Projects:SphericalWaveletsInITK - Revision history

Ygao at 01:13, 16 November 2013

2013-11-16T01:13:57Z

Melonakos at 01:37, 28 November 2007

2007-11-28T01:37:57Z

Melonakos at 13:49, 4 September 2007

2007-09-04T13:49:24Z

Melonakos at 13:38, 4 September 2007

2007-09-04T13:38:35Z

Melonakos at 01:28, 4 September 2007

2007-09-04T01:28:44Z

Melonakos at 16:32, 21 August 2007

2007-08-21T16:32:02Z

Melonakos: NA-MIC/Projects/Structural/Shape Analysis/Spherical Wavelets in ITK moved to Projects:SphericalWaveletsInITK

2007-08-21T16:12:10Z

NA-MIC/Projects/Structural/Shape Analysis/Spherical Wavelets in ITK moved to Projects:SphericalWaveletsInITK

Delphine: /* Description */

2007-01-09T19:12:19Z

Description

Delphine: /* Implementation */

2007-01-08T21:33:18Z

Implementation

Ygao at 19:04, 7 January 2007

2007-01-07T19:04:58Z

← Older revision		Revision as of 01:13, 16 November 2013
Line 1:		Line 1:
−	Back to [[NA-MIC_Collaborations\|NA-MIC_Collaborations]], [[Algorithm:~~GATech~~\|~~Georgia Tech~~ Algorithms]], [[Algorithm:UNC\|UNC Algorithms]]	+	Back to [[NA-MIC_Collaborations\|NA-MIC_Collaborations]], [[Algorithm:Stony Brook\|Stony Brook Algorithms]], [[Algorithm:UNC\|UNC Algorithms]]

	= ITK Spherical Wavelet Transform Filter =		= ITK Spherical Wavelet Transform Filter =

@@ Line 1: / Line 1: @@
   Back to [[NA-MIC_Collaborations|NA-MIC_Collaborations]], [[Algorithm:GATech|Georgia Tech Algorithms]], [[Algorithm:UNC|UNC Algorithms]]
-'''Objectives'''
+= ITK Spherical Wavelet Transform Filter =
 For a general description of how we are using spherical wavelets for shape analysis, see [[Algorithm:GATech:Multiscale_Shape_Analysis|Multiscale Shape Analysis]]
 This page outlines the steps we will take to code the Spherical Wavelet transform in ITK.
@@ Line 24: / Line 24: @@
 * The forward wavelet transformation is carried out on the configuration of the previous step and a set of wavelet coefficients are obtained, called Gamma coefficients. The backward transformation can recover the Gamma coefficients into an approximation of the original scalar function.
-'''Progress'''
+''Progress''
 * Before the spherical wavelet transformation, the scalar function is interpolated onto a sphere which is generated from recursively subdividing an icosahedron and which has the least number of vertexes more than that of the original mesh.
@@ Line 48: / Line 48: @@
 * We will discuss the filter interfaces to fit this into the whole procedure of shape analysis.
-''References''
+= Key Investigators =
 * Georgia Tech: Yi Gao, Delphine Nain, Xavier LaFaucheur, John Melonakos
@@ Line 57: / Line 55: @@
 * UNC: Martin Styner
-'''Links'''
+= Links =
 * [[NA-MIC/Projects/Structural/Shape_Analysis/3D_Shape_Analysis_Using_Spherical_Wavelets|3D Shape Analysis Using Spherical Wavelets]]
 * [[NA-MIC/Projects/Structural/Shape_Analysis/ITK_Spherical_Wavelets_API|ITK Spherical Wavelets API]]

@@ Line 1: / Line 1: @@
 = ITK Spherical Wavelet Transform Filter =
-  Back to [[NA-MIC_Collaborations|NA-MIC_Collaborations]]
+  Back to [[NA-MIC_Collaborations|NA-MIC_Collaborations]], [[Algorithm:GATech|Georgia Tech Algorithms]], [[Algorithm:UNC|UNC Algorithms]]
 '''Objectives'''

@@ Line 3: / Line 3: @@
   Back to [[NA-MIC_Collaborations|NA-MIC_Collaborations]]
-'''Objective'''
+'''Objectives'''
 For a general description of how we are using spherical wavelets for shape analysis, see [[Algorithm:GATech:Multiscale_Shape_Analysis|Multiscale Shape Analysis]]
@@ Line 47: / Line 47: @@
 * We will discuss the filter interfaces to fit this into the whole procedure of shape analysis.
 '''Key Investigators'''
-* GaTech: Yi Gao, Delphine Nain, Xavier LaFaucheur, John Melonakos
+* Georgia Tech: Yi Gao, Delphine Nain, Xavier LaFaucheur, John Melonakos
 * GE: Jim Miller
 * Kitware: Luis Ibanez

