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iii

Interactive Correction of the Error in Image

Superimposed by Virtual Studio with Augmented

Reality

Tomoaki MIYATAKI

Abstract

Recently there are many TV programs produced by Virtual Studio. By using

Virtual Studio, it is possible to overlay an image from a camera on an image

created by Computer Graphics (CG). On the other hand, in the field of Virtual

Reality (VR), it is proposed to present a stereoscopic display including three

dimensional (3D) virtual space together with real space using a see-through

Head Mounted Display(HMD) and a stereoscopic projector. This technique

is called ê Augmented Reality (AR) ë . This paper considers a the situation

in which a human manipulating a virtual object using AR is shot by Virtual

Studio.

In this paper, the human who manipulates a virtual object in the studio is

called ê caster ë , and those who watch the real video images from a camera

overlaid on CG with a floor monitor are called ê viewer ë . In order to obtain

video images for the scene in which the caster manipulates a virtual object using

AR, the following two kinds of consistencies are required. One is the consistency

in position between the real space and the virtual space for using AR. The other

is that between the real space and the virtual space to superimpose the images

of the two spaces using Virtual Studio. The former occurs due to the difference

in the caster ì s perception of the real space and the virtual space. In order to

realize these consistencies, it is necessary to cope with the following two errors.

One is the error due to a difference between the caster ì s perception of the real

space and the virtual space through a stereoscopic display. The other is the

error caused by incomplete camera calibration. In previous work, it has been

tried to correct each of these errors individually in advance. However, complete

correction of the errors often requires special facilities and skills. On the other

hand, when the purpose of the error correction is to synthesize video images

for the situation in which a caster manipulates a virtual object, the acceptable

range of the errors depends on the virtual object manipulation shown by the

Page 5:  · ~Gq f t}óJvQyJ Mf 6 pr Qv w3y J{ ¶ ö 8 9} QUM O J M½G¾QØQÙJqQïOiGuQUM½ Jß Jn ÒåtJöOi â ãÕv JqM Gr à U Ô tJq}{Qv 8 9 (S Üf ' Q M G O½Q¾QØQÙJ kQmÝq ' 3Ò

iv

video images. In this situation, even if the errors are corrected up to some

extent in advance following the previous approach, there is no guarantee that

the correction of the errors is sufficient for synthesizing video images of virtual

object manipulation. In this paper, it is proposed to determine the acceptable

range of the error and to correct the error so that they are within the acceptable

range at the same time through the process of virtual objects manipulation by

the caster in the studio. The errors that are caused by a stereoscopic perception

and a camera calibration are counted as a single error for the difference in

position between the real space and the virtual space. In this work, the goal is

not to correct the error completely, but to make it within the acceptable range

as the result of the error correction. This acceptable range depends on virtual

objects and the task of object manipulation. In virtual object manipulation,

it is often considered a physical constraint for the positions of virtual object

similar to the object manipulation in real space for the convenience of object

manipulation in virtual space with AR. Examples of the physical constraint are,

ê each object can be handled on its surface ë , ê each object does not collide

with other objects ë , and so on.Since the caster tries to satisfy the constraint in

manipulating virtual objects, the object manipulation has to be realize under

the constraint in order for the errors to be within the acceptable range. In this

paper, the positions of virtual objects are corrected so that the caster’s object

manipulation for pointing satisfies the physical constraint. This error correction

is executed interactively through the process of virtual object manipulation

when the position of a virtual object to be manipulated by a caster does not

satisfy the constraint.

In order to evaluate the effectiveness of the method, the following experi-

mental results will be presented. It is assumed that a caster points static objects

with a real pointer. Different size of objects are presented to the caster for this

pointing. The resultant error corrected through the pointing is evaluated. As

the result, it is shown that the amount of the error decreases as the pointing

manipulation is repeated, and that the resultant error becomes smaller when

the size of virtual object becomes smaller. It means that the error correction

attains the acceptable range dependent on the object size.

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kK�!��� d i J!L &!'h[ P &!'�[�~��!e n!o A m ] . - f�� B!� 4!�y P &!' . J!L &!' pKq!r y��!� A i .I��� - f R k B F!:!�!��� 2 u p &!'p�q0r y��!� A i .��!� - f T . / z7f g F!:!�!� l � 4!� y!��j!i P &!' pO!P M+N+� / p 3 �!� q�r [ q!r!������� /���� A�B 2 p�� k���� - f J!L!MN+� / p�q�r . J!L &�' p�q!r yK�!� A i���� ] � [ �!� - f�y B��+  p 2 u

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p m ]¢¡K£+¤ / O!P M�N . J�L!M�N p�q�r | d p�¥�¦ yK§�¨�f g 1 u l B0� 4� kHMD

