The purpose of this thesis was to develop a 3-dimensional (3D) reconstruction algorithm
which can more accurately generate a 3D shape model of a human face from a single
2-dimensional (2D) image. Like most present day approaches to building 3D human
facial models, the proposed algorithm stemmed from the statistical approach pioneered
by Blanz and Vetter [13], who used a morphable 3D model which was con gured to
match a 2D image.
With current 3D shape model reconstruction using statistical modelling, the accuracy
of the reconstruction is highly dependent on the nature of the source data and the behaviour
of the feature extraction algorithm. The most commonly applied representation
algorithm for 3D modelling is principal component analysis (PCA). However, there are
inherent problems in using principal components as a feature space. Firstly, the principal
components only represent the directions of the maximum variance in the source
data and therefore, may be better at representing general trends rather than subtle
individual shape di erences. Secondly, the principal components in PCA are orthogonal,
hence they are better suited for representing multivariate, Gaussian source data.
Although PCA usually provides a good basis for reconstruction, it is not necessarily
more accurate when analysing data that provides low variance directions.
The reconstruction approach proposed in this thesis used two sets of information
computed by both, PCA and independent component analysis (ICA) to recover the
geometric information from a single image. The reconstruction was conducted in PCA
and ICA feature spaces in succession. This method allowed both the global trends and
the local subtle features to be preserved and well represented.
To reinforce the robustness of the algorithm, kernel canonical correlation analysis(
KCCA) was applied to determine the relationship between texture information and
depth. A quantitative analysis was then applied to test the performance of the approach.
The results showed that the proposed algorithm generated more accurate results than
reconstructing 3D models with PCA or ICA alone or in succession.
However, by examining the performance of the proposed hybrid reconstruction algorithm,
we have found that the Z-dimensional shape error was signi cantly larger than the other two dimensions. This was due to the limited shape information contained
within the 2D image. Subsequently, we used local binary patterns (LBP) to encode the
texture information of the 2D image. Based on the LBP codes and their corresponding
depth values to the shape models used in the training shape model database, we used
kernel canonical analysis (KCCA) to train a depth value predictor.
We then added the depth value predictor into the hybrid shape reconstruction algorithm
to predict the depth values of the landmarks of the objective face. The depth
values and the existing 2D information of the landmarks from the input image were
then used to generate the nal 3D shape reconstruction.
The enhanced shape reconstruction algorithm based on the above methodology was
then tested using the Binghamton Human Face Database [147]. The results showed
that the enhanced shape reconstruction algorithm greatly reduced the Z-dimensional
shape error while maintaining the same accuracy in the other two dimensions. Thus the
overall accuracy of the reconstruction operation has been signi cantly improved from
the hybrid shape reconstruction algorithm.