Basic Image AlgorithmS Library
2.8.0
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A quadric as a 4x4 matrix describing a surface in 3d projective space defined by a quadratic equation, e.g. More...
#include <Geometry/Quadric3D.hh>
Public Types | |
typedef const T * | const_iterator |
typedef const T & | const_reference |
typedef T | element_type |
typedef T * | iterator |
typedef T * | pointer |
typedef T & | reference |
typedef Subscript | size_type |
typedef T | value_type |
Public Member Functions | |
void | AbsIP () |
absolute values of all elements of the matrix (in place) More... | |
Matrix< QUADRIC3D_TYPE > | Adjoint () const |
computes the adjoint matrix More... | |
void | clear () |
stl conform interface More... | |
QUADRIC3D_TYPE | det () const |
calculate the determinant recursively using sub matrices of size 3x3 More... | |
Subscript | dim (Subscript d) const |
void | GaussJordan () |
use the Gauss Jordan Algrithm to transform the matrix to reduced row echelon form. More... | |
Quadric3D | GetDualQuadric (bool UseSVD=false) const |
computes the dual quadric (points <-> planes) More... | |
Matrix< QUADRIC3D_TYPE > | GetMax (Matrix< QUADRIC3D_TYPE > &m) |
returns an matrix the same size as the matrix n and m with the largest elements taken from n or m More... | |
Matrix< QUADRIC3D_TYPE > | GetMin (Matrix< QUADRIC3D_TYPE > &m) |
returns an matrix the same size as the matrix n and m with the smallest elements taken from n or m More... | |
unsigned int | GetSignature () |
computes signature of matrix, (no. More... | |
initialize (M, N) | |
bool | IsIdentity (double eps=0.0) const |
Checks if the matrix a an identity. More... | |
bool | IsZero (double eps=0.0) const |
Checks if the matrix is a null matrix. More... | |
void | Kronecker (Matrix< QUADRIC3D_TYPE > const B, Matrix< QUADRIC3D_TYPE > &dest) const |
Kronecker-product with matrix, result in dest. More... | |
Subscript | lbound () const |
double | LocatePoint (const HomgPoint3D &point3D) const |
determines if point3D is inside/on/outside the surface More... | |
void | Mult (const Vector4< QUADRIC3D_TYPE > &argvec, Vector4< QUADRIC3D_TYPE > &destvec) const |
matrix - vector multiplicate this matrix with Vector4, storing the result in destvec, calculates: destvec = (this Matrix) * argvec More... | |
void | Mult (const Matrix4x4< QUADRIC3D_TYPE > &argmat, Matrix4x4< QUADRIC3D_TYPE > &destmat) const |
matrix-matrix multiplication with other Matrix4x4, storing the result in destmat using 'manual inlining' More... | |
Matrix< T > & | newsize (Subscript M, Subscript N) |
Matrix4x4 & | newsize (int rows, int cols) |
just neccessary to avoid resizing of this 'fixed size' matrix because it is derived from the resizable Matrix Should be removed if Matrix4x4 becomes a base class. More... | |
bool | Normalize () |
sets trace of upperleft submatrix3x3 to unity More... | |
Subscript | num_cols () const |
Subscript | num_rows () const |
reference | operator() (Subscript i) |
const_reference | operator() (Subscript i) const |
reference | operator() (Subscript i, Subscript j) |
const_reference | operator() (Subscript i, Subscript j) const |
Quadric3D & | operator= (const Matrix< QUADRIC3D_TYPE > &M) |
T * | operator[] (Subscript i) |
const T * | operator[] (Subscript i) const |
std::ostream & | Print (std::ostream &s, const int width, const int precision, bool scientific=true) const |
std::ostream & | Print (std::ostream &s, const bool intCastOutput=false, const bool binaryOutput=false, const bool forceFullPrecision=false) const |
std::ostream & | PrintPretty (std::ostream &s, const std::string &name="", const int width=8, const bool alignLeft=true) const |
Quadric3D () | |
Quadric3D (const MatrixInitType &i) | |
set default matrix values More... | |
Quadric3D (const Matrix< QUADRIC3D_TYPE > &M) | |
Quadric3D (const HomgPoint3D &C, const CovMatrix3x3 &cov, const double &dScale=GAUSS3D_CONFIDENCE_20_PERCENT) | |
constructs an ellipsoid around the center C More... | |
std::istream & | Read (std::istream &s, const bool intCastInput=false, const bool binaryInput=false) |
JW. More... | |
set (value) | |
void | SetIdentity () |
set the elements of this matrix to the identity matrix (posisbly overriding the inherited method) More... | |
Subscript | size () const |
void | SwapRows (const int i, const int r) |
swaps two rows More... | |
Matrix4x4 | Transpose () const |
void | TransposeIP () |
tranpose this matrix "in place" example: 0 1 2 3 –> 0 4 8 12 4 5 6 7 –> 1 5 9 13 8 9 10 11 –> 2 6 10 14 12 13 14 15 –> 3 7 11 15 More... | |
void | Vec (Vector< QUADRIC3D_TYPE > &dest) const |
vec-operator returns the elements of the matrix columwise as vector More... | |
Arithmetic | |
void | Mult (const Matrix< QUADRIC3D_TYPE > &arg, Matrix< QUADRIC3D_TYPE > &result) const |
matrix multiplication, result is not allocated More... | |
void | Mult (const Matrix< QUADRIC3D_TYPE > &arg) |
in Place matrix multiplication this is equal to M = M * arg, but faster More... | |
void | Mult (const Vector< QUADRIC3D_TYPE > &arg, Vector< QUADRIC3D_TYPE > &result) const |
matrix vector multiplication, result is not allocated More... | |
void | AddIP (const QUADRIC3D_TYPE &scalar) |
in place addition function More... | |
void | AddIP (const Matrix< QUADRIC3D_TYPE > &arg) |