@@ Line 1: / Line 1: @@
   Back to [[NA-MIC_Collaborations|NA-MIC_Collaborations]]
-== Description ==
+'''Objective'''
 For a general description of how we are using spherical wavelets for shape analysis, see [[Algorithm:GATech:Multiscale_Shape_Analysis|Multiscale Shape Analysis]]
@@ Line 22: / Line 24: @@
 * The forward wavelet transformation is carried out on the configuration of the previous step and a set of wavelet coefficients are obtained, called Gamma coefficients. The backward transformation can recover the Gamma coefficients into an approximation of the original scalar function.
-== Implementation ==
+'''Progress'''
 * Before the spherical wavelet transformation, the scalar function is interpolated onto a sphere which is generated from recursively subdividing an icosahedron and which has the least number of vertexes more than that of the original mesh.
@@ Line 37: / Line 39: @@
 For a preliminary API, see [[NA-MIC/Projects/Structural/Shape_Analysis/ITK_Spherical_Wavelets_API|ITK Spherical Wavelets API]]
-== Current Status ==
+''Current Status''
 * Basically it's all set. All thing we need are stored internally.
 * So the only thing needs to be done is to choose what data to output and how to output them to fit in the whole process of shape analysis pipeline.
-== Next Steps ==
+''Next Steps''
 * We will discuss the filter interfaces to fit this into the whole procedure of shape analysis.
-== Members ==
+'''Key Investigators'''
-* Yi Gao (Gatech)
+* GaTech: Yi Gao, Delphine Nain, Xavier LaFaucheur, John Melonakos
-* Delphine Nain (Gatech)
+* GE: Jim Miller
-* Xavier LeFaucheur (Gatech)
+* Kitware: Luis Ibanez
-* John Melonakos (Gatech)
+* UNC: Martin Styner
-== Links ==
+'''Links'''
 * [[NA-MIC/Projects/Structural/Shape_Analysis/3D_Shape_Analysis_Using_Spherical_Wavelets|3D Shape Analysis Using Spherical Wavelets]]
 * [[NA-MIC/Projects/Structural/Shape_Analysis/ITK_Spherical_Wavelets_API|ITK Spherical Wavelets API]]

← Older revision		Revision as of 16:32, 21 August 2007
Line 1:		Line 1:
		+	Back to [[NA-MIC_Collaborations\|NA-MIC_Collaborations]]
		+
	== Description ==		== Description ==

← Older revision	Revision as of 16:12, 21 August 2007
(No difference)

@@ Line 28: / Line 28: @@
 * The processes going within the class are:
 # The hierarchy of the recursive subdivision is built from the icosahedron. The parameters needed for wavelet decomposition are calculated and stored in the internally. The level of the subdivision is chosen so that the finest sphere in the subdivision coincides with the one in the previous interpolation step.
 # The scalar function is set using the API SetScalarFunction().
 # The wavelet coefficients are calculated from the finest level and downward. It's and implementation of the lifting scheme of the second generation of wavelet transformation.
 # The coefficients of all levels are stored in one structure of vector and can be exported to a file if needed.
 # If needed, the reconstruction of function can be carried out from the coefficients. The difference between the reconstructed function and the original function is around 10^{-16}.

@@ Line 12: / Line 12: @@
 In this paper, it is shown how to do decompose a scalar signal defined on a spherical mesh into spherical wavelet coefficients (analysis step, also called forward transform), and vice-versa (synthesis step, also called inverse transform).
-* With the goal of analysizing the scalar function defined on a spherical topological surface, the spherical parametrization is needed as the first step. Then, we can deem the function to be defined on a sphere. (If the function is a vector one, we can apply the analysis component by component. Thus the scalar function is used for simplicity in the future.)
+* With the goal of analyzing the scalar function defined on a spherical topological surface, the spherical parametrization is needed as the first step. Then, we can deem the function to be defined on a sphere. (If the function is a vector one, we can apply the analysis component by component. Thus the scalar function is used for simplicity in the future.)
-* For our specific case of SHAPE representation, the function we are going to analize are the x, y and z coordinates of the original triangulated surface.
+* For our specific case of SHAPE representation, the function we are going to analyze are the x, y and z coordinates of the original triangulated surface.
 * The numerical computation of spherical wavelet analysis requires the scalar function to be defined on a special triangulated sphere, the one generated by a recursive subdivision process. Also for a better performance, the base shape of the triangulation is selected as an icosahedron. The scalar function defined on the original spherical mesh is then interpolated onto the mesh generated by the recursive subdivision using bi-linear interpolation.
@@ Line 31: / Line 31: @@
 # The scalar function is set using the API SetScalarFunction().
-# The wavelet coefficients are calculated from the finest level and downward. It's and implementation of the lifting scheme of the second generation of wavelet transformatiom.
+# The wavelet coefficients are calculated from the finest level and downward. It's and implementation of the lifting scheme of the second generation of wavelet transformation.
 # The coefficients of all levels are stored in one structure of vector and can be exported to a file if needed.