| dc.description.abstract | The windowed scattering transform is an operator that is invariant to small translations,
deformations and rotations. The transform can be used in conjunction
with a classification algorithm to perform image recognition. This thesis consists
of one theoretical part and one numerical part. In the theoretical part the underlying
theory of the windowed scattering transform, namely Fourier analysis and
wavelets, is briefly introduced. Then, the construction of the windowed scattering
transform and its numerical approximation is explained in detail. The numerical
part consists of examples showcasing the properties of the transform, and
the transform applied in image recognition on a dataset of handwritten letters.
An error rate of 10.2% was achieved, using the k-nearest neighbors algorithm for
classification. The error rate is high compared to other more sophisticated image
recognition procedures. Most of the errors stem from inaccurate classification on
classes with few samples, and from incorrect classifications on letters that are similar
in shape. Some suggestions are given on how the error rates could be improved
in further work. | |
