Volumetric Video Motion Detection for Unobtrusive

0 downloads 0 Views 2MB Size Report
The system produces time-varying volumetric data at real-time rates (10-. 30Hz) .... Intrinsic calibration checkerboards with features automatically detected . . . 15.
SANDIA REPORT SAND2002-0801 Unlimited Release Printed April 2002

Volumetric Video Motion Detection for Unobtrusive Human-Computer Interraction

Daniel E. Small, Jason P. Luck, and Jeffrey J. Carlson Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Livermore, California 94550 Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000. Approved for public release; further dissemination unlimited.

Issued by Sandia National Laboratories, operated for the United States Department of Energy by Sandia Corporation.

NOTICE: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government, any agency thereof, or any of their contractors or subcontractors. The views and opinions expressed herein do not necessarily state or reflect those of the United States Government, any agency thereof, or any of their contractors. Printed in the United States of America. This report has been reproduced directly from the best available copy. Available to DOE and DOE contractors from U.S. Department of Energy Office of Scientific and Technical Information P.O. Box 62 Oak Ridge, TN 37831 Telephone: (865)576-8401 Facsimile: (865)576-5728 E-Mail: [email protected] Online ordering: http://www.doe.gov/bridge

Available to the public from U.S. Department of Commerce National Technical Information Service 5285 Port Royal Rd Springfield, VA 22161 Telephone: (800)553-6847 Facsimile: (703)605-6900 E-Mail: [email protected] Online order: http://www.ntis.gov/ordering.htm



       

                             !"  #  $  %  "           &  ' () *  &++ , - * .

 

/0  1   2  0  %   1   3  0  21 " ,4 5 0  1    %  % 3 0  3   )  1 05  0  3   !00 3  /0  0   &  5  0  %    "        3   /  0 3  0   6  7 /0 "   1" % 1         6 8 .9:7 /0   0 3 3 & " 1   %    "  % 0  0 +     " 5     0    &  $ 0  0  5 1 5 0 1  5 0 2     1 0 0  &0  1    &    0 )     03 0 ;         5  3    < 3%&&       %  0 %0     $$$  /0    5  2%  &1   1  /0  05     35   1      /5 " 3 03 0  % 0 5      0    1 3  5  = 01   )      3 0           % $ 0    1 5 3 5  

   % >1   0   3    1   & .  %     /0 0  0     " )   0 1  5 & 5     1 0    

         





           

 '11 5                                        03 0 /0 +                         . =0"  /0   / ?                           



 @

     !"  #$# $

%

&      

%

 # # &                                   ( %  &                               . 03 0                                . . .. .B

" 0                   # # &  ,0 %"           ( %   !  %    0 )  $    3 03 0      

   

   

   

   

   

   

   

   

   

   

   

   

   

   

 A    . @

' ()    *

&

+        , - .!        / / ! " 0          1 

&& &, &, &

B    1 ;                            



  . B *

2

 @ @ @. @B @* @A @@ @@

$   :              / % 3  ("       1             / >   "    1   #       

    

    

   -   / ! "

    

    

    

    

    

    

    

    

    

    

    

    

$   :                            / %  /5 "/5 % 3 ; 9 , / / %                          & / %                          9 / %                          C  ;&                         ; (" / %                    #      ; (" / %              ; = 3 / %                  

.

             

             

             

             

             

             

             

             

             

             

.

. . B B B

'

B B BB BB B* BA BA * *

   . B * A  @   . B * A  @    . B * A

 @ .

   3 0   0                       %       #  D  3 3 #                                 $     &  0 & 5 0 3   "        % 3 )    &                       & " 6 1 57                                >0   3 3                            E5  % 3                              )    &  > $                              , 0 %  !  %                          05   .                             1   %                             #   0 5 0 05 1                     #   0  1  & "  0                 $1 .                                    0 % &3    %                    0 % 3    %                    '  &  0 %                              .  5 0   &  0 %                      1% 3 3 0  ) C   % 0               1% 3 3 0 9"& C   % 0              )  3  %   3 60 5 %0  0    50  0 5 %0  0 5  50 0  30 5"    5 7             /0 - %   5 3 " % : &"  " 6%  0  5  & 3 5 0 0  5 07           /0  &"     3   ) % 3 3  6     7 5 0 3 % 3 3    & 6 %7    0 % 3 3 0                                  C)  )  %  3 50 0  0    %   5 0 0                                          , %  %    /0 30    05 0 D   0      50 3   %       "  +         /0  %00        %  " 6  F @ %7 50  3   %    %   +               1 %  %     5    05  50 0 1  % 

  6    A  & )   A7                    1  3&  ' 0 3   0 . 1    0  %0     " 3 0 1)  5 0 0   &    0     >  /0 #   /0   05 0   3  %     %  0     %  '   /0  05 0    3 0 3 0   %  G.H                      >  /0 #   /0   05 0   3  %     %  0     %  '   /0  05 0    3 0 3   %  G.H                      B

  * A    . * * A   @ . . .. .B .* .* .@ B B B.

