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essential_to_fundamental_matrixT_essential_to_fundamental_matrixEssentialToFundamentalMatrixessential_to_fundamental_matrixEssentialToFundamentalMatrixEssentialToFundamentalMatrix (Operator)

Name

essential_to_fundamental_matrixT_essential_to_fundamental_matrixEssentialToFundamentalMatrixessential_to_fundamental_matrixEssentialToFundamentalMatrixEssentialToFundamentalMatrix — Berechnung der Fundamental-Matrix aus der Essential-Matrix.

Signatur

essential_to_fundamental_matrix( : : EMatrix, CovEMat, CamMat1, CamMat2 : FMatrix, CovFMat)

Herror T_essential_to_fundamental_matrix(const Htuple EMatrix, const Htuple CovEMat, const Htuple CamMat1, const Htuple CamMat2, Htuple* FMatrix, Htuple* CovFMat)

Herror essential_to_fundamental_matrix(const HTuple& EMatrix, const HTuple& CovEMat, const HTuple& CamMat1, const HTuple& CamMat2, HTuple* FMatrix, HTuple* CovFMat)

void EssentialToFundamentalMatrix(const HTuple& EMatrix, const HTuple& CovEMat, const HTuple& CamMat1, const HTuple& CamMat2, HTuple* FMatrix, HTuple* CovFMat)

HHomMat2D HHomMat2D::EssentialToFundamentalMatrix(const HTuple& CovEMat, const HHomMat2D& CamMat1, const HHomMat2D& CamMat2, HTuple* CovFMat) const

void HOperatorSetX.EssentialToFundamentalMatrix(
[in] VARIANT EMatrix, [in] VARIANT CovEMat, [in] VARIANT CamMat1, [in] VARIANT CamMat2, [out] VARIANT* FMatrix, [out] VARIANT* CovFMat)

IHHomMat2DX* HHomMat2DX.EssentialToFundamentalMatrix(
[in] VARIANT CovEMat, [in] IHHomMat2DX* CamMat1, [in] IHHomMat2DX* CamMat2, [out] VARIANT* CovFMat)

static void HOperatorSet.EssentialToFundamentalMatrix(HTuple EMatrix, HTuple covEMat, HTuple camMat1, HTuple camMat2, out HTuple FMatrix, out HTuple covFMat)

HHomMat2D HHomMat2D.EssentialToFundamentalMatrix(HTuple covEMat, HHomMat2D camMat1, HHomMat2D camMat2, out HTuple covFMat)

Beschreibung

Die Fundamental-Matrix beschreibt die Epipolarbedingung in Bildkoordinaten (C,R), während die Essential-Matrix das Gegenstück für 3D Richtungsvektoren (X,Y,1) ist: 

             T                                     T
     / C2 \             / C1 \           / X2 \             / X1 \
     | R2 | * FMatrix * | R1 | = 0  and  | Y2 | * EMatrix * | Y1 | = 0 .
     \  1 /             \  1 /           \  1 /             \  1 /

Bildkoordinaten resultieren aus 3D Richtungsvektoren durch die Multiplikation mit der Kameramatrix CamMat: 

     / C \              / X \
     | R |  =  CamMat * | Y | = 0 .
     \ 1 /              \ 1 /

Die Fundamental-Matrix FMatrixFMatrixFMatrixFMatrixFMatrixFMatrix kann daher aus der Essential-Matrix EMatrixEMatrixEMatrixEMatrixEMatrixEMatrix und den Kameramatrizen CamMat1CamMat1CamMat1CamMat1CamMat1camMat1, CamMat2CamMat2CamMat2CamMat2CamMat2camMat2 mittels folgender Formel berechnet werden: 

                        -T                    -1
     FMatrix  =  CamMat2   * EMatrix * CamMat1    .

Die Transformation geht einher mit einer Fortpflanzung der Kovarianzmatrizen von CovEMatCovEMatCovEMatCovEMatCovEMatcovEMat zu CovFMatCovFMatCovFMatCovFMatCovFMatcovFMat. Sollte CovEMatCovEMatCovEMatCovEMatCovEMatcovEMat leer sein, so wird CovFMatCovFMatCovFMatCovFMatCovFMatcovFMat ebenfalls leer sein.

Der Konvertierungsoperator essential_to_fundamental_matrixessential_to_fundamental_matrixEssentialToFundamentalMatrixessential_to_fundamental_matrixEssentialToFundamentalMatrixEssentialToFundamentalMatrix wird besonders zur Visualierung der Epipolarlinienstruktur mittels der Fundamental-Matrix verwendet, was die zu Grunde liegende Stereogeometrie verdeutlicht.

Parallelisierung

Parameter

EMatrixEMatrixEMatrixEMatrixEMatrixEMatrix (input_control)  hom_mat2d → HHomMat2D, HTupleHTupleHTupleHHomMat2DX, VARIANTHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong) (double / Hlong) (double / Hlong)

Essential-Matrix.

CovEMatCovEMatCovEMatCovEMatCovEMatcovEMat (input_control)  number-array → HTupleHTupleHTupleVARIANTHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong) (double / Hlong) (double / Hlong)

9x9 Kovarianzmatrix der Essential-Matrix.

Defaultwert: []

CamMat1CamMat1CamMat1CamMat1CamMat1camMat1 (input_control)  hom_mat2d → HHomMat2D, HTupleHTupleHTupleHHomMat2DX, VARIANTHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong) (double / Hlong) (double / Hlong)

Kameramatrix der 1. Kamera.

CamMat2CamMat2CamMat2CamMat2CamMat2camMat2 (input_control)  hom_mat2d → HHomMat2D, HTupleHTupleHTupleHHomMat2DX, VARIANTHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong) (double / Hlong) (double / Hlong)

Kameramatrix der 2. Kamera.

FMatrixFMatrixFMatrixFMatrixFMatrixFMatrix (output_control)  hom_mat2d → HHomMat2D, HTupleHTupleHTupleHHomMat2DX, VARIANTHtuple (real) (double) (double) (double) (double) (double)

Berechnete Fundamental-Matrix.

CovFMatCovFMatCovFMatCovFMatCovFMatcovFMat (output_control)  real-array → HTupleHTupleHTupleVARIANTHtuple (real) (double) (double) (double) (double) (double)

9x9 Kovarianzmatrix der Fundamental-Matrix.

Vorgänger

vector_to_essential_matrixvector_to_essential_matrixVectorToEssentialMatrixvector_to_essential_matrixVectorToEssentialMatrixVectorToEssentialMatrix

Alternativen

rel_pose_to_fundamental_matrixrel_pose_to_fundamental_matrixRelPoseToFundamentalMatrixrel_pose_to_fundamental_matrixRelPoseToFundamentalMatrixRelPoseToFundamentalMatrix

Modul

3D Metrology

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