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1 1304 ｪﾖｧｦ 000ｹﾖｸ fl ｹ1 016ｧ I. A ｧｮ03fi03 ﾖapple060402fi ｯapple ｸ900 ｨC 0000apple060402fi fi ｮ , 00066ｧ fi ｭｹ10208 ｨC ｷ fi03, ｭｮﾖｮ , 00066ｧ fi ics.forth.grg ｨC0006fl fi ｧ apple apple ｧ apple ｧｹ00ｸ , 00fl00 06 apple08020ｹ fi apple0208fi ' apple 06080ｹ fl 03apple fl apple ｧｧ apple apple0208fi apple ｹｧ90ｹ apple ｹ fi apple ｧｧ apple ｹｧｸ fl0ｸ fi ｧｧ , apple ｧ803apple apple apple ｹ1 0803fi03 apple fl apple ｧｹ apple080600fl fl ｧｹｸ apple08fl08 apple fl fi apple ｷ3060ｸｷｧ fl, ｧ apple08 0ｸｧｸ700 0ｹｸ apple ｧ fl fl fi03 (fixated image pair). 6ｧｧｹｸｧ80ｷ apple ｹｧ apple ｹ fi apple080600fl ｸ fl apple06086ｧ9060ｹ apple fl ｧｧｧ fi 09 03apple fi 01fl apple ｧ fl ｹｹ1 020ｸｸｧｷ30601fi03 apple fi fl 0400 apple026ｧｸ fl fl 020ｸｸ700, apple08fl apple ｧ9apple ｧｹ fl0ｸｧｧ

2 1304 ｪﾖｧｦ 000ｹﾖｸ fl ｹ1 016ｧ I. ﾖｭｱ03 ﾌ00 ﾌ apple apple ｧｧ fi fl fi apple0208fi , fi fl apple ｧｧｧ900 apple0803 apple ｹ1apple apple fi ｷ300060ｸ fi060ｸ700. ｭ 06 fl ｷ36ｧ apple ｧｧｹｸ900 08apple020601fi03 apple0208fi , apple08fl fl fl ｸ700 apple ｧ80ｷ apple00 08apple ｹ fi ｮ6ｧ fi fl ｧ90ｸｧｹｹ apple 066ｧ90ｹｧ900 apple apple08fl 03apple080600fl ｹ00900fl apple ｸ906 apple ｷｸｧｧ90009 apple fl apple00 6ｧ900 6ｧｹ fl fl ｧｧ8apple ｷ308066ｧ903 6ｧｸ70402 apple ｧ , fl ｹ00ｸ fl ｸ fi fl apple0208fi ﾇ00 apple08020ｹ fl ｹ00ｸ fl fl ｧ , fl ｧ apple08fl 0ｹ06ｧｧ apple fi 020ｸｧ8020ｸｧ apple060ｷ36ｧｧ90ｹ fi030006, ｧｹｧ apple020601fi apple0208fi fl apple020601fi apple ｷ3fl apple ｧ apple fi 09000ｸ706fl Marr [1], 040ｹ1030ｷ30ｸ apple08fl ｹ apple fi fl fi 0200apple ｸｸ apple ｧ804000ｸ , ｸ apple fl ｧ fl apple0803 0ｹｧ apple ｷ30806fl ｧ apple ｧｧｸ706fl 0302fi 06 0ｹ00ｸ706fl fl fl apple ｧｧｧ , 0208 apple apple0208fi ｧ applefl ｹ108 apple ｧ8020ｸ700: 03000ｸ7060ｸｧ900 apple fi apple fl ｸ703 apple apple ｧ , 0208 apple060ｸ90208 apple fl apple ｷｸ fi03 apple ｷ3fi apple ｧｷ300026ｧｧ fl apple fi, 036ｧ9040ｸ fl ｸ700 apple ｧ80ｷ fl0803. ｮ08 000ｹ apple ｷ308066ｧｹ006fi apple 06 apple6ｧ8000ｸ7 apple ｷ3fi apple fl fi04000ｸ700 apple apple ｧｷ3 02fi fl apple fi ｹ00ｸｮ08 apple060ｸ90208 apple fl ｸ apple apple ｹ1 0803fi03 apple fl (structure from motion) [2],[3] ｹ apple apple ｹ fl (motion planning) [4],[5] apple ｧｸ fl0ｸ fi apple02 fl fi ｸ706fl 03, apple fl apple02fi 000ｷ fi ｸ700 apple ｸ7applefl apple apple ｹ1 0803fi03 apple fl ｧｧｹ0000ｹ apple ｹ1 (apple ｹ1) 6 56ｧ , 0902 fi fi fl apple ｧ fl0803 apple apple fi ｧｹ apple060804apple6ｧ apple0803 6ｧ90ｹ fl applefl apple fi fi03 apple fl ｧｷ36ｧ fi 020ｹ fl00 06 apple08020ｹ1 0ｹﾇ020406, apple 066ｧｷ36ｧｧ8020ｸ apple08fl ｷ36ｧ apple06020ｹ apple