Algorithms

A Framework to Train the Activation Functions of a Neural Network The aim of this repository is to facilitate the reproduction of the results reported in the research papers It enables a seamless integration of deep spline activation functions in a custom neural network.

References

• P. Bohra, J. Campos, H. Gupta, S. Aziznejad, M. Unser, Learning Activation Functions in Deep (Spline) Neural Networks, IEEE Open Journal of Signal Processing, vol. 1, pp. 295-309, November 19, 2020.

• S. Aziznejad, H. Gupta, J. Campos, M. Unser, Deep Neural Networks with Trainable Activations and Controlled Lipschitz Constant, IEEE Transactions on Signal Processing, vol. 68, pp. 4688-4699, August 10, 2020.

This is a plug-in for Icy that implements fast active contours for image segmentation. Their representation in terms of spline curves allows for a natural and intiutive manipulation of the active contour through control points. The software allows one to manage several active contours simultaneously, and to keep record of their location and size through the ROI persistence capability of Icy.

This is a plug-in for Icy that implements fast active surfaces for 3D image segmentation. Their representation in terms of spline surfaces allows for a natural and intuitive manipulation of the surface. The software allows one to manage several active contours simultaneously, and to have synchronized 2D and 3D viewers simultaneously.

This is a package for Icy that encapsulates tools to design and implement parametric active contours. The package provides fast 2D and 3D filters for image preprocessing, and a framework to create and evolve snakes defined by a set of control points.

Feature Detector

The Icy Feature Detector plug-in implements a series of optimized contour and ridge detectors. The filters are steerable and are based on the optimization of a Canny-like criterion. They have a better orientation selectivity than the classical gradient or Hessian-based detectors.

Potts Segmentation

The plug-in implements a segmentation algorithm based on the Potts model. It works with graylevel, color or vector-valued images. The user can edit segments (e.g. merge or refine) and export the segments to the ROI manager. A quick preview function is available.

PSF Generator is a piece of software that allows to generate and visualize various 3D models of a microscope PSF. The current version has five different models: the Gaussian model, the simulated defocus, the scalar-based diffraction model Born & Wolf, the scalar-based diffraction model with 3 layers Gibson & Lanni, and finally, the vectorial-based model Richards & Wolf.

This plug-in implements a user-friendly way to design shape-priors for the Active Cells plug-in.

This is a plug-in for Icy that implements a stereo vision system. Renders 3D stacks simulating a dual view camera. Each 3D view is rendered in fullscreen in a different monitor.

This plugin implements active contours to segment cell aggregates. They are robust to membrane gaps and to high levels of noise. Their subdivision-based representation allows for an intuitive manipulation of the curves through control points.

This plugin implements fast active contours for biomedical image segmentation. Through the interface, one can locally increases the degrees of freedom of the curves. It allows to catch details of intricate shapes.

This plugin implements fast active contours for biomedical image segmentation. They adapt the resolution of their curve to the level of details of their target. Their subdivision-based representation allows for an intuitive manipulation of the curves through control points.

This plugin implements active surfaces to segment biomedical volumes They adapt the resolution of their curve to the level of details of their target. Their subdivision-based representation allows for an intuitive manipulation of the curves through control points.

This plugin implements active contours to segment structures with similar intensity distribution and low contrast with the background. They are trained on-the-fly from small collections of pixels provided by the user. Their parametric representation allows for an intuitive manipulation of the curves through control points.

This ImageJ plugin smoothes an image without altering its edges. The smoothing is applied by the way of a bi-exponential filter, itself realized by a pair of one-tap recursions. It is therefore very fast; moreover, its computational cost is truly independent of the amount of smoothing. Meanwhile, the preservation of edges is obtained by a range filter akin to the range filter found in a bilateral filter.

This ImageJ plugin (CGE) is a semi-automatic tool to detect and track moving cell, and to measure the fluorescent protein expression level. CGE extracts the trajectory of the cells by tracking their displacements, makes the delineation of cell nucleus or whole cell, and finally yields measurements of various features, like reporter protein expression level, cell displacement.

CosinorJ is a Java software tool to quantify circadian oscillatory gene expression profiles. It fits a cycling function to accurate estimate of the period, mesor, accrophase and amplitude of any rhythm signals of chronobiology.

