15862 Final Project - Object Modeling with Layers.
-Charudatta Phatak
Link
to the paper (pdf)
Link to presentation (ppt)
Section 1: Layered PCA model
Regular appearance models
build a statistical model of an object describing its shape and texture.
However when we have objects in which the certain landmark/features are
completely absent, it poses a problem for constructing a model. Eg. Cars.
Figure 1. Features like license plate are completely absent
in first 2 cars. Fog lights are absent in the first car but present in the
second car.
So we separate the objects
into different layers corresponding to each feature. We then construct the
model for each layer. This way we can account for the absence of a layer by
putting weights.
Figure 2. Image showing
different layers.
(a)
(b)
Figure 3. (a) Novel car image
constructed by random sampling through the layered PCA model. (b) Similar image
constructed using regular model.
(a)
(b)
Figure 4. (a) Original car.
(b) Adding a license plate to the car.
(a)
(b)
Figure 5. (a) Original Car.
(b) Replacing the grill of the car.
Section 2: LLE model
PCA model is based on the least
square method which minimizes the cost of reconstruction. We can improve this
by using LLE model, which uses only nearest neighbor information for
reconstruction of images. We calculate the reconstruction weights and then
compute the lower dimensional space coordinates from the weights.
Figure 6. Algorithm for LLE.
(a)
(b)
Figure 7. Comparison of LLE with
PCA. The images on top show the points plotted using first 2 coordinates of PCA
and the bottom two images for LLE. (a) Comparison shown by Roweis et al. (b)
Similar comparison for car data set.