  We introduce bendlets, a shearlet-like system that is based on anisotropic
scaling, translation, shearing, and bending of a compactly supported generator.
With shearing being linear and bending quadratic in spatial coordinates,
bendlets provide what we term a second-order shearlet system. As we show in
this article, the decay rates of the associated transform enable the precise
characterization of location, orientation and curvature of discontinuities in
piecewise constant images. These results yield an improvement over existing
directional representation systems where curvature only controls the constant
of the decay rate of the transform. We also detail the construction of shearlet
systems of arbitrary order. A practical implementation of bendlets is provided
as an extension of the ShearLab toolbox, which we use to verify our theoretical
classification results.
