BSpline registration: Detecting folding and Background: Difference between pages

Revision as of 16:39, 7 March 2012

In this section . . .

Background
References

Designed specifically for medical researchers, MIPAV concentrates on providing those researchers with the tools needed to do their work. It reads image files of many different formats and allows images to be displayed and measured using the most meaningful method to achieve research goals. MIPAV's flexibility becomes apparent when its capabilities are expanded and fine tuned through the development of plug-in programs that tailor solutions to meet specific requirements.

Using MIPAV to display, label, and measure brain components in Talairach space demonstrates both: MIPAV's native ability to display and measure brain images in Talairach space and the tailoring provided through the Talairach Transformation wizard and the FANTASM (Fuzzy and Noise Tolerant Adaptive Segmentation Method) plug-in programs, developed by the Johns Hopkins University.

Background

In 1988 Jean Talairach and Pierre Tournoux developed a three-dimensional proportional grid system that can be used to identify and measure brains from any number of patients despite the variability of brain sizes and proportions. The premise of the system is that brain components that cannot be seen or identified can be defined in relation to other anatomic cerebral structures. In the Talairach system, the anterior commissure (AC) and posterior commissure (PC) are the structures from which the system of reference is developed.

The Talairach system establishes the maximal dimensions of the brain in three planes of space: x, y and z:

AC-PC line (X axis)-A horizontal line running through the anterior and posterior commissures.

VCA line (verticofrontal line, or Y axis)-A vertical line passing through the anterior commissure

Midline (Z axis)-A line forming the interhemispheric sagittal plane

Often referred to as the "origin," the anterior commissure is commonly used to describe structures. For example, a structure is described as "AC 13 mm" for the frontal lobe or "AC - 35 mm" for the occipital pole. These descriptions assume that the anterior commissure is in the positive direction. However, the Talairach system does not use positive and negative directions. Instead, it labels quadrants according to number and letters ([TechGuide_Background.html#1005540 FigureÂ 15]A). The AC-PC line defines the horizontal plane, the VCA line defines the vertical plane, and the midline defines the depth plane. Because the anterior commissure and posterior commissure do not occur in the same axial slice, reslicing is necessary to put the brain into Talairach space.

File:TechGuide Backgrounda.gif

Jean Talairach and Pierre Tournoux, Co-Planar Stereotaxic Atlas of the Human Brain, Thieme Medical Publishers, New York, 1988.

This technical guide explains how to install and use two MIPAV plug-in programs-the Talairach Transformation wizard and FANTASM to:

Create the x, y, and z planes of space in an image of a brain

Transfer Talairach labels to an image of a brain

Measure brain components in Talairach space

**Figure 15. Talairach space: (A) Quadrants labeled by number and letters and (B) horizontal, vertical, and depth planes**

Talairach Transformation wizard

The Talairach Transformation wizard is a plug-in program for MIPAV that performs a semimanual transformation of image datasets of the brain to Talairach (stereotaxic) coordinates, providing atlas-based labeling. The Talairach coordinates allow researchers to easily identify subregions of the brain and measure their volume. It includes labels for 148 different substructures of the brain at various scales, obtained from the [ http://ric.uthscsa.edu/projects/talairachdaemon.html ]Talairach Daemon database, along with a set of volumetric images of the labels.

FANTASM

The FANTASM plug-in program is a different version of the Fuzzy C-mean algorithm for segmenting 2D and 3D images. It incorporates a spatial constraint that requires neighboring pixels to be similar and reduces the noise effect obtained with the Fuzzy C-mean algorithm. It can deal with outliers. Plans for a future version of FANTASM incorporates inhomogeneity correction.

References

ICBM atlas created by the International Consortium on Brain Mapping (ICBM), automatic
(http://www.loni.ucla.edu/ICBM/ICBM_BrainTemplate.html).

Jean Talairach and Pierre Tournoux, Co-Planar Stereotaxic Atlas of the Human Brain, Thieme Medical Publishers, New York, 1988.

Neva Chernizasky, Medical Imaging: Orientation, Paper prepared for Matthew McAuliiffe, Ph.D. Center for Information Technology, National Institutes of Health, August 31, 2001.

Dzung L. Pham, "Spatial Models for Fuzzy Clustering," Computer Vision and Image Understanding, vol. 84, pp. 285-297, 2001.

