Homography estimation using adaptive GNC

© 2021 NEC Corporation

This repository is an official MATLAB implementation of the paper "Fast and Robust Homography Estimation by Adaptive Graduated Non-Convexity", ICIP2019 [1].

License

This software is released under the NEC Corporation License. See LICENSE before using the code. If you use this code, please cite the paper.

@inproceedings{nakano2019fast,
  title={Fast and robust homography estimation by adaptive graduated non-convexity},
  author={Nakano, Gaku and Shibata, Takashi},
  booktitle={2019 IEEE International Conference on Image Processing (ICIP)},
  pages={2556--2560},
  year={2019},
  organization={IEEE}
}

For commercial use, please contact Gaku Nakano <[email protected]>.

Usage

Install

Copy gnc_homography folder and set a path to folders by addpath('gnc_homography','gnc_homography/3rdparty').

Function API

[H, inliers] = gnc_homog_nakano_icip2019(m1, m2, 'param1', value1, 'param2', value2, ...)

INPUTS
  m1, m2     : (2xN or 3xN matrix)
               2D point correspondences in inhomogeneous coordinates
               [x1, x2, ... xN
                y1, y2, ... yN]
                  or
               homogeneous coordinates (will be normalized by [xi/zi; yi/zi])
               [x1, x2, ... xN
                y1, y2, ... yN
                z1, z2, ... zN]

OPTIONS
  lambda_max : (scalar, default: 1e3)
               The maxilambdam pixel error for determining inliers.

  lambda_min : (scalar, default: 2)
               The minilambdam pixel error for determining inliers.

  rho        : (scalar, default: 0.95)
               Decreasing factor for updating lambda = rho*lambda in each iteration.
               If lambda_new - lambda < 0.5 for any rho, lambda_new = lambda - 0.5.

  method     : (char, default: 'symtrans')
               Homography estimation method which minimizes
               'symtrans'      : symmetric transfer error
               'singletrans'   : error in the first image
               'reproj'        : reprojection error
               'sampson'       : Sampson error (1st approximation of reprojection error)
               'algebraic'     : algebraic error

  weightfunc : (char, default: 'truncL2') 
               Weighting function of the IRLS scheme
               'truncL2'       : truncated L2
               'Tukey'         : Tukey's biweight
               'GemanMcClure'  : Geman-McClure
               'L2log'         : L2-log
               'Entropy'       :
               'MFT'           : Mean-Field function

  w          : (Nx1 or 1xN vector, defalut: ones(n,1)) 
               Initial weight for the point correspondences (0<=wi<=1).
               Given this parameter, the initial homography H is computed by weighted least squares and
               lambda_max is overwritten based on residuals of w > 0.5 points. Ohterwise, H is given by eye(3).

  choosebest : (logical, default: true)
               Return the best model if true. Otherwise, return the
               model at the final GNC iteration.

  verbose    : (logical, default: true)
               Display outputs at each GNC itereation. 

OUTPUTS
  H          : (3x3 matrix)
               Homography matrix such that m2 = H*m1.

  inliers    : (1xN logical vector)
               Indeces of inlier points.

Run demo/demo_gnc_homog_icip2019.m to understand how it works.
Please refer to [2] and [3] for the details of GNC, IRLS (M-estimator), and weight functions.

Reference

1. Gaku Nakano and Shibata Takashi, "Fast and Robust Homography Estimation by Adaptive Graduated Non-Convexity," ICIP 2019. (pdf)

2. Michael J. Black and Anand Rangarajan, "On the unification of line processes, outlier rejection, and robust statistics with applications in early vision," IJCV, 19(1):57-91, 1996, Springer. (pdf)

3. Zhengyou Zhang, "Parameter estimation techniques: A tutorial with application to conic fitting," IVC, 15(1):59-76, 1997, Elsevier. (pdf)

Contributors

• Gaku Nakano, Central Research Laboratories, NEC Corporation.
  [email protected]
  (ENG) https://www.nec.com/en/global/rd/people/gaku_nakano.html
  (JPN) https://jpn.nec.com/rd/people/gaku_nakano.html

• Takashi Shibata, Central Research Laboratories, NEC Corporation.
  [email protected]