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.

A Label Geometry Image Filter for Multiple Object Measurement

Computing local curvatures of a given surface is important for applications, shape analysis, surface segmentation, meshing, and surface evolution. For a given smooth surface (with a given analytical expression which is sufficiently differentiable) curvatures can be analytically and directly computed. However in real applications, one often deals with a surface mesh which is an insufficiently differentiable approximation, and thus curvatures must be estimated. Based on a surface mesh data structure (\code{itk::QuadEdgeMesh}~\cite{itkQE}), we introduce and implement curvature estimators following the approach of Meyer\etal\cite{Meyer02}. We show on a sphere that this method results in more stable curvature approximations than the commonly used discrete estimators (as used in VTK: \code{vtkCurvatures}).

Surface Mesh Discrete Curvature Estimators

We have previously developed a new surface mesh data structure in itk (\code{itk::QuadEdgeMesh}~\cite{itkQE}). In this document we describe a new filter (\code{itk::QENormalFilter}) to estimate normals for a given triangular surface mesh in this data structure. Here we describe the implementation and use of this filter for calculating normals of a \code{itk::QuadEdgeMesh}.

Surface Mesh Normals Filter

A novel point-set registration algorithm was proposed in [6] based on minimization of the Jensen-Shannon divergence. In this contribution, we generalize this Jensen-Shannon divergence point-set measure framework to the Jensen-Havrda-Charvat-Tsallis divergence. This generalization permits a ﬁne-tuning of the actual divergence measure between robustness and speciﬁcity. The principle contribution of this submission is theitk::JensenHavrdaCharvatTsallisPointSetMetric class which is derived from the existing itk::PointSetToPointSetMetric. In addition, we provide other classes with utility that would extend beyond the point-set measure framework that we provide in this paper. This includes a point-set analogue of the itk::ImageFunction, i.e. itk::PointSetFunction. From this class we derive the class itk::ManifoldParzenWindowsPointSetFunction which provides a Parzen windowing scheme for learning the local structure of point-sets. Finally, we include the 
itk::DecomposeTensorFunction class which wraps the different vnl matrix decomposition schemes for easy use within ITK. 


A Novel Information-Theoretic Point-Set Measure Based on the Jensen-Havrda-Charvat-Tsallis Divergence

Graph-based algorithms have enjoyed renewed interest for solving computer vision problems. These algorithms have been the subject of intense interest and research. In order to maintain the ITK library au courant, we developed a framework for graph-based methods of energy minimization in ITK which employ energy functions derived within a Markov Random Field (MRF) context. This required not only the implementation of the energy minimization methodology but also the more general requirement of introducing graph-related data structures into ITK which can be used for other graph-based algorithms pertinent to future extensions of the ITK library. 

Please note that some of the algorithms described in this paper may be covered by patents and, as such, it is incumbent upon the user to seek licenses before building the binaries which utilize this code. Also note that “research use” is not exempt from acquiring such licenses. The only exemption from patent restrictions is “. . . amusement, to satisfy idle curiosity, or for strictly philosophical inquiry.”

Graph Cuts, <i>Caveat Utilitor</i>, and Euler's Bridges of Konigsberg

This document describes a new class for the Insight Toolkit~(ITK www.itk.org) for reading images across a network. Network access is handled by CURL (http://curl.haxx.se/libcurl/), an Open Source library for client-side URL transfer. CURL supports the FTP, FTPS, HTTP, HTTPS, SCP, SFTP, TFTP, TELNET, DICT, LDAP, LDAPS and FILE protocols.

This paper is accompanied with source code and a test to load a NRRD file across the network and verify that is is read properly.


ImageNetworkReader: an ITK Class for Loading Images Across a Network

An implementation of the minimum error thresholding algorithm is presented. In this implementation, two versions of the minimum error thresholding algorithm are made available, one utilizing a Gaussian- and the other utilizing a Poisson- mixture model. Two ITK classes are created: The first one (MinErrorThresholdImageCalculator) is used to compute the threshold; the second (MinErrorThresholdImageFilter) is used as an image-thresholding filter. The results indicate code correctness and are comparable to those of Otsu’s thresholding algorithm.

ITK Implementation Of The Minimum Error Image Thresholding Algorithm

In a surgical environment, there are many tools and objects (including the patient) being used. In a computer-aided surgery, the position of each of these tools in the operating room is very critical and generally will be tracked in their own coordinate systems. To show the surgeon a real time picture of the operating environment on a computer monitor, we need to know the position of each object with respect to one common coordinate system, which in turn can be achieved by knowing each coordinate system and the transforms between them. Image-Guided Surgical Toolkit is a software toolkit designed to enable biomedical researchers to rapidly prototype and create new applications for image-guided surgery. In IGSTK, in which the coordinate systems and the transforms are being successfully used, there is no central data structure or repository, which will hold all the coordinate systems and the transforms between them. Such a data structure could help the IGSTK software developers to have more confidence in the code they have written. This project develops a tool, which will create such a data structure and dynamically show the changes to it, to help such software developers to write better code.

Scene Graph: Visualization of Coordinate Systems in the Image Guided Surgical Toolkit

This technical note presents an alternative threading model for the Insight Toolkit. The existing ITK threading model is based on a \"scatter / gather\" model and divides work evenly amongst all threads. Though suitable for many filters, considerations such as memory allocation per thread are important in some classes of filters. We propose to use the ZThread (http://sourceforge.net/projects/zthread/) library to explore a threading model based on an execution pool. The ZThread library is a cross platform, open source thread abstraction library loosely based on Java\'s threading model.