Pierre-Louis Bazin, Dzung L. Pham, William Gandler, and Matthew McAuliffe. "Free Software Tools for Atlas-based Volumetric Neuroimage Analysis," to be published in the Proceedings of the SPIE Medical Image 2005 Conference, The International Society for Optical Engineering (SPIE), Bellingham, Washington, 2005.

@@ Line 1: / Line 1: @@
-== Contents ==
+'''In this section . . .<br />'''
+*Background<br />
+*References <br />
+Designed specifically for medical researchers, MIPAV concentrates on providing those researchers with the tools needed to do their work. It reads image files of many different formats and allows images to be displayed and measured using the most meaningful method to achieve research goals. MIPAV's flexibility becomes apparent when its capabilities are expanded and fine tuned through the development of plug-in programs that tailor solutions to meet specific requirements.<br />
-[[B-Spline Automatic Registration]] chapter contains several sections:
+Using MIPAV to display, label, and measure brain components in Talairach space demonstrates both: MIPAV's native ability to display and measure brain images in Talairach space and the tailoring provided through the Talairach Transformation wizard and the FANTASM (Fuzzy and Noise Tolerant Adaptive Segmentation Method) plug-in programs, developed by the Johns Hopkins University.
-*[[B-Spline Automatic Registration]]
+== Background ==
+In 1988 Jean Talairach and Pierre Tournoux developed a three-dimensional proportional grid system that can be used to identify and measure brains from any number of patients despite the variability of brain sizes and proportions. The premise of the system is that brain components that cannot be seen or identified can be defined in relation to other anatomic cerebral structures. In the Talairach system, the anterior commissure (AC) and posterior commissure (PC) are the structures from which the system of reference is developed.<br />
-*[[BSpline registration: Detecting folding | B-Spline automatic registration: Detecting folding - you are here]]
+The Talairach system establishes the maximal dimensions of the brain in three planes of space: <span style="font-weight: normal; text-decoration: none; text-transform: none; vertical-align: baseline">''<font color="#000000">x, y</font>''</span> and <span style="font-weight: normal; text-decoration: none; text-transform: none; vertical-align: baseline">''<font color="#000000">z</font>''</span><nowiki>: </nowiki>
-*[[Examples of BSpline registration]]
+<div style="font-style: normal; font-weight: normal; margin-bottom: 0pt; margin-left: 24pt; margin-right: 0pt; margin-top: 5pt; text-align: left; text-decoration: none; text-indent: -24pt; text-transform: none; vertical-align: baseline"><font color="#000000">  <span style="font-weight: normal; text-decoration: none; text-transform: none; vertical-align: baseline">''<font color="#000000">AC-PC line (X axis)</font>''</span>-A horizontal line running through the anterior and posterior commissures. <br /></font></div><div style="font-style: normal; font-weight: normal; margin-bottom: 0pt; margin-left: 24pt; margin-right: 0pt; margin-top: 5pt; text-align: left; text-decoration: none; text-indent: -24pt; text-transform: none; vertical-align: baseline"><font color="#000000">  <span style="font-weight: normal; text-decoration: none; text-transform: none; vertical-align: baseline">''<font color="#000000">VCA line (verticofrontal line, or Y axis)</font>''</span>-A vertical line passing through the anterior commissure<br /></font></div><div style="font-style: normal; font-weight: normal; margin-bottom: 0pt; margin-left: 24pt; margin-right: 0pt; margin-top: 5pt; text-align: left; text-decoration: none; text-indent: -24pt; text-transform: none; vertical-align: baseline"><font color="#000000">  <span style="font-weight: normal; text-decoration: none; text-transform: none; vertical-align: baseline">''<font color="#000000">Midline (Z axis)</font>''</span>-A line forming the interhemispheric sagittal plane<br /></font></div>
-*[[User Dialogs in MIPAV | B-Spline Automatic Registration Dialog box]]
+Often referred to as the "origin," the anterior commissure is commonly used to describe structures. For example, a structure is described as "AC 13 mm" for the frontal lobe or "AC - 35 mm" for the occipital pole. These descriptions assume that the anterior commissure is in the positive direction. However, the Talairach system does not use positive and negative directions. Instead, it labels quadrants according to number and letters ([TechGuide_Background.html#1005540 FigureÂ 15]A). The AC-PC line defines the horizontal plane, the VCA line defines the vertical plane, and the midline defines the depth plane. Because the anterior commissure and posterior commissure do not occur in the same axial slice, reslicing is necessary to put the brain into Talairach space.
