 |
Select Interface Language:
 
|
There are currently
18 visitor(s) that are online.
|
| |
| Project title: | Studienarbeit: Analyzing Riesz Transforms of Arbitrary Order in Radon Space | | Participants: | Fleischmann, O., Wietzke, L. |
Creating a model for image analysis which extends the well known analytic signal from
one-dimensional case to two dimensions is still a challenging task. In order to create a
model which is able to split the signal into independent properties, also known as split
of identity, and which is invariant under operations such as rotation, a lot of approaches
have been made. Up to now they all only cover special type of signals or lack some of
the features mentioned above. M. Felsberg introduced the monogenic signal in which
allows an orthogonal decomposition of intrinsically one dimensional signals into local
amplitude, local phase and local orientation. It uses the Riesz transform as a generalization
of the Hilbert transform in two dimensions. Although intrinsically one-dimensional
signals can completely be described in a rotation invariant manner, the monogenic signal
is not able to describe intrinsically two dimensional signals.
Recently an extension of the monogenic signal has been introduced by D. Zang. The
monogenic curvature tensor describes two-dimensional signals in a dierential geometric
setting. Signals are interpreted as surfaces in Monge patch form to extract curvature
information. The mean and gaussian curvature characterize the surface and therefore
give rise to the intrinsic dimension of the signal. Using the monogenic curvature tensor,
a way to determine the main orientation and the local phase of intrinsically one- and
special two-dimensional signals has been shown.
In this work we will pick up the idea to construct a tensor pair which is able to describe
a signal. Instead of using dierential geometry we will use the fact, that second order
derivatives can be expressed in terms of the Riesz transform which we will express in
terms of the Radon transform. The Radon transform provides a descriptive way to represent
the Riesz transform. It is even possible to visually follow the steps involved in the
Riesz transform. Properties of the Radon transform will enable us to determine the main
orientation and phase of intrinsically one-dimensional signals as well as the main orientation
and the apex angle of intrinsically two-dimensional signals which are superpositions
of two one-dimensional signals. Assuming the main orientation of the single intrinsically
one-dimensional signals to be known, we will even be able to determine the local phases
of the two signals. It will turn out that our tensor pair is exactly the monogenic curvature
tensor and that the main orientation proposed in is equivalent to the main orientation
we determined. |
|
| | |
|