DeconvolutionLab2 is freely accessible and open-source for 3D deconvolution microscopy; it can be linked to well-known imaging software platforms, ImageJ, Fiji, ICY, Matlab, and it runs as a stand-alone application. The backbone of our software architecture is a library that contains the number-crunching elements of the deconvolution task. It includes the tool for a complete validation pipeline. Inquisitive minds inclined to peruse the code will find it fosters the understanding of deconvolution. At this stage, DeconvolutionLab2 includes a friendly user interface to run the following algortihms: Regularized Inverse Filter, Tikhonov Inverse Filter, Naive Inverse Filter, Richardson-Lucy, Richardson-Lucy Total Variation, Landweber (Linear Least Squares), Non-negative Least Squares, Bounded-Variable Least Squares, Van Cittert, Tikhonov-Miller, Iterative Constraint Tikhonov-Miller, FISTA, ISTA.

References

• D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, M. Unser, DeconvolutionLab2: An Open-Source Software for Deconvolution Microscopy, Methods—Image Processing for Biologists, vol. 115, pp. 28-41, February 15, 2017.

New method based on B-spline snakes (active contours) for measuring high-accuracy contact angles of sessile drops.

This ImageJ plugin (ESnake) implements a fast parametric active contour for segmenting nearly elliptic objects. ESnake outlines the targets using exponential B-splines, and it allows one to keep record of the curve with the ROI Manager from ImageJ.

The extended depth of focus is a image-processing method to obtain in focus microscopic images of 3D objects and organisms. We freely provide a software as a plugin of ImageJ to produce this in-focus image and the corresponding height map of z-stack images.

This Java package computes the fractional spline wavelet transform of a signal or an image and its inverse.

This Java class for ImageJ implements 6 operations based on the spatial differentiation of an image. It computes the pixel-wise gradient, Laplacian, and Hessian. The class exports public methods for horizontal and vertical gradient and Hessian operations (for those programmers who wish to use them in their own code).

The local normalization tends to uniformize the mean and variance of an image around a local neighborhood. This is especially useful for correct uneven illumination or shading artifacts. Thanks to our fact implementation of the Gaussian filtering, the Local Normalization is running very fast.

References

• D. Sage, M. Unser, Easy Java Programming for Teaching Image Processing, Proceedings of the 2001 IEEE International Conference on Image Processing (ICIP'01), Θεσσαλονίκη (Thessaloniki), Ελληνική Δημοκρατία (Hellenic Republic), October 7-10, 2001, vol. III, pp. 298-301.

MIJ offers the missing link between two imaging software: ImageJ/Fiji and Matlab. The goal of the package mij.jar is to provide static methods to exchange images and volumes. MIJ allows also to access to all built-in functions of ImageJ and to third-part plugins of ImageJ. MIJ is integrated in Fiji with a super-easy script to use it. Thanks to the Fiji team, MIJ is now super-easy to use using a Matlab script Miji.m which is integrated in Fiji. ImageJ/Fiji becomes a image-processing librairie of Matlab.

References

• D. Sage, D. Prodanov, J.-Y. Tinevez, J. Schindelin, Daniel Sage: MIJ: Making Interoperability Between ImageJ and Matlab Possible, ImageJ User & Developer Conference (IUDC'12), Mondorf-les-Bains, Grand Duchy of Luxembourg, October 24-26, 2012.

This ImageJ plugin performs multiresolution monogenic analyses of 2D images. It extracts wavelet-domain features that characterize the local orientation, the phase and the dominant frequency of an image patch at various levels of resolution.

References

• M. Unser, D. Sage, D. Van De Ville, Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform, IEEE Transactions on Image Processing, vol. 18, no. 11, pp. 2402-2418, November 2009.

This Java class for ImageJ performs the assembly of a mosaic of overlapping individual images, or tiles. It provides a semi-automated solution where the initial rough positioning of the tiles must be performed by the user, and where the final delicate adjustments are performed by the plugin.

This Java class for ImageJ was developed to facilitate the tracing and quantification of neurites in two-dimensional (2D) fluorescence microscopy images. The tracing is done interactively based on the specification of end points; the optimal path is determined on the fly from the optimization of a cost function using Dijkstra's shortest-path algorithm.

The aim of this ImageJ plugin is to characterize the orientation and isotropy properties of a region of interest (ROI) in an image, based on the evaluation of the structure tensor in a local neighborhood. OrientationJ has four functionalities: visual representation of the orientation, quantitative orientation measurement, making distribution of orientations and corner detection (Harris Corner)

The purpose of this ImageJ plugin is to detect elliptical bright blobs in images and to quantify them. It allows one to keep record of their location and size.