Adds arg to this. More... | |
void | SubIP (const Matrix< QUADRIC3D_TYPE > &arg) |
Subtracts arg from this this -= arg. More... | |
void | SubIP (const QUADRIC3D_TYPE &scalar) |
in place subtraction function More... | |
void | Add (const QUADRIC3D_TYPE &scalar, Matrix< QUADRIC3D_TYPE > &dest) const |
addition function, storing data destination matrix More... | |
void | Sub (const QUADRIC3D_TYPE &scalar, Matrix< QUADRIC3D_TYPE > &dest) const |
substraction function, storing data destination matrix More... | |
void | MultiplyIP (const QUADRIC3D_TYPE &scalar) |
in place multiplication function More... | |
void | Multiply (const QUADRIC3D_TYPE &scalar, Matrix< QUADRIC3D_TYPE > &dest) const |
multiplication function, storing data destination matrix More... | |
void | MultLeft (const Matrix< QUADRIC3D_TYPE > &arg) |
in Place matrix multiplication this is equal to M = arg*M, but faster More... | |
void | MultLeft (const Vector< QUADRIC3D_TYPE > &arg, Vector< QUADRIC3D_TYPE > &result) const |
vector matrix multiplication result=arg*this. More... | |
void | MultiplyWithTransposeOf (const Matrix< QUADRIC3D_TYPE > &arg, Matrix< QUADRIC3D_TYPE > &result) const |
matrix matrix multiplication for multiplication with the transpose of the given matrix, result=this*arg^T. More... | |
void | DivideIP (const QUADRIC3D_TYPE &scalar) |
in place division function More... | |
void | Divide (const QUADRIC3D_TYPE &scalar, Matrix< QUADRIC3D_TYPE > &dest) const |
division function, storing data destination matrix More... | |
void | DivideElementwise (const Matrix< QUADRIC3D_TYPE > &arg) |
elementwise division function in place More... | |
void | GetSystemMatrix (Matrix< QUADRIC3D_TYPE > &dest) const |
compute square system matrix dest = A^T * A More... | |
Get Functions | |
QUADRIC3D_TYPE | GetMax () const |
Returns the maximum value of the matrix elements. More... | |
QUADRIC3D_TYPE | GetMin () const |
Returns the minimum value of the matrix elements. More... | |
QUADRIC3D_TYPE * | GetData () |
get the pointer to the data array of the matrix (for faster direct memeory access) More... | |
const QUADRIC3D_TYPE * | GetData () const |
const QUADRIC3D_TYPE ** | GetDataArray () const |
returns zero based arry for data access More... | |
QUADRIC3D_TYPE ** | GetDataArray () |
QUADRIC3D_TYPE ** | GetDataArray1 () const |
returns 1 based array to data access More... | |
unsigned int | GetRows () const |
unsigned int | GetCols () const |
const QUADRIC3D_TYPE * | GetDataLast () const |
Get a pointer to the last data element Do not use this on unitilized matrices with <= on pointers because on an unitilized matrix GetData() will be NULL and last Element < (typically FFFFF8) We don't want an if here for performance reasons of the innerst loop. More... | |
QUADRIC3D_TYPE * | GetDataLast () |
Vector< QUADRIC3D_TYPE > | GetRow (const int &row) const |
return a copy of row "row" of this matrix, zero based counting More... | |
Vector< QUADRIC3D_TYPE > | GetCol (const int &col) const |
return a copy of column "col", zero based counting More... | |
void | GetSubMatrix (const size_t startRow, const size_t startCol, const size_t numRows, const size_t numCols, Matrix< QUADRIC3D_TYPE > &submatrix) const |
return a submatrix from this. More... | |
void | GetSubMatrix (const Vector< int > &rows, const Vector< int > &cols, Matrix< QUADRIC3D_TYPE > &submatrix) const |
return a submatrix from this. More... | |
Matrix< QUADRIC3D_TYPE > | GetSubMatrix (const Vector< int > &rows, const Vector< int > &cols) const |
return a submatrix from this. More... | |
void | SetSubMatrix (const size_t startRowInThis, const size_t startColInThis, const Matrix< QUADRIC3D_TYPE > &submatrix, const size_t startRowInSub, const size_t startColInSub, const size_t numRows, const size_t numCols) |
sets a submatrix in this. More... | |
void | SetSubMatrix (const size_t startRowInThis, const size_t startColInThis, const Matrix3x3< QUADRIC3D_TYPE > &submatrix) |
sets a 3x3 submatrix in this. More... | |
void | SetSubMatrix (const size_t startRowInThis, const size_t startColInThis, const Vector3< QUADRIC3D_TYPE > &subvector) |
sets a 3x1 submatrix in this. More... | |
void | SetRow (const int row, const Vector< QUADRIC3D_TYPE > &data) |
set a row of matrix from vector More... | |
void | SetCol (const int row, const Vector< QUADRIC3D_TYPE > &data) |
set a col of matrix from vector More... | |
void | Set (const int row, const int col, const Matrix< QUADRIC3D_TYPE > &data) |
Copies the contents of data into this at the position indicated by row and col. More... | |
void | Set (const int row, const int col, const Vector< QUADRIC3D_TYPE > &data) |
Copies the contents of data into this at the position indicated by row and col. More... | |
void | SetTranspose (const int row, const int col, const Vector< QUADRIC3D_TYPE > &data) |
Copies the contents of data into this at the position indicated by row and col. More... | |
int | GetNumElements () const |
Returns the total number of elements. More... | |
void | GetMaxMin (QUADRIC3D_TYPE &max, QUADRIC3D_TYPE &min) const |
return biggest and smallest entry More... | |
void | GetAbsMaxMin (QUADRIC3D_TYPE &max, QUADRIC3D_TYPE &min) const |
return biggest and smallest absolute values More... | |