B* BA BB B@

.

C  0   1      % &  )  0  /0  05 0 %  3   1  0       0 " /0 %0 %"  I 0 &  &D  0 1  0  0 

  3 0 D   /0  %"  0   3 0   3 0 D         3 0 1  0            

*

B@

         

A

      



    0  1   "      0 &      1   %   "  1    "  3  6   " 07 +        % ( 3 0    & 3     +  % 0        .    %     &  ,0 5 0  " &   0  2  & 0  " 50 %  + 

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

                                                                    !                  " #                       " $  %      

&       %     '    %        

&&     '       " (                          " /0 2 1    "   0  &" "   3 0 &D /0   1     0 3 &"   3 0 &D  % " 0  "   1   5    1 % 0 1   3 0 " = 0 0 " 0 )  5     /0 2      :     0     0   3   % 0 1   3   % 0 5 5 05 05  " 1  1  3& 3 0  %  0  ; 5 % 0  & 3 " 3 0   3 0    3 0 D  1   "  "   3 0  %  

   &    0 2  3 0  %  



   

/0 0 & 0 5 0  3 03 0 '  3 0 %  3 0  0 

  0%0 " 1 %   3  % 0  0 3     +     /0     3   /  0 3  0   6 7    %   0   M

  

  &    0 )      0 D      

/0 &  3  % .   0 5     ) 0 %    3 0    &"   &   /0  5  3  0  &   

/0 2  0     50 0  0   3 0  /0    3   0 )    50 0  0          3 0  0   1   )    " /  0 0         3  03 0      &  &      "  0 )   0  3   3" % 0 % 0  )  50 0 01 0 % 5 0    & %  % /0                     = 5  &  "  0  5   1 0 + /0  3  0 D           D 0 )  0   0 1    50 0        ; % 05 0 &  0  )  %  0 &"  1  0  /0 1  0  %  "   3 0  0   0 & " 3 0 03  0 0 +   1  1   / +      1   0 KN  4  50   1  & L /  O   0 D       &  0  %  1 " 3 0 + = 5 1 5  3 0 0 +   5    )      "  3 5 0 + 50 0 5      



       

/0   "             3 03 0 ;    &%     0 5    E 5  3 5 &  9 %    3 0  & )     5     5 0 0 & +   " 951 0 %  0  " 0       /03 5   " 0  &  3  % %  0          3  %  " 0 5      0     3       % 0  " 5     &   1 %      "   &   1   3     0   "    " 1 &   % " 6%    /0  % 4 K;  3 ( L G.H 0  0 ; G.BH  0  %  4 '   G.AH7 0  "   &    0  3 1   " 0        % 3   ! 5   

1 1 1  % 3 = 0 0 1  3 % %0:  %   3  %  % % 3   5   &   &    1    5 0 &  " 50 0   1 "      0     % 3 0    % 0  0 + 5   0 & "     . )   3 0 1 % &D   1       0     = 5    5  " % 0     0 &  3 %  % " 0  . 1 5 = 5   05   3    3 3 1 1      3 5 03 0  % 0 50 0 5     0   3 0  0   "   0  0       0 3 0   0 3        " #0 %   O  G-H $ 0  5     1     3 0 %  3 0 &" /0 3 3 0  0 

   0 05 +   3  "     0   0"  &   

1  Æ  " $ #0  5 5 1   11 5 3  5 0  3 03 0 /0       " 5 0   5   &   @

#0 .  & 0       0  3          3 )    0 )   #0 B % 1       "  3 5  % 0 0 5      "    & 3 11 5 3  1    3 0  0  %" #      % 1 #0 *    3 3 5   & #0 A

           /0 & %    0 " 3 03 0 0   0  M   &   & %  &  6 0 )  7   1    





! 