-== BSpline registration - Detecting folding ==
+{| align="left"
+|
+[[Image:TechGuide_Backgrounda.gif]]
+|}
-The situation of folding in a 2D or 3D B-spline transformation occurs when there is a negative value in the computed deformation. The computation of the deformation is described in Section "Deformation". This section describes a method for detecting if such folding occurs given the current positions for the lattice of the B-spline control points. Given the lattice structure of the B-spline control points, folding can be detected by geometric means. In two dimensions, consider any interior control point and its 8 neighboring control points forming a polygon. Construct 8 triangles involving the chosen interior control point each time with the 8 pairings of adjacent control points on the polygon perimeter. The intersection of any one triangle with the other 7 triangles should each be empty in order for there to be no folding. Alternatively, the area of the polygon should be identical to the union of the areas of the 8 triangles.
+<br clear="all" />Jean Talairach and Pierre Tournoux, <span style="font-weight: normal; text-decoration: none; text-transform: none; vertical-align: baseline">''<font color="#000000">Co-Planar Stereotaxic Atlas of the Human Brain</font>''</span>, Thieme Medical Publishers, New York, 1988.<br />
-The issues are similar in three dimensions by considering the 26 neighboring control points forming a polyhedron. In this case, 48 tetrahedrons are constructed involving the chosen interior control point each time along with the triples of control points from the 48 triangles forming the polyhedron mesh. The intersection of any one tetrahedron with the other 47 tetrahedrons should each be empty in order for there to be no folding. Alternatively, the volume of the polyhedron should be identical to the union of the volumes of the 48 tetrahedrons.
+This technical guide explains how to install and use two MIPAV plug-in programs-the Talairach Transformation wizard and FANTASM to:
-A sufficient but not necessary condition to conclude that folding occurs in the case of two dimensions is the premise that any interior control point is outside the polygon formed by its 8 neighboring control points. In the case of three dimensions, the premise is that any interior control point is outside the polyhedron formed by its 26 neighboring control points.
+<div style="font-style: normal; font-weight: normal; margin-bottom: 0pt; margin-left: 24pt; margin-right: 0pt; margin-top: 5pt; text-align: left; text-decoration: none; text-indent: -24pt; text-transform: none; vertical-align: baseline"><font color="#000000">  Create the <span style="font-weight: normal; text-decoration: none; text-transform: none; vertical-align: baseline">''<font color="#000000">x, y,</font>''</span> and <span style="font-weight: normal; text-decoration: none; text-transform: none; vertical-align: baseline">''<font color="#000000">z</font>''</span> planes of space in an image of a brain<br /></font></div><div style="font-style: normal; font-weight: normal; margin-bottom: 0pt; margin-left: 24pt; margin-right: 0pt; margin-top: 5pt; text-align: left; text-decoration: none; text-indent: -24pt; text-transform: none; vertical-align: baseline"><font color="#000000">  Transfer Talairach labels to an image of a brain<br /></font></div><div style="font-style: normal; font-weight: normal; margin-bottom: 0pt; margin-left: 24pt; margin-right: 0pt; margin-top: 5pt; text-align: left; text-decoration: none; text-indent: -24pt; text-transform: none; vertical-align: baseline"><font color="#000000">  Measure brain components in Talairach space<br /></font></div><div style="font-style: normal; font-weight: normal; margin-bottom: 0pt; margin-left: 0pt; margin-right: 0pt; margin-top: 0pt; text-align: left; text-decoration: none; text-indent: 0pt; text-transform: none; vertical-align: baseline"><font color="#000000"> <br /></font></div><div style="font-style: normal; font-weight: normal; margin-bottom: 0pt; margin-left: 0pt; margin-right: 0pt; margin-top: 0pt; text-align: left; text-decoration: none; text-indent: 0pt; text-transform: none; vertical-align: baseline"><font color="#000000">