apple08020ｹｧ903 apple000606apple020ｸ , 036ｧ90ｹ fi ｧ90ｹ fl fi ｧ8apple ｹｸｸｸ7applefl apple ｧ8, apple ｧ8 apple ｧｸｧ8apple08060ｸ700 0ｹｸｹ00ｸ apple fl 01 02' 006ｧ apple ｹ1 6 56ｧ apple ｧｧ apple fl apple ｷｧ903 apple fi 02026ｧ8 03apple ｹ apple ｹ , 04030ｹ0006ｧ8 00fl ｧ apple080ｹ apple0208fi ﾖfl ｹ apple00066ｧ apple0803 6ｧ90ｹｹ00900fl apple00 066ｧ80ｷｹ0080ｷｧ8 apple ｧｷｹｸ9apple fi apple fl ｧ [6], [7] fl090002, ｸ9apple ｹ fl ｧ apple fl ｧ8apple ｧｸ700 apple ｹｸ fl0ｸｧｧ [8] ｧ apple fi , 040ｹｹ apple ｹｹｹ1 6 56ｧ `` ｧ '' ｹｧｸ fl0ｸ fi ｧｧ , apple fi fi apple apple fi. ﾌ fl fi 1

3 ｧ , apple066ｧ9apple apple fl ｹ06ｧｸ703 apple ｧ apple fiapple ｹ fl0ｸ700, ｸ fl 0902 fi fl ｹ apple fl ｹ apple fi. ｮｧ apple 066ｧ90ｹｷ30ｸ apple ｷ30806fl0003 apple , apple ｹｸ apple080600fl 00 00fl00 06 apple08020ｹ1 0ｹ006fi ｹ00ｸ [9]. ｮ 01fl ｧ8apple apple apple ｧ fl00 06 apple ｧ8 apple ｷ fl ｸ700 Huang fl [10], 09 08apple08fl 00apple ｧ9apple ｧ apple fi 00 03apple fl ｸｸｹ fl0ｸｧ apple08fl fl ｧ fl ｧｧ apple fl apple 066ｧｷ fi 01fl ｧｹ1 0ｸ703 apple appleflapple apple ｧ apple fl ｷ36ｧｧ8 apple fi fi apple ｧ , ｹ0000ｹ apple apple ｸ900 apple ｷｸ900, ｧｸｹ00ｸ fl apple ｧ apple00000ｹｸ706fl fi apple fi ｹ (purposive and qualitative active vision) [11], [12]. ｱ030008apple ｧ8, 03apple ｹｷ36ｧｸ706fl 0302fi 03apple ｹ apple apple fi020ｸｸ apple fl ｧｹ apple0803 6ｧ90ｹｧｹ , 04010ｸｧｧｹ apple ｧ apple fl fl fi03 020ｸｸ700 6ｧｸ apple ｧ80ｷｹ apple ｹ103 apple0803 apple066ｧ9apple ｹ100. II ﾖｮ00 ｪｹ fi 01fl apple fi 0ｸ703 apple apple ｧ , apple fl ｧｷ30ｸｸ fl0ｸ fl 020ｸｸ700 apple ｧ80ｷｧｧ903 6ｧ90ｹ apple08-026ｧｷ fl ｧ8apple08060ｸｧ8020ｸ700, 09 08apple08fl 0806fl ｧｧ apple00 fl08 apple0803 apple ｧ80ｷ apple ｹ applefl ｮ08 apple00 fl ｧ apple00 fl08 08apple020601fi fi03 (optical flow field). ｱ0ｹ1030ｷ30ｸ fi 09000ｸ706fl, 0208 apple060ｸｧｧ fl ｧ9040ｸｸ700 0ｷ308066ｧ fl apple ｹ1 (dense) apple00 fl apple020601fi fi ｹ00ｸ903, 0208 apple apple ｹ apple020601fi fi fl ｧｧ apple ｧ apple fl 016ｧ8apple apple08096ｧｹｧｷ3fi apple00 fl0803 (apple.0ｹ ) apple08fl ｷ3 02fl fi 020ｹ10409 [13]. ｮ6ｧ apple08096ｧｧｹ00ｹ , apple fl ｹｸｸ700 apple ｹ apple ｹｧ903 apple000606apple020ｸﾇ00 6ｧ apple ｧ90ｹｧｷ30ｹ apple00 fl apple020601fi fi ｧｷ30ｸｸ fl0ｸ fl ｸｷ300fl apple ｧｹ fi 01fl apple fi 0ｸ703 apple apple ｹ fl [14]. 