Graphics Reference
In-Depth Information
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Figure 9.10
Construction of the cell images for a single surface patch. The appearance of the patch is
extracted from all the images, then warped to a right triangle. The sequence of cell images,
which are tiled into the lower image, represents the appearance of the cell for each rotation
angle. The tiled image is purely for illustration and has no relation to the response matrix.
(After images courtesy of Ko Nishino.)
as described below. The method uses a normalized luminance/chrominance space
instead of RGB colors.
The compression process works as follows. First, the values of each cell im-
age are flattened (aligned vertically) into a column vector, then these vectors are
placed into the columns of a matrix. As in the general response matrix described
above, each row of this matrix therefore contains the variation in a particular pixel
with view direction; each column contains the spatial variation over the patch for
a particular view direction. Next, the average value of the matrix elements is
subtracted from each matrix element. This way, the average value of the matrix
elements is zero, and each matrix element contains what is called the
deviation
from the mean
. PCA is then applied to the resulting cell matrix. A small num-
ber of basis eigenvectors are selected to serve as the approximate basis for the
eigenspace; these are the
eigen-texture
of the cell. The remaining eigenvectors are
projected onto these basis vectors and the resulting linear coefficients (weights)
are recorded in place of the vectors themselves. By virtue of the additivity of light,
the synthesis of an image from an arbitrary rotation angle can be accomplished by