#  &   5    1   G-  @  . B *H (3  1     5 )  1 " 1 % 0 2  3 0%" G  H # &    "  ) % . 3  3  % # &  0 +  &   2  5 % M 0%  0 +    3 &  0 +  3  &  0 +    0 0%  0 + G H ; 0    5  0%  0 + ( 5 5   1  %  1    &  5 0 0 35 & 3  0   "   5 0 ) " 5   %    951 0  2  3 1 5 3 20"     % & " 3  D    1"  & 3  )  /"  "   0 " 5 01 1 5 01  2  3 1 5 &5 A   @  /0  +    &  0 + 0     % 0 Æ   3       / G-H 05 05    "  "         3 0  1   " $3   5 0  5 2  3 1 5    "  & "          0  5 & 5 )  &"   0  /0  0     "  " 0    5   %    > 0" G .H )   &  3    & 951 0  0    & 0   5"  0 1 0  )    3 0  &  3          /0     0     0  0  % 3 0       $     &      &  0 + 0        &  % 0 0 .  &  % /0   5 3     &   % 6 %  %   0 57 0       0 .  &   % 0 0 5 3  2 =    GH   30 1  P0 %4 5  "# & G@H =  0   &  3       0 ' #C  1   &" G@H 50 0  &  "# & P0 %   0 0 "# &  % 0 5 &   "       0      0 ' #C &" 5   &   &  2        0 &"  3 )   % 0   0 &     E5  %  05 ; % 





!  ' %$

'     3   &  1 1 5 %             3 0 & % 5     0     /0 0 & % "     3    0        .  %  &" ) 0  5  &   1    5    " /0 

           !                " !  

    #     $      $    %          &   '         (

       

    )          ¾

ÊÌË ¿        



 =  "  9 -

   ÊÌË

     >        

5   5 0  > $ 6 05 ; % @7 0  5 0      2    %    0 %         0 5 0 .     ) 2  /0  1 5 01     &     5 0 0 /0  

  2  3 0 %  3 &" 0  $      : &" 0 %  *  *  )  %0&0 3 0     0     /0  1  3    & ) 0 3 0   3 0 % '   %    0 

1   3    2  0 )    /0  > $  5 3       &      &  0  5    " '  0      )    3 0  01 &   0 )     & 0  1  &1 &"  0  ' "    &       ) 3   $ & 3 " 0 1)        & D  0 3 0  %  % 0 )         &   3 0  /0  % 0   0  1    & 

 05  % 0 . 50     !"#      . 6    7     3   &       0  )     6Q  Q7 0 0      % 0      )    &   3 0  $  " 0    5   3 0  0      0 1) 0    %   )    3 0  $ 0   &  2  0          6  7       )             0  2 "     % 0  ) 0  0 % ' .&   % "    3 &" 3 " /0     1)   &  50   :  B  #$%&%       &" 650        0 & 3 1)  0   1 )7 /0  3     !"#  05

 % 0 B /0  &       3 J  /0   3 0 .        5 0 "  3    /0  % 0    0 1   &   '6#7 50 #  0 & 3 1)  0 1  /0 3       !"#  '6 7 /0   0 & 3            0 0 & 3 1) 



 2 #      !$  ,   89$                "                     %                !       ," ?          %                     "

" $ &4  % 0M # .     /&   M  1   %  1)  :      0          3   &   M    &  0   .   0 1      0  %    5!/6 " 7 )# 89

  )      "      :    





(  )  /0 0 % 0 &5 0 5 1   2  M    



   S F  

 

6 7

=  0  !        0 %    3" % 05  )    0  #0 %4 " GBH 5       & 30    2 " 0 %  % 3 0  5 0   &"   %      % 5     %   3  3 0    0      5   : &"  %   &  3 0 +      3    /0  &     21  % 2   %  /0    3   : 0  !  %  5     0   " 00  &1 0 1 "  "  &" 05   0 E /0 ) &  5  5 0    1   &     1   1" 5  " &5  50 0     &    0  00  1     3  0  & " 01  !      '  5"  1  0     %       0   1   3    3 % /0    3 0 0 3    "   %  & % 

%    1     GH /0   1   % )  0   3 0 %    )  3 0   1   % 6   %   3 -*   %7  05 ; %  /0   1       0  %    &        1  " ( %0      0 %0   1   1    0 0 % 3      5 01  0 5   1   0 0 % 3  0   3 /0   0  !    01 1"  !    0  

  '      ,               74   "            &            A    %   %        "              "             00  %             "         00             %           " = % 0 5 0 6   "  !  %   0  !  %7    %  A

 0  &0 3   E) &  /0  3    05  % 0 *

" $ +4  % 0M )  0 3 ( %   M  1    >( % M  & "  0 () 061    7 "  D         

 0G DH F  S  F  G DH   G DH S % F  G DH%   G DH% S & F  G DH&    G DH&   6  6 S  $   S%  $   S&  $ 77 $  6 S  ! $   S%  ! $   S&  ! $ 7 $  0G DH F