026ｧｧ9apple apple00 fl08 08apple020601fi fi ｷ36ｧ apple apple00 fl08 01fl (motion field), apple08fl08 6ｧ90ｹｧｸ fi 6ｧ fl apple apple fi ｧｹ00ｹｧ fl fi03 apple6ｧ8000ｸ appleflapple Verri Poggio 6ｧｹ108 apple00 fl 00fl ｸ903 fl apple08020ｹｧ903 apple000606apple020ｸ [15]. ｮ6ｧ , fl fl ｧｹ00ｹ apple fi fi fi03 00fl00 06 apple08020ｹ fl ｹ1apple ｹ apple00 fl08 08apple020601fi fi03 [16], [17]. ﾌ apple 06 apple6ｧ8000ｸ , 09 apple080ｷ30ｹ apple fl apple00 fl08 08apple020601fi fi apple ｹｹ006fi apple00 fl ｧ fi apple08fl fl ｧ90ｹｮ08 apple00 fl08 016ｧ fi03 6ｧ90ｹｹ apple fl apple fl ｧｹ00ｹ , apple.0ｹ [18]. ｯapple08096ｧ fl ｸ700 03apple080600fl ｸ fl ｹ0fi ｧ I(x1 7 y1 7 t) 0ｹ108 0ｹ00ｸｸ900 (x1 7 y) ｹ fi fi03 (t) ｸｷ30ｸｹ1 0002fl ｹ00ｸ fl0ｸｹ006016ｧ fl02 06, fi fl040ｸ70409 apple ｹ apple020601fi fi03 (optical flow constraint equation) ｧ fl [19]. I x u + I y v + I t = 0 (1) ｱｹ06ｧ fi (u1 7 v) 00fl ｧ apple020601fi fi I x 1 7I y 1 7I t ｧ903 apple 066ｧ86 70ｸｧ I 0ｸ703 apple x1 7 y1 7 t. ﾌ066ｧ80ｷｧｷ3fi 00040ｸｹｧ (I x 1 7I y ) (u1 7 v)=;i t (2) ｧ9apple apple ｧ9apple apple apple fi apple020601fi fi ｧ fl ｧ (intensity gradient), apple08fl08 00fl ｧ fi fl ｹ fl (2) 2

4 13 apple fl fi 6ｧ9010ｷ apple fi fl (aperture problem), 040ｹ1030ｷ30ｸ apple08fl fl apple ｸ apple020601fi fi ｧ8 03fi ｹｷ fi03 apple fi fl ｧ apple06016ｧ fi apple fi apple020601fi fi ｧ8 03fi fl040903, q ｧｧ fi (normal flow) apple (2) fi fi fl00 06 fl ;I t = I 2 x + I 2 y. ｱ0208 [15] apple ｹｷ308066ｧｹ1 020ｸｸｸｧ fi apple00 fl ｧ fl ( apple fi apple00 fl fl ｧ8 03fi fl040903) 00fl00 06 fl di di, 00apple0803 jjrijj ｧ fl ｧ fi apple 066ｧ86 70ｸ I 0ｸ703 apple jjrijj dt dt ｹｧｧ9apple0006, ｧ fi 00fl fi apple ｧ apple00 fl ｧ fl fl apple ｧ fl fl ｧ III. ｮ04 ｱｯｱｮｱｯ09 ｮﾖｮ03 ﾌ01 ﾖｸ706080ｹｹｧ9000ｸ700 OXY Z apple08fl08 00fl00 06 apple ｧ apple ｧｧ , 6ｧｸｧ OZ appleflapple apple ｧﾇ04020ｸ7 00applefl ｧ fl ｸ703 apple fi fi ｷ fi 01fl t =(U1 7 V1 7 W) apple ｷ30601fi 01fl ! =( ) 00apple0ｸ703 0ｷ3 fl ｹ0fi03 1. Y V ｦﾂ O ｦﾁ U X f y O x ｦﾃ W ｱ0ｹ0fi03 1: ｮ08 040ｹｧ9000ｸ apple0006flapple020ｸ fi 00fl ｸｧｹ apple0006flapple020ｸ apple ｧ fl fl fi fl ｸ703 apple fi ｷ fi 02 0ｹ00ｹ ; t apple ｷ30601fi ;! ｹ00ｹ fl0803 P =(X1 7 Y1 7 Z) 0ｸ703 apple ｹｧ9000ｸ700 OXY Z 00fl00 06 fl ;! P ; t, 00apple fl ｸｧｧ9apple0006, ｹ00ｹ P 00fl00 06 fl (dx=dt1 7 dy=dt1 7 dz=dt) = (;U ; Z + Y1 7 ;V ; X + Z1 7 ;W ; Y + X) (3) 0406 apple 06 apple6ｧ8000ｸｸｹ apple ｹｧ90ｹｹ00002fl apple00 fl08 01fl apple ｧ fl t 01 06!. Z IV. 00 ﾖｭｱｰｧ apple apple ｧｹ apple080600fl 6ｧｹｸ700, 016ｧ apple apple08fl0003 apple fl fi apple ｷ3060ｸｷ fl fl ｧｸｧ apple fl fl fl08 F fi03. ﾇ00 026ｧｹｸ700, 00fl ｸｸ703 3