PSF Generator is a piece of software that allows to generate and visualize various 3D models of a microscope PSF. The current version has five different models: the Gaussian model, the simulated defocus, the scalar-based diffraction model Born & Wolf, the scalar-based diffraction model with 3 layers Gibson & Lanni, and finally, the vectorial-based model Richards & Wolf.

References

• H. Kirshner, F. Aguet, D. Sage, M. Unser, 3-D PSF Fitting for Fluorescence Microscopy: Implementation and Localization Application, Journal of Microscopy, vol. 249, no. 1, pp. 13-25, January 2013.

• H. Kirshner, F. Aguet, D. Sage, M. Unser, Least-Square PSF Fitting for Localization Microscopy, Second Swiss Single Molecule Localization Microscopy Symposium (SSMLMS'12), Lausanne VD, Swiss Confederation, August 29-31, 2012.

PixBleach is a ImageJ plugin which fits fluorescence photobleaching decay in the temporal sequence for every pixels. Three common decal models are available: the mono-exponential, the bi-exponential, and the stretched exponential. Bleach rate (time-constant) and other fitted parameters can be visualized as 32-bit image and exploited for further analysis.

The ImageJ plug-in PixFRET allows to visualize the FRET between two partners in a cell or in a cell population by computing pixel by pixel the images of a sample acquired in three channels.

References

• J.N. Feige, D. Sage, W. Wahli, B. Desvergne, L. Gelman, PixFRET, an ImageJ Plug-in for FRET Calculation That Can Accommodate Variations in Spectral Bleed-throughs, Microscopy Research and Technique, vol. 68, no. 1, pp. 51-58, September 2005.

This Java class for ImageJ allows the user to pick some points in an image and to save the list of pixel coordinates as a text file. It is also possible to read back the text file so as to restore the display of the coordinates.

The purpose of this ImageJ plugin is to propose a high-quality denoising algorithm of multidimensional fluorescence microscopy images (2D+t, 3D or color).

This ImageJ plugin changes the size of an image to any dimension using either interpolation, or least-squares approximation.

RodCellJ is freely available to the community as a package of several ImageJ plugins to simultaneously analyze the behavior of a large number of rod-shaped cells in an extensive manner. The integration of different image-processing techniques in a single package, as well as the development of novel algorithms does not only allow to speed up the analysis with respect to the usage of existing tools, but also accounts for higher accuracy.

The purpose of this ImageJ plugin is to generate sampled versions of the Shepp-Logan phantom. Their size can be tuned.

The purpose of this ImageJ plugin is to detect circular bright blobs in images and to quantify them. It allows one to keep record of their location and size.

SpotCaliper is a wavelet-based image-analysis software providing a fast automatic detection scheme forcircular patterns (spots), combined with the precise estimation of their size. It is implemented as an ImageJ plugin with a complete user interface. The user is allowed to edit the results by modifying the measurements (in a semi-automated way), extract or load data, or do further analysis. The fine tuning of the detections includes the possibility of adjusting or removing the original detections, as well as adding further spots.

This ImageJ plugin determines intra-nuclear 3D cross-distances between fluorescent spots in multi-channel z-stack of image.

This ImageJ plugin is a robust and fast computational procedure for tracking fluorescent markers in time-lapse microscopy. The algorithm is optimized for finding the time-trajectory of single particles in very noisy image sequences.

This Java class for ImageJ performs the recursive registration (alignment) of a stack of images, so that each slice acts as template for the next one.

A complete parametric framework and set of Java tools for computing steerable wavelet frames in 2-D.

This ImageJ plugin implements a series of optimized contour and ridge detectors. The filters are steerable and are based on the optimization of a Canny-like criterion. They have a better orientation selectivity than the classical gradient or Hessian-based detectors.

This Java class for ImageJ performs the registration (alignment) of two images. The registration criterion is least-squares. The geometric deformation model can be translational, conformal, affine, and bilinear.

This Java class for ImageJ performs the elastic registration (alignment) of two images. The registration criterion includes a vector-spline regularization term to constrain the deformation to be physically realistic. The deformation model is made of cubic splines, which ensures smoothness and versatility.

This Java plugin is able to segment an image using the watershed algorithm by directly flooding graylevel images. This implementation is in contrast with the classical approach working on the distance map image obtaining after thresholding. The grayscale watershed segmentation is useful to segment particles in contact when the model of shape is unknown a priori.