QUADRIC3D_TYPE | GetMean () const |
Returns the mean value of the matrix elements. More... | |
QUADRIC3D_TYPE | NormL1 () const |
Return the L1 norm: |a| + |b| + |c| + ... More... | |
double | NormL2 () const |
Return the L2 norm: a^2 + b^2 + c^2 + ... More... | |
double | NormFrobenius () const |
Return Frobenius norm = sqrt(trace(A^t * A)). More... | |
QUADRIC3D_TYPE | Trace () const |
QUADRIC3D_TYPE | DetSquare () const |
Set Functions | |
void | SetZero () |
Sets all values to zero. More... | |
void | MakeSymmetric () |
componentwise: this = 0.5(this + this^T) yields symmetric matrix only allowed for square shaped matrices More... | |
void | Fill (const QUADRIC3D_TYPE &scalar) |
Takes the elements of a Vector and put them as diagonal elements into a matrix. More... | |
Scaling and Normalization | |
void | NormalizeColsToOne (const int norm_row_index) |
divides each column of the matrix through the element norm_row_index. More... | |
void | NormalizeRowsToOne (const int norm_col_index) |
divides each row of the matrix through the element norm_col_index. More... | |
void | NormalizeRows () |
Normalizes each row to L2 norm one. More... | |
void | NormalizeCols () |
Normalizes each coloumn to L_2 norm one. More... | |
void | ScaleRow (int NoRow, QUADRIC3D_TYPEscale) |
Scales row NoRow with scale. More... | |
void | ScaleCol (int NoCol, QUADRIC3D_TYPEscale) |
Scales column NoCol with scale. More... | |
Input / Output | |
bool | Load (const std::string &filename) |
method to load directly from a given filename. More... | |
bool | Save (const std::string &filename) const |
method to save directly to a given filename. More... | |
int | WriteMatlab (std::ostream &ostr, const std::string &name) const |
Write the matrix in Matlab format to the given stream. More... | |
bool | BinRead (const char *filename) const |
This method reads a matrix from a given file in binary format. More... | |
bool | BinWrite (const char *filename) const |
This method writes a matrix to a given file in binary format. More... | |
Protected Member Functions | |
void | copy (const T *v) |
void | destroy () |
void | initialize (Subscript M, Subscript N) |
void | set (const T &val) |
Protected Attributes | |
Subscript | m_ |
Subscript | mn_ |
Subscript | n_ |
T ** | row_ |
T ** | rowm1_ |
T * | v_ |
T * | vm1_ |
Related Functions | |
(Note that these are not member functions.) | |
template<class T > | |
Matrix< T > | operator* (const Matrix< T > &A, const Matrix< T > &B) |
template<class T > | |
Vector< T > | operator* (const Matrix< T > &A, const Vector< T > &x) |
template<class T > | |
Matrix< T > | operator+ (const Matrix< T > &A, const Matrix< T > &B) |
template<class T > | |
Matrix< T > | operator- (const Matrix< T > &A, const Matrix< T > &B) |
std::ostream & | operator<< (std::ostream &s, const Matrix< char > &A) |
std::ostream & | operator<< (std::ostream &s, const Matrix< unsigned char > &A) |
template<class T > | |
std::ostream & | operator<< (std::ostream &s, const Matrix< T > &A) |
std::istream & | operator>> (std::istream &s, Matrix< unsigned char > &A) |
std::istream & | operator>> (std::istream &s, Matrix< char > &A) |
template<class T > | |
std::istream & | operator>> (std::istream &s, Matrix< T > &A) |
A quadric as a 4x4 matrix describing a surface in 3d projective space defined by a quadratic equation, e.g.
a sphere.
Quadric3D is a 4x4 matrix Q, which describes a surface in 3d. All points x that lie on this surface, fulfill x^T Q x = 0, which is a quadratic equation in the components of x. For quadrics such as spheres or ellipsoids you can check if a point is inside or outside the quadric using LocatePoint(), for others you can also get the "side" the point lies relative to the Quadric. If the Quadric is a normalized ellipsoid, points inside yield negative values while LocatePoint computes positive ones for points ouside.
Projective cameras map quadrics to conics (see Conic2D) in the image plane.
Construction of Quadrics (i.e. ellipsoids) from covariance matrices: You can construct a Quadric3D from a CovMatrix3x3, the 3d surface will then represent all points of some constant probability of the 3d-normal distribution. The decision which probability to choose as a threshold, and thus how large the ellipsoid should become, depends on the desired probability for a new measurement to lie inside the quadric.
The standard confidence region is the set of points which lie inside the ellipsoid defined by main axes' length = sigma_i The probability that a measurement falls into this region is only 20%. If you want to increase the confidence that a point falls into your ellipsoid, you may enlarge the main axes by multiplication with a constant factor (see 3D column in subsequent table). For comparison purposes, the coresponding factors for 1D/2D are also given in the table:
Suppose you have a covariance matrix and want to create an ellipsoid, where 99% of new measurements will fall in. In that case you have to use main axes of length (sigma_i*3.37)
Definition at line 106 of file Quadric3D.hh.
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Definition at line 110 of file Quadric3D.hh.
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set default matrix values
Definition at line 113 of file Quadric3D.hh.