5 ｧｹｸ700 (fixated image pair) apple080600fl ｷ300fl apple00 6ｧｹｹｸ900, apple08fl fl ｧｧｸ apple fl ｧｧ fl08 F, apple08fl ｧ fl fl (fixation point) ｧ fi ｸｸ900 0ｷ3 fl ｹ0fi03 2, apple08fl08 00fl0ｹｹ fi 096ｧｹ1 020ｸｧ8020ｸｧ9000ｸｧｨC fi ｧ apple ｹ (stereo system), apple08fl apple fl 6ｧ fl fl 00 00fl00 06 apple 066ｧ apple0ｸｹ0006ｧ fl apple06016ｧ fi ｧ fi 00fl ｹｧ8 000ｹ apple ｹ00900fl ｹ fi 01000ｷ3 02fi 00apple0ｸ fi apple0803 apple ｧ80ｷ [20] fl00 06 apple08020ｹｧｧｹｹ apple0601fi Y Y ｯ Z ｯ Z F ｦﾈ X f f O O ｯ X ｯｱ0ｹ0fi03 2: ｸ fl fi ｸ700 0ｹｸ apple ｷ30806fl ｧｧ apple ｹ fl applefl (disparities) 020ｸ700 apple ｸｸ fl0ｸ fi appleflapple00 020ｸ700 0ｹｸ700. ｮ03apple06016ｧ8, 09 00apple fl apple ｹｹｹ0000ｹ apple ｸ applefl04000ｸｧ9040ｸ fl0ｹ (correspondence) 020ｸ700 apple ｸｸ fl0ｸｹｧ90ｹ fl ｧｧ9040ｸｸ fi fl ｸ70008apple08fl (triangulation). ｮ apple apple066ｧ fl applefl apple fi fl0ｹｧ apple apple ｧ fl 06 0ｷ fi apple ｧ , 09 08apple08fl 0000 apple fl apple02fi applefl apple fi ｹ1. ﾇｹｸ700 apple ｧ apple00 6ｧ apple ｹ , 03apple080600fl ｸ fl fl ｸ fl ｹｧｧ fl ｨC066ｧ , 6ｧｧｹｸ700 00fl fl apple ｧｷｹｧ , 09 08apple08fl ｹ fi fi t 09 fi ｧ fi03 ( ｧ803) 016ｧ apple ｹ fi ｹ fi fi t ｧｧ803 ( fi03) ｧ fi fl ｧ apple08 0ｸ apple fl ｧｹ006016ｧｧｧ9060ｹ apple fl fl fi03, 0ｹ00ｸ706fl03 00 apple ｧ90ｷｹ1060ｸ7 apple ｧ OX, OZ. 00 apple ｹ apple 06 02fi , 03apple080600fl ｧｧ80900 apple apple0601fi03 006ｧ apple ｧ fl ｹ00ｹｧ apple ｹ fi 096ｧｸｸ apple ｹ fi apple ｹ1 6 56ｧ fl ｧ apple fi03 01fl ｧｧｧｧｧ fi apple fi03 01fl , 0208 apple ｧ fl ｧｧｧｹｧ80ｷ fl 06 0ｹ fi fi apple fi 01fl ｧ fl apple apple ｧ apple00 00, fi apple0006flapple020ｸ fl apple ｧ80ｷ apple00 apple02080ｹｸｮ applefl apple ｹ0fi 6 70ｹ1060ｸ7 apple ｧｸｸ700 00fl ｧ903, 00apple ｧ9apple apple ｸ700 0ｹ00ｸ706080ｹｸｸ900 apple ｸ96 70ｸｧ , 6ｧｧ fi03. ﾖapple06apple026ｧ90800, apple ｹ0fi 6 70ｹ1060ｸ7 apple apple ｧ , 00fl ｷ fi 09 apple ｧ fl ｹｹ1 020ｸｸｧｹ103 apple060808apple020601fi03 apple fi03 (weak perspective projection). ｱ0ｹ1030ｷ30ｸｧ , 6ｧ fl08 P ｧ (X1 7 Y1 7 Z) 0ｸ703 apple ｹｷ308066ｧ803 apple fl00 06 apple ｧｧ , apple ｧ fl08 (x1 7 y) appleflapple , 0300 x = sx 1 7 y = sy (4) 00apple0803 s 00fl fi ｧ8, fi090ｸ703 fl f=z 0 00apple0803 f Z fi apple (focal 4

6 13length) ｧｧ apple ｹ apple ｧ fl ｹ fi03 apple060808apple020601fi apple fi fl 0400 apple026ｧｸ fl fl ｹ06ｧ (4) 00fl ｧ903 0ｸ703 apple X1 7 Y. ﾖｧｧ apple ｧ fi03 apple060808apple020601fi apple fi, fi fl apple fl 01 02fi apple ｧ apple060808apple020601fi03 apple fi fl apple fl ｧ apple ｧｧ806 apple ｧｧｧｸｸ700 [9]. V. ｯｨC ﾌｭｱ0104 ｰ 06 ｭ03 ｮ03 ｮｭ 04 ｯｯｰ 03060ｹ0fl ｸ apple ｹ00002fl ｧ fi apple ｧ fl ﾇ04020ｸ fl08 (X1 7 Y1 7 Z), apple08fl08 036ｧ9040ｸｹ103 apple060808apple020601fi03 apple fi03 apple fl fl08 (x1 7 y) fi(u1 7 v) apple00 fl fl fl08 (x1 7 y) 00fl ' ｹ1 fl dx dt 1 7 dy dt u = dx dt = sdx dt 1 7 v = dy dt = sdy dt fl apple (3), 08apple (5) ｧ fl u = s(;z + Y ; U) 1 7 v = s(;x + Z ; V ) (6) ｹｹ apple fi 01fl ｧ apple ｷ36ｧ apple 06 apple6ｧ8000ｸ7 6 7fl ｷ308066ｧ8 apple fi 016ｧ apple ｹ fi apple ｧ fl fi apple ｧ80ｷ apple ｧ apple apple6ｧ apple ｷ3 00fl ｸ (6). ｱｧ900, apple ｹ0fi03 3 0ｷ3 fl ｹｧ9000ｸ700 OXY Z 03apple080600fl ｷ fl 0ｸ apple6ｧ O 0 X 0 Y 0 Z apple ｷ3fi 6 70ｹ1060ｸ7 apple ｧ OY, ｷ308066ｧｧ OX ｷ308066ｧｧ OZ fi ｧ903 apple ｧ80ｷ apple apple ｧ U1 7 W 0002fl ｹ0. 