 F GG G DHG G DH% G G DH& H

 F G G DH G DH%  G DH& H   S F   ½½ ¼¼  6S ! S 7 $  0G DH F

















  1G DH ,  1G DH% -  1G DH&   6 S  !   S%  ! %  S&  ! & 7 $  0G DH F

      

/0   3 0 & %   !  %  % 0  05 ; % . /0 05 01 & 3 " 1 /0    )  01 &   2   0  % 0    &  % 0 *  )    2   0   "     "  &   )    2   0   1       "    )    2   0 0  %      " %  /0   3 0   2   &  ; % B 50 0   2  )  01 &  1  & "  0 $ ; % * 0 1      %   % )0 &    3 0   0 5   0 1      %  0 % -

 !                                         A      

    " )  

,             " )  

,             " )  

,             "     !       4"

 + )                             !"     !       4" /0  &  5  5 2 % 0  0  0  0 /"  " 3 0     3  0 %     3 00  %  3  " 0  3 0 %   3   0   0 50 0 50 D   0   . 0 ' 0 5  0 0 % 3   =   3   0 ' #C &" 6 G@H7 0   & " %   5 1 0 0" 3  M )      0    0  /0 )  5  2 0    %   5 0 0 1       2 0  )  %   5 0 0 1  : /0  0 0 &  ! 3 1 % 0  3 0 %  0   1 %   3 0 & %  ;  " 0 3  

0 ' #C &"  3  %0      ; % A 05 0  0

% &3    %   ; % - 05 0  0 % 3    %



 4   (          !              

   '        %     !"

+

,     

=    5  !  03 0  % 0 50 0 5 01 M 7  ) C    7 9"& C  (0  % 0  "  &      0  3 & D   /0  ) C   % 0  05  % 0 A $ 5  &" 1 % 1" 1) 0 1     % 0 6  7   0 % 0 0 1)    D  $ )  0    )  0  0 %   3 0"    5 0 0  0 0 1)       $3   %   )    0  0 0 0 1)     " ( 5 5    0 3 3  %  0 2%  "   :  5    0  %  1)  0 1    0    3 0 0 2% /0    6    7   )  @

 6 '           

 "

   

/      

 7 '           /       &      

 "            

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

" $ ,4  % 0M  ) C  0 3  0  M  0M  " 3  0 % M 1 M  & " . 1   % : )#-#6 $9 "       D              #  617 F 1)  /& G D H  6 0G  1H FF 7 $

  1  3 0   3 &   / 1     0   5   01 50 3 E" % 0%0 0 .   % 3     D &   "   %

3  3 0 /0    3 " 0  1 5  % 0 0   & % "  0  &"  %  "  3 ) )  % 50   "  %   & 3 0  3 0 03 0  /0  5   5    "   " 0 0  & 3   3  % 0 .  50   5"  % 0 L&L  3 ) % N  0  3 0 5  &   )  0   3  & 1  3 0 " 0   &     0 1    1   01 &   &" 0 1  3   &  %   " 5     3  5&  : 1  0 "   5 0  1  &   /0  & " 3   & % 0    +   3 0 0 3  0   % 1   5 0 &     0 ) & %  3 0  0  %"

05 $   01        0   & " 3  &   &  1 3 0    /0  5 5"   0   /0 2   &   " 3  &  0    %   0   &  &    &  &" 0  /0  " &   3 0 %0   " & 3   % " 5 5   1  0  & " 3  1  &    3  &  

(  ) )    0   & 3     1 1 % 0            . 0    % 0 &  0 %0 " 1  %      0  1   "      0 &    1   %   "  1    "  3       1   3    " 0  01   3    0    %  % " 0 0 &   3 5   0  2  951 0    1 5 3 5   0  % >1   0   3    1   & .  %    

.A

$     0  1 0  % 0  &  1 &3 1   % "  & 5  "  " G H  /0  +    M 0 D " 3 1  5  0 .   5     /0    M  "   0    % 2         01 0        % 3  1  &"  . /0  % M 35 &"   01                B /0 %  0 M  " 01  0     %  0 * /0 .  M 35 " 01  .       0   % "  % .   1 0 &    5 0  1 % . 3  3  1 5 G H $     >1 4 0  % 5 & 1 0 0  5 0 +   3   % "  &  "  " A  "    3  %     & 3 3      - # &  3 0  +    1   &      3 /0 0  0     " )   0 1  5 & 5      0 0  % $ 0    5 5 1 0     3   % "   '  

% " 5  0%0 5 D 1   /0 2 1    "   0  &" "   3 0 &D /0   1     0 3 &"    3 0 &D  % " 0  "   1   5    1 % 0 1   3 0 " = 0 0 " 0 )  5     /0 2      :     0     0   3   % 0 1   3   % 0 5 5 05 05  " 1  1  3& 3 0  %  0  ; 5 % 0  & 3 " 3 0   3 0    3 0 D  1   "  "   3 0  %      &    0 2  3 0  %  

*

½

+  ,   -

/0 2 "  "   0  &" "   3 0 0 &D  % " 0  1 % 3 3 6';7    0      3 0 &"     & 0  )    % 5 0 3    0 

.-

.

