Welcome to ShearLab.org!
Applied harmonic analysts introduced in recent years several
approaches for directional representations of image data, each one
with the intent of efficiently representing highly anisotropic image
features. Examples include curvelets, contourlets, and shearlets.
These proposals are inspired by elegant results in theoretical
harmonic analysis, which study functions defined on the continuum
plane (i.e. not digital images) and address problems of efficiently
representing certain types of functions and operators. One set of
inspiring results concerns the possibility of highly compressed
representation of `cartoon' images, i.e. functions which are
piecewise smooth with singularities along smooth curves. Another set
of results concerns the possibility of a highly compressed
representation of wave propagation operators. In `continuum theory',
anisotropic directional transforms can significantly outperform
wavelets in important ways.
Accordingly, one hopes that a digital implementation
of such ideas would also deliver performance benefits
over wavelet algorithms in real-world settings.
In many cases, however, at the time this webpage was set-up, there were no publicly available implementations
of such ideas, or the available implementations were only sketchily tested
or the available implementations were only vaguely related to the continuum transforms
they are reputed to represent. Accordingly, we had not yet seen a serious exploration
of the potential benefit of such transforms, carefully comparing the
expected benefits with those delivered by specific implementations.
We aim at providing both:
- A rationally designed shearlet transform implementation.
- An comprehensive framework for quantifying performance of
parabolic scaling algorithms.
Our ultimate goal with this webpage is public release of a reproducibly-tested
rationally-designed implementation.
We invite you explore this website, which provides you with information about
our philosophy on a rational design for software development, the digital shearlet transform we developed,
and the framework for quantitative performance measures we introduced, publications about these topics,
downloadable software, and much more!
We also welcome any comment or suggestion!
The research presented at this website has been sponsored by German Research Foundation (DFG) Grants
KU 1446/8, KU 1446/13, and KU 1446/14.
© Gitta Kutyniok 2010