00 apple ｷ3fi 6 70ｹ1060ｸ7 apple ｧ OY 00fl ｧ fi 0ｷ308066ｧ8, 00apple08036ｧ9000ｸ703 00fl00 06 > applefl fl ｧ903 0ｷ3080ｹ1 6ｧ90ｹ fl ｷ308066ｧ8 apple fi00 020ｸｸｸ700 OX1 7 OZ, 00apple08036ｧ9000ｸ703 00fl00 06 U<01 7W < apple 066ｧ V 00fl00 06fl ｧ900. F Z ｦﾂ Z ｯ (5) -U -W X ｦﾂｦﾈ 0ﾍ1 O O ｯｱ0ｹ0fi03 3: 6ｧｸｧ8020ｸｧ9000ｸｧｧ OY, O 0 Y 0 00fl ｧ appleflapple fl 03, ｷ308066ｧ8 apple ｸｧ apple 06 apple6ｧ8000ｸ7, ｸ (6) apple0208apple ｹ fi fi apple00 fl ｧ fl fl00 06 fl u n = (u1 7 v)( Ix jjrijj 1 7 X ｯ u = s(;z ; U) 1 7 v = 0 (7) I y )= jjrijj 5 Ix s(;z ; U) (8) jjrijj

7 13 ｯapple08096ｧ I x 6= 0, fl 040ｹ06ｧ apple080600fl ｷ30200fl u n jjrijj I x = ;sz ; su (9) ｨC fl apple00 fl08 016ｧ fl apple00 fl08 016ｧ fi03, 03apple ｹ fi u n fi fi apple00 fl ｧ fi03, 09 08apple08fl 00apple0ｸ703 6ｧ90ｹ fi 09 00fl fl00 06 fl ; It. 026ｧｧ9apple0006, fl040ｸ70409 (9) 6 7fl jjrijj ; I t I x = ;sz ; su (10) ｱ fl , apple ｹ apple00020ｹ10ｹ apple ｧｧｷ3fi03 r(z)=az + B 00apple0803 A B 6ｧｸｧｧ fi 00fl fi apple apple060804fi apple Gauss 020ｸ700 00apple060ｷｸ900 apple0803 apple fl , apple 066ｧ90ｹｧ apple fi apple ｷ3fi ｹ0fi [9] ｸ706080ｹｸ906 6ｧｹ fl0ｸ700 P 1 1 7P ｧ ( ｯｦ 1 ) ( ｯｦ 2 ) fl ｹｧ I 1 1 7I (10) fl fl 03026ｧ8 ; I1 t I 1 x = ;sz 1 ; su ; I2 t I 2 x 030ｷｸｧ8 036ｧ apple 06 apple6ｧ8000ｸ7 040ｹ06ｧｧ90ｹ = ;sz 2 ; su (11) B ; I1 t + I2 t = I 1 x I 2 s(z 2 ; Z 1 ) (12) x ｧ s1 7 > 0, 0208 apple ｷ308066ｧ803 Z 2 ; Z 1 00fl00 06 fl apple B ｮｹ apple080600fl apple apple ｹ fi fi, ｷ3 02fl ｧ8apple ｹ0fi ｧ fl 0409 (fixation) ｧ apple08fl fl fl apple fl ｸｧｸｸｧ8 00fl apple ｧ90008 apple ｧｧｧ8 pixels ｧ fl040ｸ70409 (12) 00apple ｧ9apple ｹｷ308066ｧｧｹ fl0ｸｧｷ308066ｧ8 6 56ｧ fi. ﾇ04020ｸ7 apple.0ｹ fl08 m ｧ80ｹｧ Z m fi fl08 M ｧｧ Z M. ｮ fl 03026ｧ8 00fl apple060ｸ fl ｹ000fl ｧ (01 026ｧ8 0ｹｧ80709) fl ｸｸ900. ﾇ04020ｸ7 00applefl fl i1 7 j fl ｹ0 6 56ｧ80909 Z i 1 7Z j. 00 (12) fl B M1 7m ; I M t I M x + I m t I m x = s(z m ; Z M ) B i1 7j ; I t i + I j t Ix i Ix j = s(z j ; Z i ) (13) ｸｧ8 036ｧｹ108 apple ｹｸ , 0ｷ3026ｧ Z i ; Z j Z M ; Z m = B i1 7j B M1 7m (14) fl040ｸ70409 (14) fl ｹ fi 06 0ｷ308066ｧ8 6 56ｧｹｸ fl0ｸ700 i1 7 j, fl ｷ308066ｧｸｸ apple fi apple (fl Z M ;Z m apple ｧ90009 apple0006flapple020ｸ70409). 6

