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AG Computational Data Analysis


Complex Shearlet-Based Ridge and Edge Measure (CoShREM) Toolbox
Haar Wavelet-Based Perceptual Similarity Index (HaarPSI)


Complex Shearlet-Based Ridge and Edge Measure (CoShREM) Toolbox

A MATLAB toolbox providing methods for the detection and analysis of edges and ridges in 2D images via the complex shearlet-based edge and ridge measures.



  1. R. Reisenhofer, J. Kiefer and E. J. King
    Shearlet-Based Detection of Flame Fronts (PDF)
    Experiments in Fluids, vol. 57(3), 41:1-41:14, 2016.
  2. E. J. King, R. Reisenhofer, J. Kiefer, W.-Q Lim, Z. Li and G. Heygster
    Shearlet-Based Edge Detection: Flame Fronts and Tidal Flats (PDF)
    Applications of Digital Image Processing XXXVIII (Andrew G. Tescher, ed.), SPIE Conference Series, vol. 9599, 2015. doi:10.1117/12.218865
  3. R. Reisenhofer
    The Complex Shearlet Transform and Applications to Image Quality Assessment (PDF)
    Technische Universität Berlin, Master's Thesis, 2014.

Haar Wavelet-Based Perceptual Similarity Index (HaarPSI)

The Haar wavelet-based perceptual similarity index (HaarPSI) is a similarity measure for images that aims to correctly assess the perceptual similarity between two images with respect to a human viewer.

In most practical situations, images and videos can neither be compressed nor transmitted without introducing distortions that will eventually be perceived by a human observer. Vice versa, most applications of image and video restoration techniques, such as inpainting or denoising, aim to enhance the quality of experience of human viewers. Correctly predicting the similarity of an image with an undistorted reference image, as subjectively experienced by a human viewer, can thus lead to significant improvements in any transmission, compression, or restoration system.

For more information and downloads please visit www.haarpsi.org. The HaarPSI is also available on github.


A regular simplex is a collection of s+1 equiangular vectors which form a tight frame for their span, which is s-dimensional. The binder of an equiangular tight frame (ETF) consists of all of the subsets of the index set which correspond to regular simplices. Such simplices, if they exist, must have the same size as the spark of the frame and thus are also the smallest circuits in the matroid associated to the frame. Directly computing the binder is very computationally expensive. A few different mathematical tricks are employed in the code of BinderFinder in order to make computing the binder of some larger ETFs tractable. The code is a short Matlab program.

Download the code here: BinderFinder.m

For more information, see "Equiangular tight frames that contain regular simplices" by Matthew Fickus, John Jasper, Emily J. King, and Dustin G. Mixon. (PDF)