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Definition at line 116 of file Quadric3D.hh.
Quadric3D::Quadric3D | ( | const HomgPoint3D & | C, |
const CovMatrix3x3 & | cov, | ||
const double & | dScale = GAUSS3D_CONFIDENCE_20_PERCENT |
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constructs an ellipsoid around the center C
The covariance matrix's stddevs along the main axes (multiplied by dSize) are used as the ellipsoid's radii for dsize==1 this is the standard confidence region (SCR) see Kanatani: "Statistical optimization ...", p.122 The probability that the point is in the SCR is about 20% See doc above for values for other probabilities
Definition at line 36 of file Quadric3D.cpp.
References BIAS::Matrix3x3< T >::GetInverse(), BIAS::SVD::GetS(), BIAS::SVD::GetU(), BIAS::SVD::GetV(), BIAS::Matrix4x4< T >::SetIdentity(), BIAS::Matrix3x3< T >::SetZero(), BIAS::Matrix< T >::Transpose(), and BIAS::Matrix4x4< T >::Transpose().
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absolute values of all elements of the matrix (in place)
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addition function, storing data destination matrix
implementation
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Adds arg to this.
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computes the adjoint matrix
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This method reads a matrix from a given file in binary format.
The file is not human read-/editable but provides full precision. A dimension check is performed.
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This method writes a matrix to a given file in binary format.
The file is not human read-/editable but provides full precision.
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stl conform interface
Reimplemented from BIAS::Matrix< QUADRIC3D_TYPE >.
Definition at line 281 of file Matrix4x4.hh.
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Definition at line 122 of file cmat.h.
Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::Matrix(), and TNT::Matrix< BIAS::BIAS::Vector< int > >::operator=().
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Definition at line 181 of file cmat.h.
Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::newsize(), TNT::Matrix< BIAS::BIAS::Vector< int > >::operator=(), and TNT::Matrix< BIAS::BIAS::Vector< int > >::~Matrix().
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calculate the determinant recursively using sub matrices of size 3x3
Definition at line 164 of file Matrix4x4.hh.
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division function, storing data destination matrix
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elementwise division function in place
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Takes the elements of a Vector and put them as diagonal elements into a matrix.
The size of this Vector must be exactly min( matrix.width, matrix.height). Optionally all other elements may be set to zero
zero_others | Must be true, if all non-diagonal elements shall be set to zero |
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use the Gauss Jordan Algrithm to transform the matrix to reduced row echelon form.
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return biggest and smallest absolute values
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return a copy of column "col", zero based counting
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get the pointer to the data array of the matrix (for faster direct memeory access)
the order of the data is linewise, which means an elemnt sequence of e.g. [0] = M(0,0) [1] = M(0,1) [2] = M(0,2) [3] = M(1,0) // next line [4] = M(1,1) ...
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Get a pointer to the last data element Do not use this on unitilized matrices with <= on pointers because on an unitilized matrix GetData() will be NULL and last Element < (typically FFFFF8) We don't want an if here for performance reasons of the innerst loop.
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Quadric3D Quadric3D::GetDualQuadric | ( | bool | UseSVD = false | ) | const |
computes the dual quadric (points <-> planes)
UseSVD | use numerically robust svd or fast analytic inverse |
Definition at line 121 of file Quadric3D.cpp.
References BIAS::SVD::Invert().
Referenced by BIAS::Conic2D::SetQuadricProjection().
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returns an matrix the same size as the matrix n and m with the largest elements taken from n or m
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Returns the maximum value of the matrix elements.
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return biggest and smallest entry
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Returns the mean value of the matrix elements.
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returns an matrix the same size as the matrix n and m with the smallest elements taken from n or m
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Returns the minimum value of the matrix elements.
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return a copy of row "row" of this matrix, zero based counting
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unsigned int Quadric3D::GetSignature | ( | ) |
computes signature of matrix, (no.
of neg. eigenvalues) - (no. of pos. eigenvalues) or vice versa if there are more pos. eigenvalues
Definition at line 91 of file Quadric3D.cpp.
References BIAS::SVD::GetS(), and BIAS::SVD::GetVT().
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return a submatrix from this.
Start index is [startRow][startCol] end index is [startRow+numRows-1][startCol+numCols-1]. submatrix is resized to numRows/numCols if necessary.
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return a submatrix from this.
Similar to matlab notation (except indexing, starts with 0 of course!). Vectors rows = '1 3' and cols = '1 2' for matrix: / 1 2 3 \ | 4 5 6 | \ 7 8 9 / results in: / 1 2 \ \ 7 8 / Matrix has to be initialized!!!
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return a submatrix from this.
Similar to matlab notation (except indexing, starts with 0 of course!), see GetSubMatrix(const Vector<int> &rows, const Vector<int> &cols, Matrix<T> &submatrix)
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compute square system matrix dest = A^T * A
dest | holds result of this->Transpose * this |
If you want to solve A * x = b, where A has more rows than columns, a common technique is to solve x = (A^T * A)^-1 * A^T * b. This function provides a fast way to compute A^T*A from A.
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Definition at line 95 of file cmat.h.
Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::Matrix(), TNT::Matrix< BIAS::BIAS::Vector< int > >::newsize(), and TNT::Matrix< BIAS::BIAS::Vector< int > >::operator=().
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Checks if the matrix a an identity.
I.e. all elements with index i==j are equal 1 and all others are zero.
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Checks if the matrix is a null matrix.
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Kronecker-product with matrix, result in dest.
Kronecker-product with matrix B, result in dest.
