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We introduce bendlets, a shearlet-like system that is based on anisotropicscaling, 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 inthis article, the decay rates of the associated transform enable the precisecharacterization of location, orientation and curvature of discontinuities inpiecewise constant images. These results yield an improvement over existingdirectional representation systems where curvature only controls the constantof the decay rate of the transform. We also detail the construction of shearletsystems of arbitrary order. A practical implementation of bendlets is providedas an extension of the ShearLab toolbox, which we use to verify our theoreticalclassification results.

Bendlets: A Second-Order Shearlet Transform with Bent Elements