You are using an outdated browser that does not fully support the intranda viewer.
As a result, some pages may not be displayed correctly.

We recommend you use one of the following browsers:

Full text

New perspectives to save cultural heritage
Altan, M. Orhan

CIP A 2003 XIX th International Symposium, 30 September - 04 October, 2003, Antalya, Turkey
a and ß planes from the origin of the absolute reference
frame, are orthogonal to their corresponding planes (eq. 7).
B'B = A'A = I
c*B = d‘A = 0
Figure 5: Geometric model (partial view)
Now let us suppose to know B and c (i.e. the ß plane), the
position in the 3D space of the eye-point E, the user’s
viewing direction v, the unit vector up of the eye-point and
m, the distance from the eye-point to a plane. Given such
parameters, we can compute the a plane, i.e. parameters A
and d of eq. 5, according to the constraints reported in eq 6,7.
These constraints mean that the two vectors generating the a
plane should be orthonormal and coincident with the columns
of matrix A, and vector d is orthogonal to them. Assuming
the view-plane (a) is orthogonal to unit vector v, it can be
easily demonstrated that matrix A becomes
A = [up I dx]
up x
dx x
up y
dx y
up z
dx z
where dx = up a v. Similarly, vector d can be easily obtained
according to following relationship:
d = (< E, v > -m) • v (9)
where the symbol <,> denotes the scalar product.
At this step we have all elements needed to determine the
projective transformation P, which maps a generic point x’ of
P plane on point x”, lying on the a plane. Let be 5 the bundle
of straight lines passing through the eye-point E,
s—>s = k/ + E; Vk e R 3 , t e R (10)
With some straightforward algebra, we get the equation of
the straight line of s, which passes through point x’:
r = k/ + E ; with k = x'-E (11)
Thus, in order to compute the value t* assumed by parameter
t, when the straight line r intersects the a plane on point x”,
we consider following equality:
k? *+E = x"= Af"+d (12)
After some substitutions and taking into account eq. 7, we get
t* =
Using eq. 10 and 13, the following fundamental relationship
is obtained, which represents the projective transformation
we searched for:
_ F-t'+g
h‘ t’ + q
Indeed, the 2D vector t’ contains the coordinates of a generic
point x’ in a p plane fixed reference frame, while the vector
t”, obtained from t’ by eq. 14 , contains the 2D coordinates of
point x” on a a plane fixed reference frame.
In order to evaluate the performance of the compression
algorithm, a server/client data transmission with the
developed split-browser has been carried out. To this end we
employed simple geometric shapes (polygons) of different
colors, as shown in figure 6. Here view A represents the
scene observed by the user at time n-1, B is the exact view as
computed by the server, to be displayed at time n, according
to user input, while the predicted view is the one obtained by
application of the projective transformation to view A on the
Figure 6: Views A (left) - Predicted views (middle)
Views B (right)
Following criterions were defined to compare the results each
1) Average bit/pixel number of compressed view B. This
parameter defines the number used on average to code
each pixel ov compressed view B. As we dealt with 24
bit RGB images, the resulting value should be lower
than 24 to pass the test.
2) Average bit/pixel number of compressed error-image. It
is similar to the previous parameter, but in this case the
threshold value for the pass/fail test should be lower
than the previous one.
3) Compression ratio. It defines the ratio between the size
(in bytes) of compressed view B and the sum of the size