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method to load directly from a given filename.
internally using stream operator
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determines if point3D is inside/on/outside the surface
For a normalized ellipsoid, a negative return value means the point is inside, a positive value means outside and 0 means exactly on the surface (you have to use epsilon environments for all tests) LocatePoint internally computes the difference of Mahalanobis distances of point3D from the center and a surface point from the center
Definition at line 137 of file Quadric3D.hh.
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matrix - vector multiplicate this matrix with Vector4,
storing the result in destvec, calculates: destvec = (this Matrix) * argvec
Definition at line 121 of file Matrix4x4.hh.
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matrix-matrix multiplication with other Matrix4x4,
storing the result in destmat using 'manual inlining'
Definition at line 190 of file Matrix4x4.hh.
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matrix multiplication, result is not allocated
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in Place matrix multiplication this is equal to M = M * arg, but faster
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matrix vector multiplication, result is not allocated
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multiplication function, storing data destination matrix
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matrix matrix multiplication for multiplication with the transpose of the given matrix, result=this*arg^T.
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in Place matrix multiplication this is equal to M = arg*M, but faster
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vector matrix multiplication result=arg*this.
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Definition at line 269 of file cmat.h.
Referenced by BIAS::Matrix< T >::Add(), BIAS::RegionMatcher::BilinearRegion(), BIAS::RegionMatcher::BilinearRegionColor3(), BIAS::ComputeCovariance(), BIAS::LDA::ComputeReductionMatrix(), BIAS::PCA::ComputeReductionMatrix(), BIAS::ContourBSplineShapeMatrix::ComputeRegularisationMatrix(), BIAS::ContourBSplineData::ComputeSplineMetricMatrix_(), BIAS::Matrix< T >::Conv(), BIAS::CamPoseCalib::CreateSecDMatrix_(), BIAS::Matrix< T >::Divide(), Eigenproblem_quadratic_matrix(), BIAS::CamPoseCalib::Estimate(), BIAS::TrackerBaseAffine< StorageType >::EvaluateResult_(), BIAS::TrackerBaseAffine2< StorageType >::EvaluateResult_(), BIAS::TrackerBaseInterface< StorageType >::EvaluateResult_(), BIAS::TrackerBaseInterface< StorageType >::Filter_ByMask(), BIAS::TrackerBaseInterface< StorageType >::Filter_BySeparableMask(), BIAS::TrackerBaseInterface< StorageType >::Filter_GradXSobel3x3(), BIAS::TrackerBaseInterface< StorageType >::Filter_GradYSobel3x3(), BIAS::TrackerBaseInterface< StorageType >::FilterLowpass_Binomial3x3(), BIAS::TrackerBaseInterface< StorageType >::FilterLowpass_ByMask(), BIAS::TrackerBaseInterface< StorageType >::FilterLowpass_BySeparableMask(), Fortran_Matrix_to_Matrix(), generalised_eigenvalue_matrix_solve(), BIAS::LDA::GenerateRandomTestData(), BIAS::SparseMatrix::GetAsDense(), BIAS::Random::GetMeanAndCovariance(), BIAS::PMatrixLinear::GetPEstSystemHom(), BIAS::PMatrixLinear::GetPEstSystemInHom(), BIAS::Matrix< T >::GetSystemMatrix(), BIAS::Kalman::Init(), BIAS::IteratedExtendedKalman::Init(), BIAS::SparseMatrix::Invert(), BIAS::SparseMatrix::InvertAndSolve(), BIAS::Matrix< T >::Kronecker(), Lapack_Cholesky_SymmetricPositiveDefinit(), BIAS::RegionMatcher::LinearRegionX(), BIAS::LevenbergMarquardtBase::LM_Compute(), BIAS::LevenbergMarquardtBase::LM_ComputeWithoutJacobian(), TNT::matmult(), BIAS::Matrix< T >::Mult(), BIAS::Matrix< T >::Multiply(), BIAS::Matrix< T >::MultiplyWithTransposeOf(), BIAS::MxArrToBIASMatrix(), BIAS::Matrix3x4< T >::newsize(), BIAS::Matrix4x4< T >::newsize(), BIAS::TextureTransformHomography::ParameterInversionJacobian(), BIAS::TextureTransformAffine::ParameterInversionJacobian(), BIAS::TextureTransformDisparity::ParameterInversionJacobian(), BIAS::TextureTransformDisplacement::ParameterInversionJacobian(), BIAS::TextureTransformRotation::ParameterInversionJacobian(), BIAS::TextureTransformEuclidian::ParameterInversionJacobian(), BIAS::TextureTransformHomography::ParameterJacobianBackward(), BIAS::TextureTransformAffine::ParameterJacobianBackward(), BIAS::TextureTransformDisparity::ParameterJacobianBackward(), BIAS::TextureTransformDisplacement::ParameterJacobianBackward(), BIAS::TextureTransformRotation::ParameterJacobianBackward(), BIAS::TextureTransformEuclidian::ParameterJacobianBackward(), BIAS::TextureTransformSimilar::ParameterJacobianBackward(), BIAS::TextureTransform::ParameterJacobianBackward(), BIAS::TextureTransformAffine::ParameterJacobianForward(), BIAS::TextureTransformHomography::ParameterJacobianForward(), BIAS::TextureTransformDisparity::ParameterJacobianForward(), BIAS::TextureTransformDisplacement::ParameterJacobianForward(), BIAS::TextureTransformRotation::ParameterJacobianForward(), BIAS::TextureTransformSimilar::ParameterJacobianForward(), BIAS::TextureTransformEuclidian::ParameterJacobianForward(), BIAS::TextureTransform::ParameterJacobianForward(), BIAS::IteratedExtendedKalman::Predict(), BIAS::Covariance3Dto2D::Project(), BIAS::Covariance3Dto2DHomg::Project(), BIAS::QRFrac(), BIAS::RegionMatcher::RegionMatcher(), BIAS::ContourBSplineShapeMatrix::SetShapeSpaceEuclidian(), BIAS::ContourBSplineShapeMatrix::SetShapeSpaceIdentity(), BIAS::ContourBSplineShapeMatrix::SetShapeSpaceMatrix(), BIAS::ContourBSplineShapeMatrix::SetShapeSpacePlanarAffin(), BIAS::ContourBSplineShapeMatrix::SetSubShapeSpaceZero(), BIAS::Matrix< T >::Sub(), BIAS::TrackerBaseAffine< StorageType >::TrackAffine_(), BIAS::MonteCarloTransform::Transform(), BIAS::UnscentedTransform::Transform(), BIAS::IteratedExtendedKalman::Update(), and BIAS::Tracker< StorageType, CalculationType >::Vector2FilterMask_().
