Collaborators:
Mark Kliger (Ben-Gurion University, Israel), Joseph
Francos (Ben-Gurion University, Israel), Radu Stoica (CWI, Netherlands),
Josiane Zerubia.
Key words:
texture, structure, periodicities, sinusoid, Gaussian
noise, Kullback-Liebler distance.
Resume:
The structure in a texture is important for its
characterization. The 2D Wold decomposition expresses a measure on the
space of real-valued fields on Z2 as a sum of components which
intuitively represent the periodicities, directionalities and noise in the
texture. In this work, we use this idea to define a "distance"
between textures, the application being the retrieval of textured images
from a database.
Given an example of the texture, the parameters of the
periodic component (the number of sinusoids, their amplitudes, their
frequencies) and of the noise component (its covariance) are learned using
a model order estimation algorithm and maximum likelihood.
These parameters express the texture measure in a compact
form. To measure the distance between two textures, we compute the
(symmetrized) Kullback-Liebler distance between the measures, which can be
expressed in a simple form in term of the parameters, and becomes easy to
compute in the Fourier basis. To render the results invariant to
translations and rotations of the texture, the distance is minimized over
the action of the Euclidean group, whose action can be expressed
analytically in terms of the parameters. The relative phases of the
sinusoidal components are preserved when comparing two textures, which
means that structure is captured.
Experiments on synthetic databases (Brodatz, VisTex) are
promising. Current work is focussed on experimenting with a database of
aerial images kindly provided by the IGN (French National Geographic
Institute), and on the use of alternative metrics on the space of
measures. |
