# CSCI  4830/5722 Assignment 2  solution

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Image  Mosaics     For  Assignment  2,  you  will  implement  an  image  stitcher  that  uses  image  warping   and  homographies  to  automatically  create  an  image  mosaic.  We  will  focus  on  the   case  where  we  have  two  input  images  that  should  form  the  mosaic,  where  we  warp   one  image  into  the  plane  of  the  second  image  and  display  the  combined  views.  This   problem  will  give  some  practice  manipulating  homogeneous  coordinates,  computing   homography  matrices,  and  performing  image  warps.  For  simplicity,  we’ll  specify   corresponding  pairs  of  points  manually  using  mouse  clicks.     Note:  There  are  some  built-­‐in  Matlab  functions  that  could  do  much  of  the  work  for   this  project.  However,  to  get  practice  with  the  workings  of  the  algorithms,  we  want   you  to  write  your  own  code.  Specifically,  you  may  not  use  any  of  these  functions  in   your  implementation:  cp2tform,  imtransform,  tformarray,  tformfwd,  tforminv,     maketform.     Provided  files:   Two  image  files  that  can  be  used  for  the  mosaic.     What  You  Have  to  Do       Task  1  (15  points)  Getting  correspondences:     Write  code  to  get  manually  identified  corresponding  points  from  two  views.  Look  at   Matlab’s  ginput  function  for  an  easy  way  to  collect  mouse  click  positions.  The   results  will  be  sensitive  to  the  accuracy  of  the  corresponding  points;  when  providing   clicks,  choose  distinctive  points  in  the  image  that  appear  in  both  views.       Task  2  (20  points)  Computing  the  homography  parameters:     Write  a  function  that  takes  a  set  of  corresponding  image  points  and  computes  the   associated  3  x  3  homography  matrix  H.  This  matrix  transforms  any  point  pi  in  one   view  to  its  corresponding  homogeneous  coordinates  in  the  second  view,  pi’,  such   that     λ*  pi  =  H  *  pi’     Note  that  pi  and  pi’  are  both  vectors  with  3  elements.  The  function  should  take  a  list   of  pairs  of  corresponding  points  (what  is  the  minimum  number  of  points  you   need?)  from  the  two  views,  where  each  point  is  specified  with  its  2d  image   coordinates.   Useful  Matlab  functions:  ‘\’  operator  (help  mldivide),  reshape
Verify  that  the  homography  matrix  your  function  computes  is  correct  by  mapping   the  clicked  image  points  from  one  view  to  the  other,  and  displaying  them  on  top  of   each  respective  image.  Be  sure  to  handle  homogenous  and  non-­‐homogenous   coordinates  correctly.     Task  3  (20  points)  Warping  between  image  planes:     Write  a  function  that  can  take  the  recovered  homography  matrix  and  an  image,  and   return  a  new  image  that  is  the  warp  of  the  input  image  using  H  .  Since  the   transformed  coordinates  will  typically  be  sub-­‐pixel  values,  you  will  need  to  sample   the  pixel  values  from  nearby  pixels.  Feel  free  to  use  the  sampleBilinear.m you   developed  for  the  first  assignment.  For  color  images,  warp  each  RGB  channel   separately  and  then  stack  together  to  form  the  output.  To  avoid  holes  in  the  output,   use  inverse  warp  rather  than  direct  mapping.       To  compute  the  bounding  box  of  the  destination  image,  you  will  need  to  warp  the   points  from  the  source  image  into  the  reference  frame  of  the  destination.  Then   sample  all  points  in  that  destination  bounding  box  from  the  proper  coordinates  in   the  source  image.  Note  that  transforming  all  the  points  will  generate  an  image  of  a   different  shape  /  dimensions  than  the  original  input.  It  is  ok  to  have  some  areas  of   the  new  image  be  black  (0).     Useful  Matlab  functions:  round, interp2, meshgrid, isnan.     Task  4  (20  points)  Create  the  output  mosaic:     Once  we  have  the  source  image  warped  into  the  destination  image’s  frame  of   reference,  we  can  create  a  merged  image  showing  the  mosaic.  Create  a  new  image   large  enough  to  hold  both  (registered)  views;  overlay  one  view  onto  the  other,   simply  leaving  it  black  wherever  no  data  is  available.  Don’t  worry  about  artifacts   that  result  at  the  boundaries.     You  are  free  to  use  a  method/convention  of  your  own  choosing  for  the  overlap   areas.         