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just neccessary to avoid resizing of this 'fixed size' matrix because it is derived from the resizable Matrix
Should be removed if Matrix4x4 becomes a base class.
(04/17/2002) Jan Woetzel
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sets trace of upperleft submatrix3x3 to unity
Definition at line 141 of file Quadric3D.hh.
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Normalizes each coloumn to L_2 norm one.
Attention each column is normaized by its own scale!
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divides each column of the matrix through the element norm_row_index.
index runs [0..num_rows-1] for example: 2 3 4 5 normalized with row '1' will be 2/4 3/5 1 1
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Normalizes each row to L2 norm one.
Attention each row is normaized by its own scale!
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divides each row of the matrix through the element norm_col_index.
index runs [0..num_cols-1] for example: 2 3 4 5 normalized with row '1' will be 2/3 1 4/5 1
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Return Frobenius norm = sqrt(trace(A^t * A)).
this method is deprecated because it is equivalent to NormL2
This function is deprecated, because it is equivalent to NormL2.
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Return the L1 norm: |a| + |b| + |c| + ...
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Return the L2 norm: a^2 + b^2 + c^2 + ...
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Definition at line 320 of file cmat.h.
Referenced by BIAS::Matrix< T >::Add(), BIAS::Matrix< T >::AddIP(), BIAS::ImageAlignment::Align(), BIAS::CamPoseCalib::ApplyCoVariances_(), BIAS::ImageAlignment::AutoAlign(), BIAS::TFTensorEstimation::Compute(), BIAS::SVD3x3::Compute(), BIAS::GaussHelmert::ComputeNormalSystem_(), BIAS::LDA::ComputeReductionMatrix(), BIAS::PCA::ComputeReductionMatrix(), BIAS::ContourBSplineShapeMatrix::ComputeRegularisationMatrix(), BIAS::PCA::ComputeScatter(), BIAS::UnscentedTransform::ComputeSigmaPoints_(), BIAS::LDA::ComputeWithinAndInterClassCovs(), BIAS::Matrix< T >::Conv(), BIAS::Matrix< T >::Divide(), BIAS::Matrix< T >::DivideElementwise(), Eigenproblem_quadratic_matrix(), Eigenvalue_solve(), BIAS::CamPoseCalib::Estimate(), Fortran_Matrix_to_Matrix(), General_singular_value_decomposition(), generalised_eigenvalue_matrix_solve(), BIAS::CamPoseCalib::GetCov(), BIAS::CamPoseCalib::GetCoVarMatrix(), BIAS::SVD::GetNullvector(), BIAS::Matrix< T >::Kronecker(), Lapack_Cholesky_SymmetricPositiveDefinit(), Lapack_LLS_QR_linear_solve(), Lapack_LU_linear_solve(), Lapack_WLLS_solve(), TNT::matmult(), BIAS::Matrix2x2< T >::Matrix2x2(), BIAS::Matrix3x3< T >::Matrix3x3(), BIAS::Matrix4x4< T >::Matrix4x4(), BIAS::Matrix< T >::Mult(), TNT::mult_element(), BIAS::Matrix< T >::Multiply(), BIAS::Matrix< T >::MultiplyWithTransposeOf(), TNT::Matrix< BIAS::BIAS::Vector< int > >::newsize(), BIAS::TrackerBaseInterface< StorageType >::NormalizeRegion_(), BIAS::Vector< T >::operator*(), BIAS::Vector3< T >::operator*(), BIAS::Vector4< T >::operator*(), TNT::Matrix< T >::operator+(), TNT::Matrix< T >::operator-(), BIAS::Matrix3x4< T >::operator=(), BIAS::Matrix4x4< T >::operator=(), BIAS::PMatrix::PMatrix(), BIAS::PMatrixBase::PMatrixBase(), BIAS::CovTransformPose::PoseEulerZYXToQuat(), BIAS::CovTransformPose::PoseQuatToEulerZYX(), BIAS::IteratedExtendedKalman::Predict(), BIAS::Covariance3Dto2DHomg::Project(), BIAS::RMatrix::RMatrix(), BIAS::RMatrixBase::RMatrixBase(), BIAS::Matrix< T >::Set(), BIAS::RParametrization::SetCovarianceMatrix(), BIAS::PoseParametrization::SetCovarianceMatrix(), BIAS::EParametrization::SetCovarianceMatrix(), BIAS::LocalAffineFrame::SetFromMatrix(), BIAS::IteratedExtendedKalman::SetProcessCov(), BIAS::ContourBSplineShapeMatrix::SetShapeSpaceMatrix(), BIAS::IteratedExtendedKalman::SetState(), BIAS::ContourBSplineShapeMatrix::SetSubShapeSpaceZero(), BIAS::GaussHelmert::Solve(), BIAS::LeastSquaresSVD::Solve(), BIAS::SVD::Solve(), BIAS::CamPoseCalib::SolveLM_(), BIAS::ImageAlignment::StrictPyramidAlign(), BIAS::Matrix< T >::Sub(), BIAS::Matrix< T >::SubIP(), BIAS::SymmetricMatrix3x3< T >::SymmetricMatrix3x3(), BIAS::TrackerBaseAffine< StorageType >::TrackAffine_(), BIAS::MonteCarloTransform::Transform(), BIAS::UnscentedTransform::Transform(), BIAS::CovTransformPose::TransformPoint3D(), BIAS::CovTransformPose::TransformPose(), TNT::transpose(), BIAS::Kalman::Update(), BIAS::IteratedExtendedKalman::Update(), and Upper_symmetric_eigenvalue_solve().
