continuation of linear features between neighbour-
ing parallel lines, the reliability can be
increased still more [Lo,1989]. The extracted
corresponding linear features pairs can be used to
generate coarse DEM, the major requirement of
generating coarse DEM with high reliability is
fulfilled.
3.3 Refinement of Coarse DEM Data by Object Space
Least Squares Matching
3.3.1 The Illumination and Reflection Model for
facet stereo matching There are three major
phenomena of the reflection : Ambient reflection,
Diffuse (Lambertian) reflection and Specular
(Mirror) reflection. It describes the relation-
ship of reflected radiance of a small facet of the
surface, the specific viewing direction, the com-
plex illumination of the scene and light reflect-
ing properties of the material. (Weisensee,1988)
proposed three models of light reflection which
can be used for Object Space Least Squares Match-
ing, they are derived from general model as fol-
lows:
La Lp Pa lm GI: B.) dw, (SR * d* R4) a
Lp : the reflected radiance cause by incident
radiance of illumination
Lyar Ra? the ambient component from half space L,,
and the semi-spatial reflectance R,
E,Ly, : N light sources having irradiance L;,
N : the surface normal
Ba : the direction to light source n
dw, : the apparent solid angle of incident
radiance from a particular light source
R,,d : the diffuse reflectance R, and its fraction
of proportion for diffuse reflectance
RS : the specular reflectance R, and its frac-
tion of proportion for specular
reflectance
In our case, we can assume that there is only one
light source (n=1,the sun) to be considered. The
amount of light reflection which independently
with the viewing direction is :
Log ® Ly,°R, * Pp NB )°dw,°d°Ry
Rd (2)
the specular Component which is rare exist and can
be omitted is:
La, 7 bp (NB ):dwp S: R,
Rs (3)
the relationship between recorded intensity Gi of
discrete pixel i by the sensor and the reflected
radiance from the terrain surface can be a linear
transformation:
G. =
i a + b° Led
(4)
if the terrain surface is perfect ambient reflec-
tion, the first reflection model can be:
6," 8, * 5; b (5)
D, is the reflected radiance of facet i, if the
terrain surface is assumed as perfect Lambertian
reflectance, the second model is:
G,= a;t b;:cos(N:B): D; = a+ b;:cos6,: Di (6)
the third model:
G, = a; + b. . D, (7)
results from applying the transformation (4) to
facets instead of windows. It means a. is still
valid for window j, the b, applies to bilinear
height/reflection facet k respectively.
3.3.2 The principle of Object Space Least
Squares Matching Back mapping of image data into
object space to get object reflectance D(x,y)
(image inversion) by referring the object surface
Z(x,y) which is approximate at the beginning, and
perform matching on the object surface. It simul-
taneously determines two functions in the object
space: the terrain relief Z(x,y) and the terrain
reflectance D(x,y) with Least Squares Adjustment
135
iteratively [Wrobel,1988] [Helava,1988] [Ebner &
Heipke,1988] [Heipke,1990]. By this way, the
digital image matching, DEM generation and ortho-
photo computation have been combined into one
approach.
The main principle of Object Space Least Squares
Matching is as follows:
The basic Observation Equation of every pixel
within the patch for matching by the Least Squares
Adjustment is:
= 5
<
*^cos0 - D( Z, K, L, À) (8)
noise or residual error in intensity
the unknown intensity value assigned to
one groundel
the angle between the surface normal and
the direction of sun
back mapping the image intensity value of
corresponding pixel to the groundel.
the heights of N x M grid points (DEM) to
represent the terrain surface Z(X,Y) which
can offer the height in any position by
bilinear interpolation.
orientation parameters of the sensor
illumination model
object reflectance model
a) The influence of L & R can be simplified by
local linear radiometric correction with offset 51
and gain 82 (But not for close range photogramme-
try and large scale photo). Therefore, (8) can
be:
© <<
m
tC
m
«xpo
v = D * cos0 - á1 - 82 * D(Z,Ä) (9)
For the patch of first image, $1 and 52 can be
assumed as constant, they are unknowns for the
patch of second, third and further images.
Transfer in A.T., Í and A are
unknowns also, expanding the nonlinear part
(32 * D(É,Á)) of (9) to linear increments from
approximate values: ( $1 , 52), = ( O ,1 ), we
obtain:
b) For Point
B * cos0 - ái - $2, * D(Z,A), - 82 *
(10)
[(8D/8£), af -(8D/GÁ), a] -?p(£,Kj, a&2
v =
coefficients indexed by o are calculated with
estimated values which will be updated during
iteration. Expanding the coefficient (0D/0£Í),
(89D/83Á), of the design matrix:
The
the
the
and
(09D/8f), - (0D/Ox .Ox/0Í) + (80D/Oy .0y/05), (11)
(0D/8Á), - (9D/8x .Ox/0K),* (0D/Oy -9y/8K), (12)
Because O0D/Ox and 8D/8y represent the gradient of
the intensity, it can be used for a quality esti-
mation (selection), and provide the different
weights accordingly in Least Squares Adjustment.
c) In case of DEM generation after A.T.. The
orientation parameters of sensor A are known
already. Therefore, the observation equation for
each pixel within the matching patch is:
B * cos0 - 81 - 82, * D(É,A), - 82, *
(13)
(@n/a%), a - p(£,R), p82
v =
If we want to obtain DEM Z(X,Y) only, the unknown
D can be eliminated (Reduced Normal Equation)
during the inversion of the normal equation to
save calculation time.
3.3.3 The characteristics of Object Space Least
Squares Matching
a) We perform the matching in Object Space instead
of in Image Space, because the disadvantage of
matching in image space would be that the multi
view image of the same object would have different
intensity or shape caused by different relief
displacement / tilt displacement / different
illumination situation / different reflection
effects from different positions of the sensor
relating to different relief of object etc.,
resulting in matching failure or poor accuracy.
b) High accuracy can be achieved by using the
Minimum Cost Matching which is based on the Theory
of Minimum Cost Sequence of Error Transformation.
This method may select the Minimum Euclidean
