  Subspace learning is an important problem, which has many applications in
image and video processing. It can be used to find a low-dimensional
representation of signals and images. But in many applications, the desired
signal is heavily distorted by outliers and noise, which negatively affect the
learned subspace. In this work, we present a novel algorithm for learning a
subspace for signal representation, in the presence of structured outliers and
noise. The proposed algorithm tries to jointly detect the outliers and learn
the subspace for images. We present an alternating optimization algorithm for
solving this problem, which iterates between learning the subspace and finding
the outliers. This algorithm has been trained on a large number of image
patches, and the learned subspace is used for image segmentation, and is shown
to achieve better segmentation results than prior methods, including least
absolute deviation fitting, k-means clustering based segmentation in DjVu, and
shape primitive extraction and coding algorithm.