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Definition at line 319 of file cmat.h.
Referenced by BIAS::Matrix< T >::Add(), BIAS::Matrix< T >::AddIP(), BIAS::ImageAlignment::Align(), BIAS::ImageAlignment::AutoAlign(), BIAS::SVD3x3::Compute(), BIAS::ImageBlender::ComputeCylCamGeometry(), BIAS::ImageBlenderIncremental::ComputeCylCamGeometry_(), BIAS::LDA::ComputeReductionMatrix(), BIAS::PCA::ComputeReductionMatrix(), BIAS::ContourBSplineShapeMatrix::ComputeRegularisationMatrix(), BIAS::PCA::ComputeScatter(), BIAS::UnscentedTransform::ComputeSigmaPoints_(), BIAS::LDA::ComputeWithinAndInterClassCovs(), BIAS::Matrix< T >::Conv(), BIAS::Matrix< T >::Divide(), BIAS::Matrix< T >::DivideElementwise(), Eigenproblem_quadratic_matrix(), Eigenvalue_solve(), BIAS::CamPoseCalib::Estimate(), Fortran_Matrix_to_Matrix(), General_singular_value_decomposition(), generalised_eigenvalue_matrix_solve(), BIAS::CamPoseCalib::GetCov(), BIAS::CamPoseCalib::GetCoVarMatrix(), BIAS::SVD::GetLeftNullvector(), BIAS::Kalman::Init(), BIAS::IteratedExtendedKalman::Init(), BIAS::Matrix< T >::Kronecker(), Lapack_Cholesky_SymmetricPositiveDefinit(), Lapack_LLS_QR_linear_solve(), Lapack_LU_linear_solve(), Lapack_WLLS_solve(), TNT::matmult(), BIAS::Matrix2x2< T >::Matrix2x2(), BIAS::Matrix3x3< T >::Matrix3x3(), BIAS::Matrix4x4< T >::Matrix4x4(), BIAS::Matrix< T >::Mult(), TNT::mult_element(), BIAS::Matrix< T >::Multiply(), BIAS::Matrix< T >::MultiplyWithTransposeOf(), BIAS::Matrix< T >::MultLeft(), TNT::Matrix< BIAS::BIAS::Vector< int > >::newsize(), BIAS::TrackerBaseInterface< StorageType >::NormalizeRegion_(), BIAS::Vector< T >::operator*(), BIAS::Vector3< T >::operator*(), BIAS::Vector4< T >::operator*(), TNT::Matrix< T >::operator+(), TNT::Matrix< T >::operator-(), BIAS::Matrix3x4< T >::operator=(), BIAS::Matrix4x4< T >::operator=(), BIAS::PMatrix::PMatrix(), BIAS::PMatrixBase::PMatrixBase(), BIAS::CovTransformPose::PoseEulerZYXToQuat(), BIAS::CovTransformPose::PoseQuatToEulerZYX(), BIAS::IteratedExtendedKalman::Predict(), BIAS::RMatrix::RMatrix(), BIAS::RMatrixBase::RMatrixBase(), BIAS::Matrix< T >::Set(), BIAS::RParametrization::SetCovarianceMatrix(), BIAS::PoseParametrization::SetCovarianceMatrix(), BIAS::EParametrization::SetCovarianceMatrix(), BIAS::LocalAffineFrame::SetFromMatrix(), BIAS::IteratedExtendedKalman::SetProcessCov(), BIAS::ContourBSplineShapeMatrix::SetShapeSpaceMatrix(), BIAS::IteratedExtendedKalman::SetState(), BIAS::ContourBSplineShapeMatrix::SetSubShapeSpaceZero(), BIAS::GaussHelmert::Solve(), BIAS::LeastSquaresSVD::Solve(), BIAS::SVD::Solve(), BIAS::CamPoseCalib::SolveLM_(), SquaredMahalanobisDistance(), BIAS::ImageAlignment::StrictPyramidAlign(), BIAS::Matrix< T >::Sub(), BIAS::Matrix< T >::SubIP(), BIAS::SymmetricMatrix3x3< T >::SymmetricMatrix3x3(), BIAS::TrackerBaseAffine2< StorageType >::TrackAffine_(), BIAS::MonteCarloTransform::Transform(), BIAS::UnscentedTransform::Transform(), BIAS::CovTransformPose::TransformPoint3D(), BIAS::CovTransformPose::TransformPose(), TNT::transpose(), BIAS::Kalman::Update(), BIAS::IteratedExtendedKalman::Update(), Upper_symmetric_eigenvalue_solve(), and BIAS::LeastSquaresLapack::WeightedSolve().
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Definition at line 146 of file Quadric3D.hh.
