TypeArithmetic1

MLModule

genre	NonScalar
author	MeVis Medical Solutions AG
package	MeVisLab/Standard
dll	MLTypeSupport
definition	MLTypeSupport.def
see also	TypeComposer, TypeFromScalars, TypeFromDimension, Info, TypeDecomposer, TypeArithmetic2, Arithmetic0, Arithmetic1, Arithmetic2, ComplexArithmetic1, ComplexArithmetic2
keywords	unary, single, arithmetics, registered, extended, carrier, datatype, converters, reformats, reorder, component, conversions, matrix, tensor, vector, complex, quaternion, invert, negate, flip, eigen, trace, project, identity, tensorarithmetic

Purpose

The module TypeArithmetic1 offers a large number of operations to modify, convert, and process images of non-scalar data types such as vec3, vec3f, mat3, matf3, vector, quaterniond, complexd, and many more.

Details

Internally, all operations are calculated in double type. For example, the two component types vecf2, complexf, complexd, and complexld are implicitly handled as type vec2, and all six component types such as vecf6, Vector16, Vector, and Vector64 are implicitly handled as vec6. The same holds for the quaternion types quaternionf, quaterniond, and quaternionld, which are handled as vec4 values.

If you need explicit operations on complex voxels, then use dedicated modules for complex arithmetic such as ComplexArithmetic1, ComplexArithmetic2, ComplexToReal, or the complex modules from ITK.

Windows

Default Panel

Input Fields

input0

name: input0, type: Image

Output Fields

output0

name: output0, type: Image

Parameter Fields

Field Index

Const Components: String

DoubleParam1: Double

Index List: String

IntParam1: Integer

IntParam2: Integer

Operation: Enum

Visible Fields

Operation

name: operation, type: Enum, default: VecToFlippedVec, deprecated name: conversion

Defines the conversion operation.

Values:

