Graphics Reference
In-Depth Information
begin
for i=0 to (KN-1)do
if(T(j)
Tau(i))then MU=i;
end
recursive procedure subdiv(P,K,Tau,T,RP1,I,J,PP);
/* PP is output and equals D [ RP 1]
ij
*/
begin
r=RP1-1;
if (r > 0) then begin
PP2=0;
PP1=0;
P1=T(J+K-r)-Tau(I);
P2=Tau(I+K-r)-T(J+K-r);
if ( P 1 <> 0) subdiv(P,K,Tau,T,r,I,J,PP1);
if ( P 2 <> 0) subdiv(P,K,Tau,T,r,I-1,J,PP2);
PP=(P1*PP1+P2*PP2)/(P1+p2);
end
else PP=P(I);
end
An iterative form for subdiv can also be found in [41].
7.4 Smoothing Discrete Splines and Vision
To recover the shape of a 3d surface from the reflectance map is an important
problem in shape from shading. Reflectance map, developed by Horn [77],
relates image brightness to surface orientation. Reflectance map, therefore,
is a powerful concept behind the recovery of the shape of a physical surface
from its image brightness values and is a major starting point. Ikeuchi and
Horn [81] initiated numerical shape from shading. David Lee [101] followed
the model of Ikeuchi and Horn [81] and constructed a smoothing spline as
a solution using regularization. He reduces the problem to solving a large
system of non-linear equations for a discrete spline. For the diculty of the
direct method, he provided an iterative method. The algorithm converges for
a range of the regularization parameter and the discrete smoothing spline is
unique for that range. It has been seen that even provably convergent iterative
schemes are dicult to devise [81, 78].
7.5 Occluding Boundaries and Shape from Shading
Occluding boundary is important and informative in the shape from shading
problem because for all points on such a boundary one can compute surface
orientations directly from image brightness values. Suppose the image domain
D of an object is connected and compact. Let ∂D be the boundary and D i
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