# Bendlets: A second-order shearlet transform with bent elements

@article{Lessig2019BendletsAS, title={Bendlets: A second-order shearlet transform with bent elements}, author={Christian Lessig and Philipp Christian Petersen and Martin Schafer}, journal={Applied and Computational Harmonic Analysis}, year={2019} }

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…

## 13 Citations

Higher order analysis of the geometry of singularities using the Taylorlet transform

- Mathematics, Computer ScienceAdv. Comput. Math.
- 2019

It is shown that the Taylorlet transform exhibits different decay rates for decreasing scales depending on the choice of the higher order shearing variables, enabling a faster detection of the geometric information of singularities in terms of the decay rate with respect to the dilation parameter.

Efficient representation of spatio-temporal data using cylindrical shearlets

- Mathematics
- 2021

Efficient representations of multivariate functions are critical for the design of state-of-the-art methods of data restoration and feature extraction. In this work, we consider the representation of…

The Role of $\alpha$-Scaling for Cartoon Approximation

- Mathematics
- 2016

The class of cartoon-like functions, classicly defined as piecewise C functions consisting of smooth regions separated by C discontinuity curves, is a well-established model for image data. The quest…

Mini-Course on Applied Harmonic Analysis

- 2019

This mini-course provides an introduction to applied harmonic analysis and its applications in the numerical analysis of partial differential equations. The standard Fourier transform exhibits…

The Role of $\alpha$-Scaling for Cartoon Approximation

- Mathematics
- 2016

The class of cartoon-like functions, classicly defined as piecewise $C^2$ functions consisting of smooth regions separated by $C^2$ discontinuity curves, is a well-established model for image data.…

TEXT LOCALIZATION IN SCENE IMAGES BY BENDELET TRANSFORM

- Computer Science
- 2019

Results show the robustness of the text localization system by successfully locating the text region in the scene images with different background and non-uniform text sizes.

A three-stage shearlet-based algorithm for vessel segmentation in medical imaging

- Computer SciencePattern Anal. Appl.
- 2021

The previous version of a method that has been used in binary segmentation for magnetic resonance angiography images (MRI) is improved and a three-stage binary image segmentation algorithm for vessel segmentation in MRI images is introduced.

Criteria for generalized translation-invariant frames

- Mathematics
- 2019

This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of…

EFFICIENT MEDICAL IMAGE COMPRESSION BASED ON INTEGER WAVELET TRANSFORM

- Computer Science2020 Sixth International Conference on Bio Signals, Images, and Instrumentation (ICBSII)
- 2020

In this work, a suitable image codec is proposed for medical images and the Lifting Wavelet Transform (LWT) is used in proposed system to overcome limitation of DWT.

An Efficient Skin Cancer Diagnostic System Using Bendlet Transform and Support Vector Machine.

- Medicine, Computer ScienceAnais da Academia Brasileira de Ciencias
- 2020

The performance of the SCC system based on Bendlet is superior to other image representation systems such as Wavelets, Curvelets, Contourlets and Shearlets.

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