8 13VI ﾌ03 ｪｭ0301 ｭ 04 ｰｨC0408 ｭ 04 ｰ 01 ﾖｮ03 ｱｮｭｱ0104 ｰｧ apple ｹｹ1 6 56ｧ apple0803 apple ｧ apple 06 apple6ｧ8000ｸ7, fl apple ｧ fi ｧ apple apple08096ｧｹ apple ｹ fl ｸ700 03apple080600fl 00 apple ｷ300fl apple ｹ0fi ｧｸｸ900, 09 01fl ｹ1 0ｹｹ006010ｸｸ apple066ｧ9apple fl fi. 026ｧｧ9apple0006, applefl ｹ1 0ｹｹ006010ｸｸ apple066ｧ9apple fl ｧｸ900 pixels. ｱ apple0006flapple020ｸｧｹ , 09 apple fl fi apple080600fl02 06 apple fl apple fl ｧｧｸｸ700. ｨC06080ｹ00ｸ7060ｸｸ703 apple apple ｷ36ｧ , applefl fl ｧｹ , 0300 apple08026ｧ apple080600fl 00 03apple fl 09 0ｹ fi fi apple 066ｧ86 70ｸｧﾌｸ7apple fl 0208 apple , 0ｹ apple080600fl apple ｹ (log-polar transform) ｹ apple fl fl08 (x1 7 y) fl08 (1 7 ) 00apple0803 = ln( q x 2 + y 2 ) 1 7 = arctan( y x ) (15) ﾖapple0006 fi ｧｧ fl , apple ｹｷ fl apple fl ｸｹｹ1 fl ｧ apple apple fl ｸ (15) 0ｷ3 fl ｹ0fi03 4. ｮ fl 0ｹｧ90ｹ fl 016ｧ CCD apple08fl apple ｹ apple fi 0400 hardware [21]. y ｦﾇ p p q x ｦﾎ q ｱ0ｹ0fi03 4: apple ｹｸ fl0ｸ700 (x1 7 y) 02 08apple08fl apple fl ｧ fl08 ( ) 036ｧ9040ｸｹ1 apple ｹｹｹ1, ｧ apple apple fl ｹ1 apple ｹ0fi 020ｸｸ fl fi ｹ0fi apple08fl08 0ｷ3 fl ｸ fl0ｸ apple00 fl0803 (x1 7 y) apple0803 apple fl ｧ fl apple00 fl0803 (1 7 ), 03076ｧ apple apple ｧ fl fl00 020ｸｸｹ101020ｸｹ0fi03 4, 03076ｧｧ8. ﾇ020406, applefl apple ｸ apple00 fl08 (1 7 ) 00fl00 06 apple08020ｹ apple ｧ apple00 fl0803 (x1 7 y), 00apple ｧ9apple apple ｹ fi fi03 apple ｸｧ apple 06 apple6ｧ8000ｸ7, 08 03apple ｧ fi03 6 7fl ｧ9040ｸｹ1 apple ｹｹｹ1. ｱ0208 [9] apple ｹｧ903 apple 066ｧ86 70ｸｧｸ703 apple x1 7 y fl fi ｸ900 0ｸ703 apple apple cos() sin() 01 @ 1 cos() (16) 7

9 13VII. ｯ0804ｨC04 ｭ00 ｱ00 03 ｭ 03ｨC04 ｮﾖ08 ﾖｱ0103 ｮ03 A. ｯapple ｸｸ900 ｨC ｸ96 70ｸ apple ｹｹ1 apple ｹｹｹ1 6 7fl ｹ006fi fi03 apple fi03 (bilinear interpolation) ｹ apple fl fl apple fl ｧｧ900 fl fl pixels ｧｸｸ700. 6ｧ fl ｧ , apple6ｧ90ｹ00006 apple ｧｸｸ700 apple fl : fl ｹ00903 apple apple ｹ fl ｮ08 6 5fi fl ｧ fl00 06 fl :5. 02apple0ｸ703 apple ｹ [9], fi apple 066ｧ86 70ｸｸ703 apple ｹ fl fl 06, ｧ apple apple fl apple00 fl08 x1 7 y fi ﾇ020406,09I t 03apple fl apple ｧｸｷ308060ｸｸ700 pixels 020ｸｸ900 apple ｸｸｧ8. ﾌ apple ｸ700 0ｹ00ｸｸｸ900 apple ｸ96 70ｸ700 I x 1 7I y 0ｹ apple080600fl ｧ Canny [22] apple ｸ700 I x 1 7I y 6 7fl ｧ9040ｸ apple ｹ1 020ｸ700 I 1 7I ｸｸ904000ｸ700 (16) apple I x 1 7I y apple fl apple' fl apple00 fl08 x1 7 y 00fl apple00 fl fl apple fl ｹ apple00 fl08 x1 7 y, ｧｧ9apple apple fl apple ｹｹ apple.0ｹ0. apple0803 0ｹ apple0806fi , 6ｧ90ｹｧｸ fl apple fl ｹ fl fl , apple0006flapple0803 5:5 0ｷ308066ｧｷ308066ｧｸ700 pixels. B fi 0300 apple 066ｧｧ apple ｧ apple0803 apple fi , apple ｹ1apple apple080ｷｹｹ06ｧｸ703 apple ｧ fl ｧ80202, apple066ｧ9apple