Image
and Video
Processing
With
the enormous growth
of visual information in digital form, the interest in image and video
processing applications is increasing dramatically. At the heart of
many image processing tasks, there is an efficient
image representation that can capture significant information of an
image in a compact form. Over the last decade or so, the wavelet
transform has emerged as the dominating tool in image processing. The
success of the wavelet transform is mainly due to its ability to
characterize certain classes of signals with few transform
coefficients. In particular, wavelets as timefrequency localized bases
are particularly suited to represent one dimensional (1D) piecewise
smooth functions.
In two dimensions (2D), the situation is much more
open. Despite their widespread success in image processing, wavelets
are not adequate at representing images. In images,
discontinuities are straight line or smooth curves. The 2D
wavelet transform is a separable transform given by the tensorproduct
of two 1D wavelets along the horizontal and vertical directions. For
this reason, this separable transform is good at isolating horizontal
and vertical edges, but it is not adequate at treating more complex
discontinuities. This indicates that more powerful image
representations are needed.
We are investigating the use of quadtree decompositions and of
directional wavelets to overcome the limitations of the separable
wavelet transform.
Main
Publications:
PhD
Students: Pancham Shukla, Rahul Shukla (at EPFL)
and Vladan Velisavlievic (at EPFL)
Collaborations and
Interactions: M. Vetterli (EPFL), M.
Do (UIUC).