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( Î 6�ÏwÐ�Ñ�4�F�Ò �w­!® )y�§�¨Kf�i!j B AR

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ARp }!~ k!Õ - f�Ö!× pKØ�Ù / l B �!� ­!®

. Î 6�ÏwÐ�Ñ?4!F�Ò �w­!® [ ¯+Ú!k Ó0Ô�- f T . k�m7Û T p!¥�¦�p ¹0º�[�a+be!� i([1]) g�A � A�B �0� ­!® l�° N p �!�!Ü!Ý kKÞ!ß�à � p / z�Û B!Î 6+ÏÐ�Ñw4!F�Ò �?­!® � Ç!È+É�á . p Ñ �Dâ�p�ã b ¡ �?kD³ ¤ - f�i�j Ô0ä k Ó!Ô

- f T . l /+1 | B ¯�Ú p Ó�Ô k�m�¸ e P ª!« . J�L!ª�« p�q!r+p | d y�� T{ /å¹çæ � d fè�0låéê� c ¡ � g � ^ B AR[ë}ç~ A i ªç« n0o kçÕåìífîÖ´× ØÙ / l B�ª!« n!o!ï0ð / §�¨�f �!� ­0® . ������­�® [ z c ��¨?j�¯7Ú�k Ó!Ôìíf T . y a7bícId7e0� f

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ð / §�¨�f2 u p�­!® [�� ¸ e À�Û B { i ­�® Ó!Ô k+m�f ù�ú+pKþ!ÿ���� � �� ª´«�� n0o��Dÿ k ��çìíf p / [3]

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« � � p�ù!ú � c þ0ÿ���� [ �!j B�> p,����� k q�r | d pB ;���y C { f!m] k ­!® Ó�Ô�[�\ ] g ­!® Ó!Ô p i!j!k B�J�L!M+N+� p Ç!È+É p�Ì É�È ?+; 8C!E y º � A i �!Ä#D!p�q�r | d p�þ0ÿ���� � cI��c�d f J!L!M�N k0À » f qr | d p�þ!ÿ���� 8 B Ç!È�É �!Ä � cFE � � d f � ��0 p O!P M�N 9 p�q!r �cI�µcId f J�L!M+N 9 p � ��0 p�q!r � c B�J!L!M�N k!À �!e� ��0 p�q!r yþ!ÿ������ k,C { f0m ] k J!L!ª!« pDq�r [�G!Ô ì�f H Ä [�I j�f g T�d k+mÛ B s!Á���Ä [ o!Á ì�f��!k B�C�E k+m!f ª�« � � p�ù�ú � c � { ¸!i q!r |d pDþ!ÿ������ kC { f!m ] k J!L!ª0« [ O!P M+N p Ç!È+É � c p�0Ä kJ�K) �#9�;!f�8 $6& c�d f g��� p�LNM0Á l B��7  p © ÛO90zöf gP 2

L 90l B ARkêm0f JçL0ªç« n0o´ïð 8

AR[w~+� iQ ?�R�6�87:�;�<�= k!À » f J!L!ª!« n�o+p Y�Z ï!ð [ �ST AwB T p�ï�ð 9�§µ¨�f ��� ­!® � �í�K��­!® B z�f � l Î 6+Ï?Ð�ÑU?!F�Ò �­!® k u ��e1�3 ì�f g�P 3

L 9!l B T p!¥�¦ [�¹!º ì�fKi!j!k a�b�cId+e ;i�Ö0× p� �!�" ?�R p!¥�¦�� k u �!e V :�f�82W+k B D 9 V :+i �!#" ?�R kÞ!ß�à2X+i ¡ - ` [ ��.!ì�f g�P 4L 9!l B� - ` pY�Z Ý [�[�\ ì�f�i!j!k

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\ ¸!i P�] p�ù!ú [ �!ì g�^  k BP 5L 9�l B { 8�j68`_ Â+p!¥K¦�� k u �eV :�f g

a2 b c d e f g h i j k l m n o p q r s t

2.1 uwv'xwy'z {}|}~#�}�w�'������������HMD ������������������������2���,�������@�� �� ¡2¢ �£�¤�¥ ��¦�§'¨ � ��©ª6«�¬­ ®�¯�°6±�²�³�´ µ � �6¶2��·¸�¹�­�º�±

( » 2.1) ¼V

p'M

pM

pR

p'Rp'V

M

qV

qM

R( ½¿¾¿À�Á ) ( ¿ÿÀÄÁ )

(Å¿Æ¿ÀÄÁ )