ｹ00ｹ : ｮ fl fl ｸｹｹ1 fl ｧｧ , 6ｧｸ apple ｧ apple060808apple020601fi03 apple fi fi apple060808apple020601fi 00 00fl ｧ fi03. ｮ08 036ｧ fl fl ｹ apple00 016ｧ8apple ｸ90ｷ30206, 0ｸｹ00ｹ apple ｧ apple00 fl ｧ fl apple apple00 fl08 016ｧ fi I x 00fl fi, 6ｧｸ fi fi apple00 fl ｧ fl fl fi. ﾌ06 016ｧｹ fl0ｸ700 apple apple ｹ apple 06 apple6ｧ8000ｸ7 apple06080ｸ8apple08096ｧ , fl040ｸ70409 (12) fl ｹ06ｧｹｧｸ700. ｮ fl 03026ｧｹｧ8 0ｹｧ8 0ｸ703 apple ｧｮ 040ｹ0fi (a) (b) 00fl0ｹｹｸｸ apple08fl ｧｧ apple0803 apple ｧ80ｷｮ08 040ｹ0fi03 5(c) 00fl0ｹｷ3fi fi 00 apple 066ｧｧ apple apple fl apple (a) (b) apple ｹ06ｧｹｹ0060ｸｹ0080ｹ fl apple08fl fl apple ｹ1 6 56ｧﾌ apple apple fl ｸｹ1 fl , 09 (14) j = m fl ｹ06ｧ apple fi apple apple fi fl08, ｧｷ308066ｧ8 apple ｧ804000ｸ700 apple apple6ｧ8060ｹ fi ｹ00ｸ fl ｧ804apple0608 0ｹ0060ｸ903, ｧ fl fl ｸ apple ｹ apple ｧｸ700 03apple apple0ｸ fl0ｸ fi03. ﾌ fl ｹ0fi (c), ｹ0fi03 5(d) 00fl0ｹ fl ｸ apple08fl apple fl ｧｸ700 pixels apple08fl 00fl apple fl ｧ fl00 06 apple0006flapple % ｸ700 pixels apple0803 apple ｧ90ｹｧ fl

10 13(a) (b) (c) (d) ｱ0ｹ0fi03 5: ﾇｧｹｧ apple apple fl ' VIII. ﾖｨC ｭ0804 ﾌ04 ｰ fl 0302fi apple fl ｧ apple ｹｧｸ fl0ｸ fi03 0ｸ703 apple ｧｧ fl fi 00applefl apple fi fl0ｹ , apple fl apple ｹｸ apple ｸ fl0ｸ700 ( ｧ fi). ﾖapplefl040903, 0000 apple fl 016ｧ8apple fl ｹ (calibration) apple ｹ fi ｧ fl apple fi ｸｹｧｸ fl apple ｹ1 6 56ｧ apple0803 apple ｧ fl apple , 03apple ｧｷ308066ｧ fi apple ｹ0fi 6 70ｹ1060ｸ7 apple00 016ｧ8apple fl fl ﾇｷ36ｧ apple apple08036ｧ9000ｸ703, 09 fi ｧ apple0ｸｹ1 apple ｸｧｸ apple06010ｸ apple ｧ804000ｸ700 apple0803 apple ｹ1apple apple ｹ006016ｧｧ , ｹｧ8apple apple 066ｧｹ00ｸﾇ fl ｷ36ｧ apple fl fi fi020ｸｹ1 6 56ｧ , apple08fl fl ｧ apple ｹ fi 096ｧ apple fi apple ｹ fi03. ｮ6ｧ apple ｹｹ apple ｹｧ apple ｷ3fi apple ｸ apple ｧ [23]. 01 ｭ0108 ｭ04 ﾌｪ03 ﾂｭ03 [1] D. Marr, Vision. San Francisco: W. H. Freeman, [2] S. Ullman, The interpretation of visual motion. Cambridge, MA: MIT Press,

11 13[3] V.S.Nalwa,A Guided tour of Computer Vision, ch. 8. Addison-Wesley, [4] Y. K. Hwang and N. Ahuja, ``Gross motion planning -- a survey,'' ACM Computing Surveys, vol. 24, pp , Sept [5] J.C.Latombe,Robot Motion Planning. Boston, MA: Kluver Academic Publishers, [6] E. Johnston, ``Systematic distortions of shape from stereopsis,'' Vision Research, vol. 31, pp , [7] H. Pick, A. Yonas, D. Gentile, P. Melendez, D. Wagner, and D. Wegesin, ``Perceptual aspects of navigation,'' in DARPA Image Understanding Workshop, pp , [8] J. Todd and Reichel, ``Ordinal structure in the visual perception and cognition of smoothly curved surfaces,'' Psychology