, / 

/   3"  % 5 +  0 0  3    :      % 0 5  /0        3  5 0 0  3 %   % 0 " )  5 0 0   )  %    0 E    %0   0   3 0 &" 6  % 0  ) 7 '  0   0 "  0 &"  +  3  

%M &"   0  0 %0     %0 #  " 0    5" &% &"   : % 0 " 951 0     " & 1   2     &3 0    0 5  ' "  "  1      03  5  & "         "  0 " "  50    % 0 5      0   :  0

.

 #$  0

 "%

/0  %   %   &   5 0 /0  % 0 2 2  0 6 7     0 % 60    0    7 3 0  =  0   0   3 0 0     0 0         3           /0     0    0 0  $ 0  5" 5  "    1 3 0  %   50 0 0   )  3 0 0    0 3 50 0 0 5  )  3 0  &5 = 0 0   % 0 5  "  0     3 0       & T  % " 5   % 0     %  %0  /0       "

&   % 0   1  3  0 1)  /0 0 %   &" 2 %       0  5 0 0 &"   3 0      /0     &"  3 %   %     0    ) .  /0  % 1 3 0   )    0    ) 3 0    /0    )         0  5 0 %     0 5 0 % 3 0  

 



. . .    . .

.  /&& 6. F # % -7  . . .

6 7

/  0  %  3      %  5   "  0  %  3  1)  0   5 0 0 &"    0  0   /0        % 3 3 0         5     0  0%0 0  1)   05 ; %  $ 0  5" 0 1)  01  !   3 0  %  50 0 1 0 &  3 01 %    50 0  %   1) &  %  951 5 5 %0 0  &" 0    0  0  %   0  1) )   %      %  0  0 30 5" ; 0 1)   0        "  %  &    0  /0 5 %0 3 0 % 

 % 1 &" 60 07  % "  0      0       0 3 ) 3     1) 0  &      "  0 %     0 1)  /0  5 %0 % %" 5  ) " 5 3  D  50 0  

 0  01        %   ) " 0 %0 $    5  " .

  C                      %      %     : 5 %0 %   "  %  30 0      3 0 1) 60   3  )   1  "  1  &"   % 7   3  1)  5 0  1"     3   %  6  0 0 7 0 5  0  &  %   " 0 %     %  : 5 %0   0 %  /0 5 %0 %  %    05 & 5   2 0 F 0        60 07 2 0 0 0  1&2,/ F   6 7  2 0 ! 0       2 0 ! 0V0 0  '  0 D    3  1)    3 0 &"    D 

   0 3 0  %   %    0   /0   3 0  %  50  0 0 D      0 1 5 & 635       5     3 0 % 7 ' "   %   50 0     % 0 &" $3 5 0   0  50 0"  ) "    0 &" 5  1   0       /0    0  1"  % 0   L L   $3  35 1)        3 0  %  0   0 0   :  0 3      %5 0     5 5 0 0      5   %5

%  % 0 3 0    >5 %     "  %0& %     3 0 &"           5    3  $ 0  5" 0    3  0  % & 0 0    0  &5 0  & 50 0     % " .@

5  0  &5  &  0 1) 0 5 1  , /0 C    "  3 9 ,1 M  1" # C     $%   %   @@@ -.6 7M  @ GH 0  # % $    &  ,0    #            = " & $   % , @@ G.H =&

 

0

 % 

' . / % 

        %  

 

GBH > #0 % / O   (%   , 9    /  " 3 & . C)    3 9 ,     $%%% !   !      

 &    "!& '((#  - B-  G*H > #0 %  C    / O  6  ," B7  0   % 6;   7 5 0 ,  G===  H  0M5  C       3 '&D 3 ,    C 5 $%%%     

 +     ,  $    +67  * * @. GH         #W     /  / % 3    9 ,   %  . 0 3  0 ,0   &   2((; ,67  -A ;&" * -   G@H > (    6  ," *7 /0 '  # C    &" G===  H  0M