MATLAB Functions for Multiple View Geometry

Please report any bugs to Andrew Zisserman [email]

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The complete set of these functions are available as a gzipped tar file allfns.tar.gz, or as a zip file allfns.zip. NOTE, it is recommended that the complete set is downloaded as many of the functions use other functions.

MIT License

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Acknowledgements: These functions are written by: David Capel, Andrew Fitzgibbon, Peter Kovesi, Tomas Werner, Yoni Wexler, and Andrew Zisserman

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VGG MultiView Compute Library

Conversions:

• vgg_KR_from_P.m extract K, R from P such that P = K*R*[eye(3) -t]
• vgg_F_from_P.m fundamental matrix from 2 cameras
• vgg_P_from_F.m 2 camera matrices from fundamental matrix
• vgg_T_from_P.m trifocal tensor from 3 cameras
• vgg_H_from_2P_plane.m inter-image homography from 2 cameras and 3D plane
• vgg_H_from_P_plane.m projection matrix from image onto 3D plane
• vgg_plane_from_2P_H.m 3D plane from 2 cameras and inter-image homography

Multiview tensors from image correspondences:

• vgg_H_from_x_lin.m homography from points in 2 images, linear method
• vgg_H_from_x_nonlin.m MLE of the above, by nonlinear method
• vgg_Haffine_from_x_MLE.m MLE of affine transformation from points in 2 images, linear
• vgg_F_from_7pts_2img.m fundamental matrix from 7 points in 2 images
• vgg_PX_from_6pts_3img.m cameras and world points from 6 points in 3 images

Preconditioning for estimation:

• vgg_conditioner_from_image.m conditioning shift+scaling from image dimensions
• vgg_conditioner_from_pts.m conditioning shift+scaling from image points

Self-calibration and similar:

• vgg_signsPX_from_x.m swaps signs of P and X so that projection scales are positive
• vgg_selfcalib_qaffine.m quasi-affine from projective reconstruction
• vgg_selfcalib_metric_vansq.m metric from projective and 3 orthogonal principal directions and square pixels

Estimation:

• vgg_X_from_xP_lin.m 3D point from image projections and cameras, linear
• vgg_X_from_xP_nonlin.m MLE of that, non-linear method
• vgg_line3d_from_lP_lin.m 3D line segment from image line segments and cameras, linear
• vgg_line3d_from_lP_nonlin.m MLE of that, non-linear method

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VGG User Interface Library

GUI's:

• vgg_gui_F.m Visualizes epipolar geometry between two views
• vgg_gui_H.m Visualizes a homography between two views

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Examples

These examples use images and matrices included in the directory vgg_examples. Change to that directory before running the example functions.

• view_homog_ex.m Example of using vgg_gui_H
• view_fund_ex.m Example of using vgg_gui_F
• Haffine_from_x_MLE_ex.m Example of using vgg_Haffine_from_x_MLE
• F_from_Ps_ex.m Example on computing F from two camera matrices using vgg_F_from_P
• H_from_image_corr_ex.m Example on computing H from points using vgg_H_from_x_lin
• testhomog_vgg.m Example of computing H from two images from a rotating camera. This example also requires ransacfithomography_vgg.m and Peter Kovesi's functions (such as matchbycorrelation.m and ransac.m). See link below.
  
  First image
  Second image (camera rotation between views)
  Inlying matches consistent with estimated homography

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Links to other highly recommended Computer Vision software

• Peter Kovesi's Matlab Functions for Computer Vision and Image Analysis
• Jean-Yves Bouguet's Matlab Calibration Software

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Note on release versions

November 2012 updates to

• ransacfithomography_vgg.m
• testhomog_vgg.m
• vgg_H_from_x_nonlin.m

To maintain compatibility with Peter Kovesi's functions and for Matlab R2012a compatibility.

Thanks to: Relja Arandjelovic, Peter Corke and Alexander Khanin.