Although phase data can take on any value, it is generally only possible to measure phase as a principle value, i.e., wrapped within the range (-pi,pi]. Determining the unwrapped phase from its principle value is a topic of considerable interest in magnetic resonance imaging (MRI), as well as many non-medical disciplines. Despite their importance in image analysis, filters for manipulating phase information have not been incorporated into ITK. This article introduces the ITKPhase module, containing filters useful for understanding, analyzing, and unwrapping n-dimensional phase data, and also serves as a practical introduction to phase unwrapping.

N-Dimensional Phase Unwrapping

This document describes the derivation of the mixture models commonly used in the literature to describe the probabilistic nature of speckle: The Gaussian Mixture Model, the Rayleigh Mixture Model, the Gamma Mixture Model and the Generalized Gamma Mixture Model. New algorithms were implemented using the Insight Toolkit
ITK for tissue characterization by means of a mixture model. 
The source code is composed of a set of reusable ITK filters and classes. In addition to an overview of our implementation, we provide the source code, input data, parameters and output data that the authors used for validating the different probabilistic tissue characterization variants described in this paper. This adheres to the fundamental principle that scientific publications must facilitate reproducibility of the reported results.

Probabilistic Tissue Characterization for Ultrasound Images

The Fast Marching algorithm is an efficient numerical method for computing the distance and shortest path between points of a domain. For that purpose, it solves a front propagation problem, which can be of interest in itself. The method has numerous applications, ranging from motion planning to image segmentation. The unit of length, for computing the path length, may vary on the domain.
Motivated by applications, we generalize the algorithm to the case where the unit of length also depends on the path direction. Segmentation methods can take advantage of this flexibility to achieve greater sensitivity and specificity, for a comparable computation time.


Anisotropic Fast Marching in ITK

Isotropic volumetric acquisition in Magnetic Resonance Imaging (MRI) is often challenging. A large number of factors such as patient or physiological motion, signal-to-noise ratio (SNR), available static magnetic field B0 and total scanning
time limit the acquired resolution. Super-resolution (SR) is a post-processing tech-
nique that optimally combines several anisotropic scans into a single isotropic volume that was not - or could not be - acquired in practice. If necessary conditions are met, the resulting isotropic volume offers clear improvements over the initial acquisitions such as reduced partial volume effect, oblique visualization and improved sharpness and SNR. This paper details the misoSR implementation of a SR isotropicreconstruction algorithm using the Insight Toolkit Library (ITK) library. It is a generic implementation that reconstructs an isotropic volume from any number of anisotropic volumes acquired from any orientation. The algorithm takes advantage of the inputs header information to handle the different scans properties such as field of view (FOV), resolution parameters and orientation. Step by step details on the implementation are given, parameters are individually detailed, and results are shown on different applications as an example of SR reconstruction. The algorithm is hosted on the Creatis Virtual Imaging Platform (VIP), which allows users to run misoSR without having to install the software on their system.

MisoSR: Medical Image Isotropic Super-Resolution Reconstruction

noindent This document describes two new classes that facilitate the use of
the doxygen{BSplineDeformableTransform} in multiresolution registration
algorithms. The first class, doxygen{GridScheduleComputer}, defines the
B-spline grid, based on a user-specified grid spacing and an input image (the
fixed image in registration). A different grid is determined for each
resolution level of the registration, given a multiresolution schedule similar
to that of the image pyramids. The second class,
doxygen{UpsampleBSplineParametersFilter}, resamples (usually upsamples) the
B-spline coefficients to a new control point grid having a different
spacing/origin/size. This can be used to transfer the result from one
resolution level to that of the next level. Summarising, suitable grid
definitions follow from the first class, and are used as input for the second
class, which performs the actual resampling.

The classes are implemented using the Insight Toolkit url{www.itk.org}. This
paper is accompanied with the source code, including a test program.

Helper classes for the BSplineDeformableTransform

Although greyscale intensity values are primarily used in image data visualization oftentimes, due to the requirements of aesthetics (whether they be self-imposed or collaborator-suggested), mapping the greyscale image to a user-defined colormap is desired. In this paper, we propose a framework for inclusion in the ITK library for converting intensity-valued images to user-defined RGB colormap images. We also include several colormaps that can be readily applied for visualization of images in such programs as ITK-SNAP or can be used as examples for creating new colormaps.

Meeting Andy Warhol Somewhere Over the Rainbow: RGB Colormapping and ITK

Many image registration algorithms are formulated as optimization 
problems with a gradient descent based solver, One difficulty with 
designing and implementing such methods is in the implementation of 
the gradient computation. This process can be time-consuming and 
error-prone. In addition some functions do not have gradients that can 
be expressed in symbolic form. Automatic differentiation is useful for 
computing gradients of complicated objective functions. It moves the 
burden of computing gradients from the programmer to the computer. So 
far, AD has not been exploited for use in image registration. This 
paper describes a software library the authors have developed to 
automate the process of computing gradients of registration objective 
functions. This can alleviate the job of registration designers 
somewhat and potentially make it easier to design better registration 
algorithms.

Image Registration with Automatic Computation of Gradients

When dealing with meshes, it is often preferable to work with a lower resolution mesh for computational
time purpose, display. The process of reducing a given mesh, mesh decimation, is thus an important step
in most of pipeline dealing with meshes. Incremental decimation algorithms, the most popular ones,
consists of iteratively removing one point of the mesh, by Euler operations such as vertex removal or
edge collapse. Here we focus on edge collapse based decimation approaches and propose a general
framework based on a surface mesh data structure (itk::QuadEdgeMesh [3]). Our implementation intends
to be as general and as flexible as possible. Indeed it can theoretically be applied on any polygonal
mesh1; the measure, functional to be optimized at each iteration, the objective to be reached, and optional
methods like point relocation to enhance the geometry of the resulting mesh, are given by the user.
We provide here two specific implementations: itk::QuadEdgeMeshSquaredEdgeLengthDecimation
and itk::QuadEdgeMeshQuadricDecimation, that could be used as example to implement additional
algorithms.

Surface Meshes Incremental Decimation Framework

The \emph{Delaunay triangulation} is the triangulation of a set of points which maximizes the minimum angle of all angles of the triangles, and thus triangle aspect ratios. So converting a non Delaunay triangulation into a Delaunay triangulation, \emph{Delaunay conforming}, improves the all triangle aspect ratios and avoid elongated triangles. Note that combining this filter with usual operations like smoothing will provide a better approximation and a better distribution a triangle aspect ratios. Here this document describes a new filter based on the $n$D $2$-manifold mesh data structure available in itk: \code{itk::QuadEdgeMesh}~\cite{itkQE} to produce (planar or surfacic) Delaunay triangulation from any non-Delaunay triangulation by edge flipping, by implementing the edge flipping method decribed in~\cite{Dyer2007sgp}.

Triangular Meshes Delaunay Conforming Filter

The itkLabelGeometryImageFilter is a new ITK filter that enables the measurement of geometric features of labeled objects. It calculates features similar to the "regionprops" command of Matlab. It is related to the itkLabelStatisticsImageFilter in that both filters measure features of labeled masks. It differs, however, in that it measures geometric features of the objects themselves rather than statistics
of image intensities under the masks defined by the objects. This document describes the mathematical background of the geometric features measured by this filter and describes the framework of the code, which is structured to enable easy expandability as new object features are desired.