References

• D. Sage, M. Unser, Teaching Image-Processing Programming in Java, IEEE Signal Processing Magazine, vol. 20, no. 6, pp. 43-52, November 2003.

• M. Tsukahara, S. Mitrović, V. Gajdosik, G. Margaritondo, L. Pournin, M. Ramaioli, D. Sage, Y. Hwu, M. Unser, T.M. Liebling, Coupled Tomography and Distinct-Element-Method Approach to Exploring the Granular Media Microstructure in a Jamming Hourglass, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), vol. 77, no. 6, paper no. 061306, 11 p., June 2008.

WingJ

WingJ is an open-source Java application using ImageJ. WingJ allows to automatically infer a model of the morphological structure of the developing Drosophila wing from confocal fluorescence images. In addition it provides valuable information on the morphology of wing, using a parametric structure model for systematic spatial quantification of gene expression.

This Java class contains methods to perform Fourier-related operations on discrete sequences, images, and volumes. The operations can be tailored to real or complex data and include forward and backward Fourier transforms, convolutions, and polar/rectangular view of complex numbers.

When being confronted with a new imaging problem, the common experience is that one has to reimplement (if not reinvent) the wheel (=forward model + optimization algorithm), which is very time consuming and also acts as a deterrent for engaging in new developments. This Matlab library aims at simplifying this process by decomposing the workflow, onto smaller modules, including many reusable ones since several aspects such as regularization and the injection of prior knowledge are rather generic. It also capitalizes on the strong commonalities between the various image formation models that can be exploited to obtain fast, streamlined implementations.

A novel spline family for hexagonal lattices. A Maple 7.0 worksheet is available for obtaining the analytical formula of any hex-spline (any order, regular, non-regular, derivatives, and so on).

A Mathematica package is made available for the symbolic computation of exponential spline related quantities: B-splines, Gram sequence, Green function, and localization filter.

This Matlab package implements the forward model as well as the reconstruction of the binary compressed imaging.

References

• A. Bourquard, M. Unser, Binary Compressed Imaging, IEEE Transactions on Image Processing, vol. 22, no. 3, pp. 1042-1055, March 2013.

A Matlab package is available for computing the fractional smoothing spline estimator of a signal and for generating fBms (fractional Brownian motion). This spline estimator provides the minimum mean squares error reconstruction of a fBm (or 1/f-type signal) corrupted by additive noise.

References

• M. Unser, Sampling and Interpolation for Biomedical Imaging, Tutorial, Third IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI'06), Arlington VA, USA, April 6-9, 2006.

• T. Blu, M. Unser, Optimal Interpolation of Fractional Brownian Motion Given Its Noisy Samples, Proceedings of the Thirty-First IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'06), Toulouse, French Republic, May 14-19, 2006, pp. III-860-III-863.

A Matlab package is available for computing the fractional spline wavelet transform of a signal or an image and its inverse.

References

• M. Unser, T. Blu, Fractional Splines and Wavelets, SIAM Review, vol. 42, no. 1, pp. 43-67, March 2000.

This is a set of Matlab routines for computing generalized Daubechies wavelet filters.

References

• C. Vonesch, T. Blu, M. Unser, Generalized Daubechies Wavelet Families, IEEE Transactions on Signal Processing, vol. 55, no. 9, pp. 4415-4429, September 2007.

This Matlab package implements the MultiLevel Thresholded Landweber (MLTL) algorithm, an accelerated version of the TL algorithm that was specifically developped for deconvolution problems with a wavelet-domain regularization.

References

• C. Vonesch, M. Unser, A Fast Multilevel Algorithm for Wavelet-Regularized Image Restoration, IEEE Transactions on Image Processing, vol. 18, no. 3, pp. 509-523, March 2009.

• C. Vonesch, M. Unser, A Fast Thresholded Landweber Algorithm for Wavelet-Regularized Multidimensional Deconvolution, IEEE Transactions on Image Processing, vol. 17, no. 4, pp. 539-549, April 2008.

This package is a collection of Matlab functions that implements analytical multi-channel MRI simulations of realistic phantoms. It should be useful for testing the validity of the numerical implementations of the parallel MRI forward model. It also provides a realistic setting that avoids the inverse crime situation which can often result in over-optimistic reconstruction performances. To facilitate the design of new phantoms, graphical interface tools are provided. For purposes of adequate visualization, exporting to the popular vector graphics formats SVG 1.1 and PDF (via the PGF/Tikz LATEX package) is supported.

