, free of the positional distortions which are
introduced in coarser levels by the convolution with the
scale generating kernels. This analysis of signals allows the
identification and classification of major signal trends, thus
making explicit the information which is inherently
contained in the signal values [Lu & Jain, 1992].
3. SCALE VARIATIONS OF CONJUGATE
FEATURES WITHIN A STEREOPAIR
The scale differences between conjugate features in a pair of
spatially overlapping images can be:
e one-dimensional, associated with the foreshortening
problem, and
e two-dimensional, associated with images which differ
substantially in their orientation parameters.
Problems of the first type are highly localized and object-
dependent. They occur only for certain features within a pair
of images of otherwise similar scales, and will be the main
focus of this paper. The extension of the presented
methodology to two-dimensional is quite simple when
taking into account the separability of two-dimensional
scale generating kernels.
left image right image
Fig. 2: Scale differences of conjugate features due to the
foreshortening problem.
Figure 2 shows the foreshortening problem for a pair of
photographs and a feature in the object space (ramp F at the
center) for which the angle between the vertical and the
surface normal is substantially different than 0. As it can
easily be observed, the feature’s inclination causes its image
fj in the left photo to be substantially larger than its image
f, in the right photo. In this manner, foreshortening causes
the images of certain objects to be recorded at different
scales in two stereomates. The geometric difference is
accompanied by differences in radiometric scales.
10
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Assuming error-free gray value registration, the recorded
gray values are quantized expressions of the amount of
energy incident to the light sensitive material at the
corresponding sensor location, expressed by image
irradiance [Wrobel, 1991]. According to the cos* law of
irradiance, image irradiance is proportional to a combined
measure of object space surface reflectance characteristics
and illumination conditions [Horn, 1986; Alvertos et al.,
1989].
left image right image
Fig. 3: Objel differences in conjugate feature registration
in a stereopair.
The gray value recorded in a pixel is essentially expressing
the irradiance of the object area which is the projection of
this pixel in object space, hereinafter referred to as object
equivalent pixel, or in short objel. In other words, the objel
expresses the object space area which is imaged in a single
digital image pixel. While all pixels of a sensor have the
same size, their object equivalents vary according to the
shape variations of the object space, as shown in Fig. 3.
The averaging operation associated with sensor charging
and subsequent gray value assignment can be considered an
operation equivalent to scale space generation. A series of
images of an object space scene from various, constantly
increasing heights, is actually forming a scale space family
of the radiometric content of this scene. Images from higher
exposure stations correspond to larger objel sizes and,
consequently coarser scale levels than images captured from
exposure stations closer to the actual object space.
Conjugate pixel groups are actually scale space
representations of their equivalent object space area, with
image orientation (and by this we refer to both rotations and
exposure station position), object space shapes, and sensor
characteristics being the parameters defining the scale
generation process. In a stereopair, the same sensor is used
and, considering the excellent performance of metric quality
cameras, it can be assumed that the effects of sensor
characteristics during image formation are similar for
conjugate features in stereopairs. The remaining combined
effect of exposure orientation and terrain shape make image
capturing through central projection unique in terms of scale
space generation: scale might actually vary within an image,
with various
terrain scale :
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