MATLAB Functions for Multiple View Geometry

Please report any bugs to Andrew Zisserman [email]

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

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

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

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

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

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

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.