We present and implement an error estimation protocol in the Insight Toolkit (ITK) for assessing the
accuracy of image alignment. We base this error estimation on a robust version of the HausdorffDistance
(HD) metric applied to the recovered edges of the images. The robust modifications we introduce to
the HD metric significantly reduce the amount of outliers in the local distance error estimation. We
evaluate the accuracy of our protocol on synthetically deformed images. We provide the source code
and datasets to reproduce this evaluation. The proposed method is shown to improve error assessment
when it is compared with conventional HD methods. This approach has many applications including
local estimation and visual assessment of registration error and registration parameter selection.

The Use of Robust Local Hausdorff Distances in Accuracy Assessment for Image Alignment of Brain MRI

Morphological erosion and dilation filters employ a structuring function, with flat structuring functions being the most common example. This article will use the term \"parabolic\", but much of the literature uses \"quadratic\" structuring functions are less well known but theoretically very important and practically very useful. This paper briefly introduces morphology using parabolic structuring functions, describes the ITK classes used to implement them and includes a number of sample applications.

Morphology with parabolic structuring elements

Semi-automatic image segmentation algorithms depend on interaction with the user to accurately define a region of interest within an image. Once such method is a dynamic programming approach called {em Intelligent Scissors} developed by Mortenson and Barret cite{Mortensen1992,Mortensen1995,Barrett1996,Barrett1997}. Standard interaction involves the user-placement of a seed point on or near the boundary of the object to be extracted. Using a gradient-based cost function, a {em live-wire} image path from the seed point to a subsequently placed boundary point is determined. As this free point is manipulated with the mouse cursor, the live-wire boundary, which extends from the seed point to the varying free point, locks onto nearby edges within the image. Although some applications do not require such user-interaction (e.g. cite{Hu2001}) warranting inclusion within the toolkit, incorporating live-wire capabilities into ITK-SNAP cite{Yushkevich2006} has been discussed and, therefore, we would like to, as a preliminary step, vet the code within the ITK community.

Live-Wire-ing the Insight Toolkit with Intelligent Scissors

Texture analysis provides quantitative information describing properties in images such as coarseness and smoothness. Two common quantification schemes are based on co-occurence matrices and run-length matrices. Although the co-occurence measures are readily available in the Insight Toolkit, no such set of classes exists for run-length measures. This submission is meant to remedy this deficiency by providing a set of classes which are modeled after the ITK co-occurence measures classes.

Run-Length Matrices For Texture Analysis

This document describes a suite of new multi-threaded classes for calculating magnetic resonance (MR) T2 and T1 parameter maps implemented using the Insight Toolkit ITK (www.itk.org). Similar to MR diffusion tensor imaging (DTI), MR T2 and T1 parameter maps provide a non-invasive means for quantitatively measuring disease or pathology in-vivo. Included in the suite are classes for reading proprietary Bruker 2dseq and Philips PAR/REC images and example programs and data for validating the new classes.

MR Parameter Map Suite: ITK Classes for Calculating Magnetic Resonance T2 and T1 Parameter Maps

This document describes a new class that takes an \doxygen{Transform} and
evaluates the deformation at points in a user-defined region.
The class is implemented using the Insight Toolkit url{www.itk.org}. \
This paper is accompanied with the source code, input data, parameters and
output data that the authors used for validating the algorithm described in
this paper.

Generating a Deformation Field from a Transform

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.