References BIAS::Matrix4x4< T >::operator=().
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method to save directly to a given filename.
internally using stream operator
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Scales column NoCol with scale.
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Scales row NoRow with scale.
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Definition at line 152 of file cmat.h.
Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::operator=().
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Copies the contents of data into this at the position indicated by row and col.
The size of *this must be big enought to carry data
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Copies the contents of data into this at the position indicated by row and col.
The size of *this must be big enought to carry data. Data i interpreted as column vector
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set a col of matrix from vector
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set the elements of this matrix to the identity matrix
(posisbly overriding the inherited method)
Definition at line 260 of file Matrix4x4.hh.
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set a row of matrix from vector
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sets a submatrix in this.
Start index in this is [startRowInThis][startColInThis] end index is [startRowInThis+numRows-1][startColInThis+numCols-1]. Entries copyed from submatrix beginning at [startRowInSub][startColInSub] and stop at [startRowInSub+numRows-1][startColInSub+numCols-1]
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sets a 3x3 submatrix in this.
Start index in this is [startRowInThis][startColInThis] end index is [startRowInThis+2][startColInThis+2].
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sets a 3x1 submatrix in this.
Start index in this is [startRowInThis][startColInThis] end index is [startRowInThis+2][startColInThis].
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Copies the contents of data into this at the position indicated by row and col.
The size of *this must be big enought to carry data. Data is interpreted as row vector.
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Sets all values to zero.
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Definition at line 212 of file cmat.h.
Referenced by Eigenproblem_quadratic_matrix(), BIAS::Random::GetMeanAndCovariance(), BIAS::Matrix< T >::operator==(), and BIAS::IteratedExtendedKalman::SetState().
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substraction function, storing data destination matrix
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Subtracts arg from this
this -= arg.
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swaps two rows
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Definition at line 315 of file Matrix4x4.hh.
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tranpose this matrix "in place"
example: 0 1 2 3 –> 0 4 8 12 4 5 6 7 –> 1 5 9 13 8 9 10 11 –> 2 6 10 14 12 13 14 15 –> 3 7 11 15
Definition at line 302 of file Matrix4x4.hh.
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vec-operator returns the elements of the matrix columwise as vector
vec-operator returns the elements of the matrix columnwise as vector
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Write the matrix in Matlab format to the given stream.
name | Is the name of the Matlab variable |
Definition at line 842 of file cmat.h.
References TNT::matmult().
Definition at line 915 of file cmat.h.
References TNT::matmult().
Definition at line 730 of file cmat.h.
References TNT::Matrix< T >::num_cols(), and TNT::Matrix< T >::num_rows().
Definition at line 752 of file cmat.h.
References TNT::Matrix< T >::num_cols(), and TNT::Matrix< T >::num_rows().
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Definition at line 703 of file cmat.h.
References TNT::Matrix< T >::Read().
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Definition at line 711 of file cmat.h.
References TNT::Matrix< T >::Read().
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Definition at line 719 of file cmat.h.
References TNT::Matrix< T >::Read().
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Definition at line 84 of file cmat.h.
Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::copy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::destroy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::dim(), TNT::Matrix< BIAS::BIAS::Vector< int > >::initialize(), TNT::Matrix< BIAS::BIAS::Vector< int > >::Matrix(), TNT::Matrix< BIAS::BIAS::Vector< int > >::num_rows(), TNT::Matrix< BIAS::BIAS::Vector< int > >::operator()(), TNT::Matrix< BIAS::BIAS::Vector< int > >::operator=(), TNT::Matrix< BIAS::BIAS::Vector< int > >::operator[](), and TNT::Matrix< BIAS::BIAS::Vector< int > >::set().
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Definition at line 86 of file cmat.h.
Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::destroy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::initialize(), TNT::Matrix< BIAS::BIAS::Vector< int > >::operator()(), and TNT::Matrix< BIAS::BIAS::Vector< int > >::size().
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Definition at line 85 of file cmat.h.
Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::copy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::destroy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::dim(), TNT::Matrix< BIAS::BIAS::Vector< int > >::initialize(), TNT::Matrix< BIAS::BIAS::Vector< int > >::Matrix(), TNT::Matrix< BIAS::BIAS::Vector< int > >::num_cols(), TNT::Matrix< BIAS::BIAS::Vector< int > >::operator()(), TNT::Matrix< BIAS::BIAS::Vector< int > >::operator=(), and TNT::Matrix< BIAS::BIAS::Vector< int > >::set().
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Definition at line 88 of file cmat.h.
Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::destroy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::initialize(), TNT::Matrix< BIAS::BIAS::Vector< int > >::Matrix(), BIAS::PMatrix::Normalize(), and TNT::Matrix< BIAS::BIAS::Vector< int > >::operator[]().
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Definition at line 90 of file cmat.h.
Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::destroy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::initialize(), and TNT::Matrix< BIAS::BIAS::Vector< int > >::operator()().
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Definition at line 87 of file cmat.h.
Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::copy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::destroy(), TNT::Matrix< BIAS::BIAS::Vector< int > >::initialize(), TNT::Matrix< BIAS::BIAS::Vector< int > >::Matrix(), BIAS::AffineTransf::Mult(), BIAS::AffineTransf::operator=(), TNT::Matrix< BIAS::BIAS::Vector< int > >::operator=(), TNT::Matrix< BIAS::BIAS::Vector< int > >::set(), and BIAS::AffineTransf::SetAsRotationMatrix().
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Definition at line 89 of file cmat.h.
Referenced by TNT::Matrix< BIAS::BIAS::Vector< int > >::initialize(), and TNT::Matrix< BIAS::BIAS::Vector< int > >::operator()().