This program implements the homographic transformation of an image using B-spline interpolation. It is part of an IPOL publication

• Thibaud Briand thibaud.briand@enpc.fr
• Pascal Monasse monasse@imagine.enpc.fr

Laboratoire d'Informatique Gaspard Monge (LIGM)/ Ecole des Ponts ParisTech

Version 1.0, released on 06/27/2018

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version.

You should have received a copy of the GNU General Pulic License along with this program. If not, see http://www.gnu.org/licenses/.

Copyright (C) 2017-2018, Thibaud Briand thibaud.briand@enpc.fr, Pascal Monasse monasse@imagine.enpc.fr

All rights reserved.

Required environment: Any unix-like system with a standard compilation environment (make and C compiler) and Cmake. Optional libraries: libpng, lipjpeg, libtiff, GSL

Build instructions:

$ mkdir build
$ cd build
$ cmake -DCMAKE_BUILD_TYPE=Release ../src
$ make

It produces library "Splinter" and programs "bspline" and "compute_order".

The program reads an homography, an input image, takes some parameters and produces an homographic transformation of the image using B-spline interpolation. The meaning of the parameters is thoroughly discussed on the accompanying IPOL article.

  Usage: ./bspline "homography" in out [order boundary eps larger]
Homographic transformation of an image using B-spline interpolation

homography: 9 matrix coefficients ("h11 h12 h13; h21 h22 h23; h31 h32 h33")
in       : filename of the input image
out      : filename of the output image
  Options:
  order    : order of interpolation (integer between 0 and 16, default 11)
  boundary : extension (constant, periodic, hsymmetric*, wsymmetric)
  eps      : relative precision (float, default 6) (eps>=1 means 10^-eps)
  larger   : compute on exact (0*) or larger domain (1)
    *default parameters

Execution examples:

1. Default parameters for an horizontal shift of 0.5 pixel:

   $ bspline "1 0 0.5; 0 1 0; 0 0 1" input.png output.tiff

2. Using order 3, constant boundary extension and relative precision of 10^-5:

   $ bspline "1 0 0.5; 0 1 0; 0 0 1" input.png output.tiff 3 constant 5

Remark: the semicolon row separators in the homography matrix are optional.

Remark: the boundary parameter can be abridged (e.g. c=const=constant)

$ ./bspline "1 0 0.5; 0 1 0; 0 0 1" ../data/lenna.pgm out.pfm
$ diff -s ../data/lenna_x+0.5.pfm out.pfm

The pfm output format is not standard and not readable by most software. Displayable output formats include pgm, ppm, png, jpeg, tiff (require optional library support)

The core part of the bspline interpolation is included in library "Splinter". If you want to use bspline interpolation in your own programs, this is the only part you need. The usage is fairly simple (see function splinter_homography):

#include "splinter.h"
splinter_plan_t plan = splinter_plan(...); // Prefiltering
double pixOut[3];                          // Output values (#channels)
splinter(pixOut, 1.3, 2.4, plan);         // Interpolate at coords (1.3,2.4)
splinter_destroy_plan(plan);               // Free reserved memory

$ cd src
$ doxygen Doxyfile

Open html/index.html to browse the documentation.

• bspline_main.c : Main program for input/output
• homography_tools.[hc] : Functions related to homographies
• splinter_transform.[hc]: Compute homographic transformation of image
• bspline.[hc] : Compute B-spline parameters and kernel (library)
• splinter.[hc] : Prefilter and indirect B-spline transform (library)

Additional files:

• iio/ : C library for opening images in any format
• xmtime.h : Clock with millisecond precision
• compute_bspline.c : Ccompute the B-spline interpolator parameters
• hom4p.c : Compute homography from 4 points (for on-line demo)