The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
COIL 1(25°) 
COIL2(50° ) 
PCA 
82.58 
74.88 
ICA 
83.88 
76.22 
PCA+ICA 
83.23 
75.55 
IPCA ICA 
87.88 
79.12 
Table III Average success rate for COIL objects database 
3.3. Results with Pose Estimation 
In this experiment, we are interested in modeling the nonlinear 
manifold formed by the object appearance under varying poses. 
The manifold is embedding into the Low-dimensional subspace 
as follows. If the pose angle parameter is a continuous variable, 
the manifold will be a smooth curve. Since it is not possible to 
capture images with the pose angle as a continuous variable, the 
manifold will appear as a piecewise continuous curve, and if the 
pose angle is fine enough, the curve will appear to be smooth. In 
our experiment, we use 15 images for learning, one at every 25 
degrees of rotation. The remaining 57 images are left for 
evaluating the pose.The manifold for the first object is shown in 
Fig 7. The non Gaussian space is constructed by using sampled 
images. The curve appears smooth with the markers showing the 
location of the non Gaussian image in the 3-D non Gaussian 
space with ql, q2, and q3 being the three most dominant non 
Gaussian vectors.. 
Perftxmance Recognition from the matchimg algorithm 
Nth nearest match 
Fig 7 Percentage recognition with nth 
Fig 8 Appearance manifold of the first object 
Nearest match (The pose angle is sampled at every 25° .) 
Also, the recognized curve seems close to the object, since the 
last view of the object is almost the same as the first one. Testing 
points for each of the object manifolds are obtained through the 
projection of the training images onto the non Gaussian 
space .The manifolds are then finely sampled through cubic 
spline interpolation. 
Finding the nearest object manifold as described in the previous 
paragraph provides an estimate of the object pose. In addition to 
the universal non Gaussian space that describes the variation in 
all the images of all the objects of the database, a separate non 
Gaussian space for each object is constructed too. The universal 
non Gaussian space is used for object identification and the 
individual object non Gaussian space is used for pose estimation. 
The manifolds obtained in the object non Gaussian space can be 
parameterized by object pose. 
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