Review, vol. 96, pp , [9] M. Lourakis, ``An alternative approach for studying space perception: Use of ordinal instead of metric depth,'' Master's thesis, University of Crete, Computer Science Department, [10] L. Huang and Y. Aloimonos, ``How normal flow constrains relative depth for an active observer,'' Image and Vision Computing, vol. 12, pp , Sept [11] Y. Aloimonos, ``Purposive and qualitative active vision,'' in DARPA Image Understanding Workshop, pp , [12] R. Bajcsy, ``Active perception,'' Proceedings of the IEEE, vol. 76, pp , Aug [13] J. Aloimonos, I. Weiss, and A. Bandopadhay, ``Active vision,'' International Journal of Computer Vision, vol. 2, pp , [14] B. K. P. Horn, Robot Vision. Cambridge, MA: MIT Press, [15] A. Verri and T. Poggio, ``Motion field and optical flow: Qualitative properties,'' IEEE Trans. on Pat.Anal.andMach.Int., vol. PAMI-11, pp , [16] R. Y. Tsai and T. S. Huang, ``Uniqueness and estimation of three-dimensional motion parameters of rigid objects with curved surfaces,'' IEEE Trans. on Pat. Anal. and Mach. Int., vol. PAMI-6, pp , [17] M. E. Spetsakis and J. Aloimonos, ``Optimal motion estimation,'' in IEEE Workshop on visual motion, pp , [18] C. Fermuller, Basic Visual Capabilities. PhD dissertation, Center for Automation Research, University of Maryland, [19] B. K. P. Horn and B. Schunck, ``Determining optical flow,'' Artificial Intelligence, vol. 17, pp , [20] K. Pahlavan and J. O. Eklundh, ``A head-eye system -- analysis and design,'' CVGIP: Image Understanding, Special Issue on Purposive, Qualitative Active Vision, vol. 56, pp , [21] J. V. der Speigel, G. Kreider, C. Claeys, I. Debusschere, G. Sandini, P. Dario, F. Fantini, P. Bellutti, and G. Soncini, ``A foveated retinal-line sensor using ccd technology,'' in Analog VLSI and Neural Network Implementations (C. Mead and M. Ismail, eds.), (Boston), DeKluwer Pubs, [22] J. Canny, ``A computational approach to edge detection,'' IEEE Trans. on Pat. Anal. and Mach. Int., vol. PAMI-8, pp , [23] D. Forsyth, J. Mundy, A. Zisserman, C. Coelho, A. Heller, and C. Rothwell, ``Invariant descriptors for 3-D object recognition and pose,'' IEEE Trans. on Pat. Anal. and Mach. Int., vol. PAMI-13, pp , Oct

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13ｨ 00ｨ 0001ｨｨ 00ｨｲ 1:28ｨC3: fl apple fi apple fl0ｸ90ｸ 13771 0100096 76ｦ0 ｨｨapple07apple07016ｦ0 ｨ 00090001090902fl 1 1ｨC3 ｨｹｪ066 5fl0ｸ70000000901 ｨ 0009000109090200, 060ｸ800 05040909fl. ｨｹ 0ｸ802 6 5 09096 7006ｦ0000909 6 507090200 016ｦ0006ｦ0026ｦ0 0100 6ｦ0apple6ｦ0