Title	Name	Deprecated Name	Description
Vec To Flipped Vec	VecToFlippedVec		Converts the vectors in voxels to vectors in voxels with the opposite component order.
Vec To Mat	VecToMat		Builds a matrix for voxels, converting each voxel’s vector into a matrix where the vector components are stored in the matrix’s diagonal.
Vec Normalize	VecNormalize		Normalizes the vector voxels.
Vec Normalize To Length	VecNormalizeToLength		Normalizes the vector voxels to an arbitrary length.
Vec Length	VecLength		Sets the length of the vector voxels.
Vec Length2	VecLength2		Sets the squared length of all vector components.
Comp Sum	CompSum	VecCompSum	Computes the sum of all components.
Comp Mul	CompMul	VecCompMul	Computes the product of all components.
Comp Max Abs	CompMaxAbs	VecCompMaxAbs	Sets the maximum of absolute values of components.
Comp Min Abs	CompMinAbs		Sets the minimum of absolute values of components.
Comp Scale	CompScale		Scales all components with the DoubleParam1, which becomes visible when this mode is selected.
Max Comp Pos	MaxCompPos	VecMaxCompDim	Calculates the position of the maximum component value; if more than one is found, then the first is taken.
Min Comp Pos	MinCompPos		Calculates the position of the minimum component value; if more than one is found, then the first is taken.
Comp Max	CompMax	VecCompMax	Sets the maximum vector component.
Comp Min	CompMin	VecCompMin	Sets the minimum vector component.
Mat To Transposed Mat	MatToTransposedMat		Transposes the matrix voxels.
Mat To Inverse Mat	MatToInverseMat		Inverts the matrix voxels or - if that is not possible - sets the identity.
Mat To Determinant	MatToDeterminant		Sets the determinant of the matrix voxels as scalar values.
Mat Trace	MatTrace		Calculates the trace of matrix voxels as scalar values.
Mat Diagonal To Vec	MatDiagonalToVec		Calculates diagonal elements of matrix voxels as vectors of the matrix dimension.
Mat To Submatrix	MatToSubmatrix		Builds a matrix for the particular row or line, selected in IntParam1 and IntParam2, which become visible when this mode is selected.
Mat Column0To Vec	MatColumn0ToVec		Extracts column 0 from the matrix voxels to vector voxels of the matrix dimension.
Mat Column1To Vec	MatColumn1ToVec		Extracts column 1 from the matrix voxels to vector voxels of the matrix dimension.
Mat Column2To Vec	MatColumn2ToVec		Extracts column 2 from the matrix voxels to vector voxels of the matrix dimension.
Mat Column3To Vec	MatColumn3ToVec		Extracts column 3 from the matrix voxels to vector voxels of the matrix dimension.
Mat Column4To Vec	MatColumn4ToVec		Extracts column 4 from the matrix voxels to vector voxels of the matrix dimension.
Mat Column5To Vec	MatColumn5ToVec		Extracts column 5 from the matrix voxels to vector voxels of the matrix dimension.
Mat Row0To Vec	MatRow0ToVec		Extracts row 0 from the matrix voxels to vector voxels of the matrix dimension.
Mat Row1To Vec	MatRow1ToVec		Extracts row 1 from the matrix voxels to vector voxels of the matrix dimension.
Mat Row2To Vec	MatRow2ToVec		Extracts row 2 from the matrix voxels to vector voxels of the matrix dimension.
Mat Row3To Vec	MatRow3ToVec		Extracts row 3 from the matrix voxels to vector voxels of the matrix dimension.
Mat Row4To Vec	MatRow4ToVec		Extracts row 4 from the matrix voxels to vector voxels of the matrix dimension.
Mat Row5To Vec	MatRow5ToVec		Extracts row 5 from the matrix voxels to vector voxels of the matrix dimension.
Mat To Ordered Eigen Values	MatToOrderedEigenValues		Sets ascending eigenvalues of matrix voxels to vector components.
Mat To Ordered Eigen Vectors	MatToOrderedEigenVectors		Sets ascending eigenvectors of matrix voxels to matrix rows.
Mat To Ordered Scaled Eigen Vectors	MatToOrderedScaledEigenVectors		Sets ascending eigenvectors of matrix voxels to matrix rows scaled with eigenvalues.
To Mat2Identity	ToMat2Identity		Sets mat2 identity voxels.
To Mat3Identity	ToMat3Identity		Sets mat3 identity voxels.
To Mat4Identity	ToMat4Identity		Sets mat4 identity voxels.
To Mat5Identity	ToMat5Identity		Sets mat5 identity voxels.
To Mat6Identity	ToMat6Identity		Sets mat6 identity voxels.
Vec3To Vec4Point	Vec3ToVec4Point		Converts vec3 to vec4 representing a homogeneous point by appending a 0.
Vec3To Vec4Vector	Vec3ToVec4Vector		Converts vec3 to vec4 representing a homogeneous vector by appending a 0.
Vec4To Vec3Point	Vec4ToVec3Point		Converts homogeneous vec4 vector to a vec3 representing a point. 0 scale components in last vector component are silently replaced by 1 to avoid division by zero.
Vec4To Vec3Vector	Vec4ToVec3Vector		Converts homogeneous vec4 vector to a vec3 representing a vector by dropping the last vec4 component.
Vec3To Mat4	Vec3ToMat4		Builds a mat4 with first 3 diagonal elements given by vec3 components and a 1 in bottom right.
Mat3To Mat4	Mat3ToMat4		Builds a mat4 with upper left 3x3 elements from mat3 and a 1 in the bottom right element (and 0 else).
Mat4To Mat3	Mat4ToMat3		Builds a mat3 from upper left 3x3 elements of mat4.
Vec6Tensor To LLRows In Mat3	Vec6TensorToLLRowsInMat3		Builds a packed tensor in vec6 to lower left mat3 triangle, where the matrix is filled row by row. Assuming that the mat3 components are indexed row by row from m0-m8, and the vec6 from v0-v5, then the resulting mat3 is ((v0,0,0), (v1,v2,0), (v3,v4,v5)).