-A condition that is both necessary and sufficient to conclude that folding occurs does exist for both 2D and 3D. In the case of two dimensions, again consider the 8 triangles formed by the chosen interior control point each time with the 8 pairings of adjacent control points on the polygon perimeter. It is important that these triangles formed by control points from the lattice be consistently counterclockwise ordered. For each triangle, let ''A =(a0,a1) ''be the 2D coordinates of the chosen interior control point, and let ''B =(b0,b1)'' and ''C =(c0,c1)'' be the 2D coordinates of the other two triangle control points taken in counterclockwise order. The normal to the plane which contains this triangle can be computed from the (right handed) cross product of the two vectors AB and AC. One way to express the calculation of the cross product involves the construction of the following matrix which contains the three triangle point coordinates:
+{| border="1" cellpadding="5"
+|+ <div style="font-style: normal; margin-bottom: 3pt; margin-left: 0pt; margin-right: 0pt; margin-top: 9pt; text-align: left; text-decoration: none; text-indent: 0pt; text-transform: none; vertical-align: baseline">'''<font color="#000000"> Figure 15. Talairach space: (A) Quadrants labeled by number and letters and (B) horizontal, vertical, and depth planes<br /></font>'''</div>
+|-
+|
+[[Image:exampleTalairachCubeBrain.gif]]
+|}
+=== Talairach Transformation wizard ===
+The Talairach Transformation wizard is a plug-in program for MIPAV that performs a semimanual transformation of image datasets of the brain to Talairach (stereotaxic) coordinates, providing atlas-based labeling. The Talairach coordinates allow researchers to easily identify subregions of the brain and measure their volume. It includes labels for 148 different substructures of the brain at various scales, obtained from the <span style="font-style: normal; font-weight: normal; text-transform: none; vertical-align: baseline"><u><font color="#000000">[ http://ric.uthscsa.edu/projects/talairachdaemon.html ]</font></u></span><span style="font-style: normal; font-weight: normal; text-decoration: none; text-transform: none; vertical-align: baseline"><font color="#000000">Talairach Daemon database</font></span>, along with a set of volumetric images of the labels.<br /></font></div>
-<div id="Eq13"></div>
+=== FANTASM ===
+The FANTASM plug-in program<span style="font-style: normal; font-weight: normal; text-decoration: none; text-transform: none; vertical-align: baseline"><font color="#000000"> is a different version of the Fuzzy C-mean algorithm for segmenting 2D and 3D images. It incorporates a spatial constraint that requires neighboring pixels to be similar and reduces the noise effect obtained with the Fuzzy C-mean algorithm. It can deal with outliers. Plans for a future version of FANTASM incorporates inhomogeneity correction. </font></span><br />
-[[File:BSplineRegistrationEq13.jpg|left|Equation 13]]
+== References ==
+ICBM atlas created by the International Consortium on Brain Mapping (ICBM), automatic <br />(<span style="font-style: normal; font-weight: normal; text-transform: none; vertical-align: baseline"><u><font color="#000000">http://www.loni.ucla.edu/ICBM/ICBM_BrainTemplate.html</font></u></span>).<br />
+<div style="font-style: normal; font-weight: normal; margin-bottom: 4pt; margin-left: 0pt; margin-right: 0pt; margin-top: 11pt; text-align: left; text-decoration: none; text-indent: 0pt; text-transform: none; vertical-align: baseline"><font color="#000000"> Jean Talairach and Pierre Tournoux, <span style="font-weight: normal; text-decoration: none; text-transform: none; vertical-align: baseline">''<font color="#000000">Co-Planar Stereotaxic Atlas of the Human Brain</font>''</span>, Thieme Medical Publishers, New York, 1988. <br /></font></div><div style="font-style: normal; font-weight: normal; margin-bottom: 4pt; margin-left: 0pt; margin-right: 0pt; margin-top: 11pt; text-align: left; text-decoration: none; text-indent: 0pt; text-transform: none; vertical-align: baseline"><font color="#000000"> Neva Chernizasky, <span style="font-weight: normal; text-decoration: none; text-transform: none; vertical-align: baseline">''<font color="#000000">Medical Imaging: Orientation</font>''</span>, Paper prepared for Matthew McAuliiffe, Ph.D. Center for Information Technology, National Institutes of Health, August 31, 2001.<br /></font></div><div style="font-style: normal; font-weight: normal; margin-bottom: 4pt; margin-left: 0pt; margin-right: 0pt; margin-top: 11pt; text-align: left; text-decoration: none; text-indent: 0pt; text-transform: none; vertical-align: baseline"><font color="#000000"> Dzung L. Pham, "Spatial Models for Fuzzy Clustering," <span style="font-weight: normal; text-decoration: none; text-transform: none; vertical-align: baseline">''<font color="#000000">Computer Vision and Image Understanding</font>''</span>, vol. 84, pp. 285-297, 2001.<br /></font></div><div style="font-style: normal; font-weight: normal; margin-bottom: 4pt; margin-left: 0pt; margin-right: 0pt; margin-top: 11pt; text-align: left; text-decoration: none; text-indent: 0pt; text-transform: none; vertical-align: baseline"><font color="#000000"> Pierre-Louis Bazin, Dzung L. Pham, William Gandler, and Matthew McAuliffe. "Free Software Tools for Atlas-based Volumetric Neuroimage Analysis," to be published in the <span style="font-weight: normal; text-decoration: none; text-transform: none; vertical-align: baseline">''<font color="#000000">Proceedings of the SPIE Medical Image 2005 Conference</font>''</span>, The International Society for Optical Engineering (SPIE), Bellingham, Washington, 2005.<br /></font></div>
