Graphics Reference
In-Depth Information
k
eigen-textures
Recovered image
a
M,0
×
+
a
M,1
×
+
a
M,2
×
=
……
Linear approximation
Figure 9.12
Synthesis of an image from a linear combination of basis vectors (eigen-textures). Differ-
ent image cells have different eigen-textures. (After images courtesy of Ko Nishino.)
numeric statistical strength than specular reflection. Consequently, the selected
eigen-textures tend to overemphasize diffuse reflection and can miss specular
highlights. This is particularly true if too few basis basis vectors are selected:
although this improves the compression ratio, other radiometric phenomena such
as specular reflection may not be captured accurately. The authors of the eigen-
textures paper got around this by increasing the number of basis vectors for cell
image sequences that include specular reflection. However, specular reflection is
still problematic for the method, because it is a highly nonlinear process and is
therefore difficult to approximate as a linear subspace.
9.3.4 Concept of Local PCA
Natural objects, geometry, functions, responses, etc., are seldom linear; however,
linear approximates often work well for local representation. For example, a plane
is an absurdly poor approximation to a sphere on the global scale, but at small
scale, a tangent plane is a very good approximation (see
Figure 9.13(a)
)
. An entire
sphere can be covered with a set of local tangent-plane approximations, although
it is difficult to get the associated planar coordinates to line up between neighbor-
ing tangent planes. This is a very general concept: fundamentally, derivatives and
differentials are locally linear approximations. As noted above, a problem with
interpolating specular reflection comes from the nonlinearity of specular lobes. In
terms of PCA, the problem is that the response matrix is difficult to approximate
with a linear subspace. One way around this is to split the response matrix into
separate sections and perform PCA separately on each. This approach is called
local PCA
,or
clustered PCA
(CPCA).