This package is a collection of Matlab functions that provides 1) analytical and rasterized multi-channel MRI simulations of realistic phantoms and 2) a collection of basic and state-of-the-art reconstruction methods including an efficient wavelet-based non-linear one. Demonstration and testing scripts are included. A detailed documentation is provided. The analytical phantom simulation tools allow sound validations of reconstruction methods. The reconstruction framework is rather general and should be easy to adapt to any linear inverse problem. Wavelet transform and wavelet coefficients can be easily manipulated like Matlab's matrices and vectors.

References

• M. Guerquin-Kern, L. Lejeune, K.P. Pruessmann, M. Unser, Realistic Analytical Phantoms for Parallel Magnetic Resonance Imaging, IEEE Transactions on Medical Imaging, vol. 31, no. 3, pp. 626-636, March 2012.

• M. Guerquin-Kern, M. Häberlin, K.P. Pruessmann, M. Unser, A Fast Wavelet-Based Reconstruction Method for Magnetic Resonance Imaging, IEEE Transactions on Medical Imaging, vol. 30, no. 9, pp. 1649-1660, September 2011.

This Matlab package implements the interscale orthonormal wavelet thresholding algorithm based on the SURE-LET (Stein's Unbiased Risk Estimate/Linear Expansion of Thresholds) principle.

Functional framework for the design of tight steerable wavelet frames in 2D. A toolbox that contains Matlab routines for computing the forward and backward generalized Riesz-wavelet transform of high order is provided. We have included utilities for orientation computation, coefficients steering, basic denoising, frame learning

References

• M. Unser, N. Chenouard, D. Van De Ville, Steerable Pyramids and Tight Wavelet Frames in L₂(ℝ^d), IEEE Transactions on Image Processing, vol. 20, no. 10, pp. 2705-2721, October 2011.

• M. Unser, D. Sage, D. Van De Ville, Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform, IEEE Transactions on Image Processing, vol. 18, no. 11, pp. 2402-2418, November 2009.

A complete parametric framework and set of matlab tools for computing steerable wavelet frames in 2-D. Specific designs include Simoncelli's pyramid, Marr and monogenic wavelets, Prolate spheroidal wavelets, and curvelets.

References

• Z. Püspöki, M. Unser, Template-Free Wavelet-Based Detection of Local Symmetries, IEEE Transactions on Image Processing, vol. 24, no. 10, pp. 3009-3018, October 2015.

• M. Unser, N. Chenouard, A Unifying Parametric Framework for 2D Steerable Wavelet Transforms, SIAM Journal on Imaging Sciences, vol. 6, no. 1, pp. 102-135, 2013.

Wavelet-based statistical parametric mapping, a toolbox for SPM that incorporates powerful wavelet processing and spatial domain statistical testing for the analysis of fMRI data.

References

• D. Van De Ville, T. Blu, M. Unser, , Integrated Wavelet Processing and Spatial Statistical Testing of fMRI Data, NeuroImage, vol. 23, no. 4, pp. 1472-1485, December 2004.

• D. Van De Ville, T. Blu, M. Unser, Surfing the Brain—An Overview of Wavelet-Based Techniques for fMRI Data Analysis, IEEE Engineering in Medicine and Biology Magazine, vol. 25, no. 2, pp. 65-78, March-April 2006.

• D. Van De Ville, M.L. Seghier, F. Lazeyras, T. Blu, M. Unser, WSPM: Wavelet-Based Statistical Parametric Mapping, NeuroImage, vol. 37, no. 4, pp. 1205-1217, October 1, 2007.

• D. Van De Ville, M. Unser, Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid, IEEE Transactions on Image Processing, vol. 17, no. 11, pp. 2063-2080, November 2008.

This ANSI-C routine performs an affine transformation on an image or a volume. It proceeds by resampling a continuous spline model.

This ANSI-C routine performs the registration (alignment) of two images or two volumes. The criterion is least-squares. The geometric deformation model can be translational, rotational, and affine.

This ANSI-C program illustrates how to perform shifted linear interpolation.

This ANSI-C program illustrates how to perform spline interpolation, including the computation of the so-called spline coefficients.

This software package implements the basic REDUCE and EXPAND operators for the reduction and enlargement of signals and images by factors of two based on polynomial spline representation of the signal.