-The determinant of this matrix is twice the signed area of the triangle. Starting with consistently counter clockwise ordered triangles from the initially placed lattice of control points, the determinant of this matrix should remain positive as control point positions are moved. The determinant will become negative when the triangle ''folds''.
-The premise for the necessary and sufficient condition to detect when folding occurs extends to three dimensions. Consider the 48 tetrahedrons formed by the chosen interior control point each time with the triples of adjacent control points from the 48 triangles forming the polyhedron mesh. It is important that the tetrahedrons formed by the control points from the lattice be consistently counterclockwise ordered, in the 3D sense. For each tetrahedron, let ''A = (a0,a1,a2)'' be the 3D coordinates of the chosen interior control point, and let ''B = (b0,b1,b2)'', ''C = (c0,c1,c2)'', and ''D = (d0,d1,d2)'' be the 3D coordinates of the other three tetrahedron control points taken in counterclockwise order. Extending the matrix determinant formulation used for two dimensions to three dimensions, the following matrix is constructed which contains the four tetrahedron point coordinates:
-<div><div align="left">
-<math>
-\begin{bmatrix} a_0 & a_1 & a_2 & 1 \\ b_0 & b_1 & b_2 & 1 \\ c_0 & c_1 & c_2 & 1 \\  d_0 & d_1 & d_2 & 1 \\ \end{bmatrix}
-</math></div> </div>
-The determinant of this matrix is 6 times the signed volume of the tetrahedron. Starting with consistently counterclockwise ordered tetrahedrons from the initially placed lattice of control points, the determinant of this matrix should remain positive as control point positions are moved. The determinant will become negative when the tetrahedron ''folds''.
-== BSpline registration - Image types ==
-The algorithm can be applied to 2D and 3D color (RGB) and grayscale images
-=== Support for color images ===
-The registration of 2D and 3D color images involves first converting the three color channels of values at each sample in the source and target color images to create single channel source and target intensity images. Once the conversion has been done, the single channel intensity source and target images are registered as described in [[BSplineRegistrationOV_withMath.html#wp1011586|Background]]. The resulting transformation map is extracted from the registration which is then used to interpolate the original source color image in order to generate the output registered source color image.
-Normally, the three color channels represent red, green, and blue intensities, and so the conversion to a single channel value usually represents overall intensity. In this manner, the conversion is simply a weighted average of the three color channels where separate weights can be provided for each channel. The current implementation uses equal weights for each channel.
-=== Support for 2.5D images ===
-A 2.5D image is actually a 3D image containing a series 2D slice images. The registration of a 2.5D intensity or color image involves a 2D registration of each slice in the 2.5D image to a reference slice also in the same 2.5D image. The reference slice can either be a xed slice or the previous slice. The resulting output registered 2.5D image contains the same number of slices as the original 2.5D image where the sample values in a slice of the registered output are from the same slice of the original only "warped" by the B-spline registration transformation.
-If the reference slice is fixed, then the reference slice will appear in the registered output as being unchanged. If the reference slice is the previous slice, then the first slice will be registered to the last slice.
-== Next ==
-*[[B-Spline Automatic Registration]]
-*[[BSpline registration: Detecting folding | B-Spline automatic registration: Detecting folding - you are here]]
-*[[Examples of BSpline registration]]
-*[[User Dialogs in MIPAV | B-Spline Automatic Registration Dialog box]]
-[[Category:Help]]
-[[Category:Help:Algorithms]]