Task  5  (25  points)  After  writing  and  debugging  your  system:     1.  [5  pts]  Apply  your  system  to  the  provided  pair  of  images,  and  display  the  output   mosaic.   2.  [10  pts]  Show  two  additional  examples  of  mosaics  you  created  using  images  that   you  have  taken.  You  can  make  a  mosaic  from  two  or  more  images  of  a  broad  scene   that  requires  a  wide  angle  view  to  see  well.  Or,  make  a  mosaic  using  two  images   from  the  same  room  where  the  same  person  appears  in  both.   3.  [10  pts]  Warp  one  image  into  a  “frame”  region  in  the  second  image.  To  do  this,  let   the  points  from  the  one  view  be  the  corners  of  the  image  you  want  to  insert  in  the   frame,  and  the  let  the  corresponding  points  in  the  second  view  be  the  clicked  points
of  the  frame  (rectangle)  into  which  the  first  image  should  be  warped.  Use  this  idea   to  replace  one  surface  in  an  image  with  an  image  of  something  else.  For  example  -­‐-­‐   overwrite  a  billboard  with  a  picture  of  your  dog,  or  project  a  drawing  from  one   image  onto  the  street  in  another  image,  or  replace  a  portrait  on  the  wall  with   someone  else’s  face,  or  paste  a  Powerpoint  slide  onto  a  movie  screen,  …   For  all  examples,  play  around  a  bit  with  the  choice  of  points  for  the  correspondence   pairs  until  you  get  a  reasonable  alignment.     [OPTIONAL]  Extra  credit       Implement  RANSAC  for  robustly  estimating  the  homography  matrix  from  noisy   correspondences.  Your  function  should  be  able  to  handle  more  than  4  point   correspondences.  Show  with  an  example  where  it  successfully  gives  good  results   even  when  there  are  outlier  (bad)  correspondences  given  as  input.  Compare  the   robust  output  to  the  original  (non-­‐RANSAC,  only  4  point  correspondences)   implementation  where  all  correspondences  are  used.       Note:  feel  free  to  attempt  using  David  Lowe’s  SIFT  Matlab  demo   (http://www.cs.ubc.ca/~lowe/keypoints/siftDemoV4.zip).  Warning:  it  only  works   in  Linux  and  Windows,  it  does  not  work  on  Mac.     The  result  of  calling  the  sift.m function  will  be  2  vectors,  one  of  features  and  one   of  keypoints.  Make  sure  you  understand  what  is  saved  in  these  two  variables  so  that   you  can  potentially  use  them  for  the  RANSAC  implementation.  If  you  can’t  get  SIFT   to  work,  you  will  need  to  select  make  than  4  pairs  of  points  using  the  function   developed  in  Task  1.     Submitting  the  assignment:   Make  sure  each  script  or  function  file  is  well  commented  and  it  includes  a  block   comment  with  your  name,  course  number,  assignment  number  and  instructor  name.   Zip  all  the  .m  and  image  files  together  and  submit  the  resulting  .zip  file  through   Moodle  as  Assignment  2  by  Friday,  September  30th,  by  11:55pm.     Acknowledgement:  project  description  and  test  images  courtesy  of  Kristen   Grauman,  University  of  Texas  at  Austin.     Tips:   • It  can  be  useful  when  debugging  to  plot  the  corners  and  clicked  points  from   one  view  on  top  of  the  second  view  after  transforming  them  via  H.  Use   axis([minx,  maxx,  miny,  maxy]);  to  adjust  the  viewing  window  so  that  you   can  see  all  points.  • You  will  need  the  inverse  of  the  homography  matrix  to  transform   “backwards”.
• Be  aware  that  Matlab’s  image  (matrix)  indices  are  specified  in  (row,col)   order,  i.e.,  (y,x),  whereas  the  plot  and  ginput  functions  use  (col,row)   order,  i.e.,  (x,y).  • Check  the  order  of  the  clicked  corresponding  points,  to  make  sure  your  code   uses  the  intended  corresponding  point  pairs.  • As  usual,  be  careful  with  how  images  are  cast  for  computations  and  display   (double  vs.  uint8).  In  particular,  for  your  sampleBilinear.m  function,  be   sure  to  pass  a  matrix  of  doubles  for  the  image  input.  • When  collecting  your  own  images,  be  sure  to  either  maintain  the  same  center   of  projection  (hold  the  camera  at  one  location,  but  rotate  between  views),  or   else  take  shots  of  a  scene  with  a  large  planar  component  (a  building,  maybe).   In  either  case,  use  a  static  scene.  Textured  images  that  have  distinctive  points   you  can  click  on  are  good.