Vec6Tensor To LLCols In Mat3	Vec6TensorToLLColsInMat3		Builds a packed tensor in vec6 to lower left mat3 triangle where the matrix is filled column by column. Assuming that the mat3 components are indexed row by row from m0-m8, and the vec6 from v0-v5, then the resulting mat3 is ((v0,0,0), (v1,v3,0), (v2,v4,v5)).
Vec6Tensor To Ordered Eigen Values	Vec6TensorToOrderedEigenValues		Computes ascending eigenvalues from 3x3 tensor (vec6).
Vec6Tensor To Ordered Eigen Vectors	Vec6TensorToOrderedEigenVectors		Computes ascending eigenvectors from 3x3 tensor (vec6). Result is stored in mat3 type.
Mat3LLRows To Vec6Tensor	Mat3LLRowsToVec6Tensor		Sets the lower left mat3 triangle of matrix to packed tensor in vec6 where the mat3 is read row by row. Assuming that the mat3 components are indexed row by row from m0-m8, and the vec6 from v0-v5, then the resulting vec6 is (m0,m3,m4,m6,m7,m8).
Mat3LLCols To Vec6Tensor	Mat3LLColsToVec6Tensor		Sets the lower left mat3 triangle of matrix to packed tensor in vec6 where the mat3 is read column by column. Assuming that the mat3 components are indexed row by row from m0-m8, and the vec6 from v0-v5, then the resulting vec6 is (m0,m3,m6,m4,m7,m8).
Vec3To Vec6Tensor Product	Vec3ToVec6TensorProduct		Computes tensor product of input vector with itself (vx^2, vx*vy, vx*vz, vy^2, vy*vz, vz^2)
Project Vec To Dim	ProjectVecToDim		Projects a vector to dimension selected in IntParam1, which becomes visible when this mode is selected.
Comp Mul Const	CompMulConst		Multiplies the values given in Const Components with the corresponding components of the input voxel. If not enough values are specified in Const Components, the list is automatically padded with zeros.
Comp Add Const	CompAddConst		Adds the values given in Const Components to the corresponding components of the input voxel. If not enough values are specified in Const Components, the list is automatically padded with zeros.
Reorder Comps	ReorderComps		Reorders the components of the input voxels, so that they are stored in the order as described in Index List. If Index List is too short, it is automatically padded with zeros. Indexes out of range will be clamped against the valid range of component indexes.
Mat Mult Const Mat	MatMultConstMat		Multiplies all matrix voxels of an input image with a given constant matrix of the same size whose values are given in Const Components. Missing values in Const Components are automatically appended as zeros.
Mat Mult Const Vec	MatMultConstVec		Multiplies all matrix voxels of an input image with a given constant vector of the same size whose values are given in Const Components. Missing values in Const Components are automatically appended as zeros.
Vec Mult Const Mat	VecMultConstMat		Multiplies all vector voxels of an input image with a given constant matrix of the same size whose values are given in Const Components. Missing values in Const Components are automatically appended as zeros.
Vec Dot Const Vec	VecDotConstVec		Multiplies all vector voxels of dimension 2-6 of an input image with a given constant vector of the same dimension and whose values are given in Const Components. Missing values in Const Components are automatically appended as zeros.
Vec To Phong Diffuse	VecToPhongDiffuse		Computes the normalized difference vector between the current voxel position and a given constant vector. The result voxel is the scalar product between the input vector voxel and the normalized difference vector. This mode operates only on input voxels of dimension 2-6.: ResultVoxel = ScalarProduct( InputVectorVoxel, Norm(ConstantVector - VoxelPosition)) This is comparable to the diffuse Phong lighting calculation often used in computer graphics. The result values can be interpreted as a similarity measurement of the current input vector and a direction vector of the current voxel coordinate relative to a given point or light source.
Sort Ascending	SortAscending		Sorts all voxel components in ascending order.
Sort Descending	SortDescending		Sorts all voxel components in descending order.
Sort Ascending Abs	SortAscendingAbs		Sorts all absolute voxel components in ascending order.
Sort Descending Abs	SortDescendingAbs		Sorts all absolute voxel components in descending order.
Sort Ascending Idx	SortAscendingIdx		Sorts all voxel components in ascending order; results are the corresponding component indexes.
Sort Descending Idx	SortDescendingIdx		Sorts all voxel components in descending order; results are the corresponding component indexes.
Sort Ascending Abs Idx	SortAscendingAbsIdx		Sorts all absolute voxel components in ascending order; results are the corresponding component indexes.
Sort Descending Abs Idx	SortDescendingAbsIdx		Sorts all absolute voxel components in descending order; results are the corresponding component indexes.

IntParam1

name: parameterX, type: Integer, default: 0, deprecated name: dimension

Sets a value for row or dimension selection.

IntParam2

name: parameterY, type: Integer, default: 0

Sets a value for column or position selection.

DoubleParam1

name: value, type: Double, default: 0

Sets a scale factor or floating-point value.

Index List

name: intList, type: String

Sets a list of source component indexes to be stored in target components.

Const Components

name: dblList, type: String

Sets a list of factors or summands to be multiplied or added with vector components.