( Ç¿È�É¿Ê )½¿¾Ë¿Ì

ÃÄÍ¿ÎÄÏÑÐ(½¿¾¿ÀÄÁ¿ÒÑÅ¿Æ )UV

S

L(RÓÕÔ VÖÄ×ÑØ¿Ù

)

UR(¿ÿÀÄÁ¿ÒÑÅ¿Æ )

» 2.1: ��������®�¯ � ²�³�������#� R Ú������#��� V ­����°@±�¼ R Û V Ü � Ý�Þ ´�Ú 3 µ�ß#àá�âã�ä ­��°å¼ AR

����æ�ç ��� ��� Þ pR Û Þ p

V èé�ê °6±��6¶`� ����������6±�ë � Û2°6±�Û�Ú�ì � �@¶2§ R í6î V ï ��ðñ � L ­�óò�Ú R Û V

��ô,õ��µ�¸�­����°6±�¼

pV = L(pR) (2.1)

ì ��ðñ L ´ö�÷�Ú�ø Þ��ù�ú Ú â ã�û ��ü ý Ú�þ�� ÿ���� �����'��� ���4

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� ������Û�§�±�¼������� �`��� 2 � � ��� R Ú V �� ��  ´ 1 � � 3 µ�ß����6Û�ò � ����°± � ­�Ú�� � 3 µ�ß������ R

¤V Û����§ 3 µ�ß�àá�â ã�ä ­,� ò�Ú “ �����

� ” Û���ÿ�Ú M ­,����°@±�¼���Ú��©,ª6«�¬ � R Üå­ �� �! � pR Ú��©,ª@«

¬��"�#���� ��  è ®�¯�°6±���������$ ��Þ�� V Ü­ � �! � qV ­�%�±�Û2°

±�¼6ì ��& Ú�� ��  ´ HMD ��ö ò�� pR � p

M � qV � q

M �����',������°±�ë � Û2°'±U¼ ì � �6¶F§�� ��  �#��± R í6î M ï � ���6� ð,ñ UR Ú V í@îM ï � ���6� ð,ñ UV Û`°���(�Ú�ì � ����²�³�´�Ú )�* � 2 ¸�­��°6ì�Û è ­º�±U¼

pM = UR(pR) (2.2)

qM = UV (qV ) (2.3)

ì � �6¶2§�+�· � *�­�� ��  ´ , �� �! ´�-�·�­�%#±�Û2��·6ò����������®¯'�/.w¶ Û º Úå� ��  ´ Þ q

V �U®�¯�°'± ��0�� pM Û q

M è�1�2 °'±��'¶F� �© ª «�¬ p

R �43�5}� � ±�ì#ÛO��§#±U¼�ì � Û º Ú,� ��  è qM Û/�76 8! ­�%

±#Û9�§ ° M Ü �;:�<�=�> � δM(qM) ­ ��°}ÛOÚ,� �� �� ����®�¯#´ µ�¸ è�?@A �6�6¶2��.���'±�¼p

M∈ δM(qM) (2.4)

ì � Ûº,� R Ü,­�� ��  è ¥ ��ò � Þ pR� �! ´�©�B �DC «/E@«�F G�­�HI �F�'±�¼ p

R �/E6«�F���������H I òU��J�îF�'± R Ü � �! � p′R ÚK� � H I

²�³'�Ú R í6î R ï ��ðñ S ­,��°�Û�Úp′R = S(pR) (2.5)

ÛU§#±U¼ ì � p′R è � ��  ��L���M�NPO �RQTSVU�W Û�òU��X��}�F�6±/Y���Ú p

′R

� L ­ ð ñ ò�� V $ �� �! p′V è HMD ��� ����� ��  ��X����F�6±�ì�Û���§

±�¼'ì � Û,º� ��  ´�ì ��Þ � UV ��� ��� p′M �Z����°@±�¼6ì � ²�³@��¸�­

��°}Û[)�* � �6¶2��§�±�¼

p′M = UV (p′V )

= UV · L · S · U−1

R(pM)

(2.6)

5

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\ ��Ú�� ��  è ] »6ò��,��������$ ��Þ ����©ª@«�¬­ ^�ò�_ ¥ �#­�º�6Û` 6�î2�6±��0���´�Úµ�¸ è ? A ò�§�a���(�§6î�§�# ¼p′M

∈ δM(qM) (2.7)

2.2 bdcRedf7gRhdiRj7kw{}|}~7lnmdoRpµ ��ÚrqPs � � ¶%§�� ��  � ����� ��®�¯ ��� îO� S��8tvu � � ¬wBPx�� � ���y�z�°6±/{�|6� · ¸�¹�°'± ( » 2)¼ ì � Y��#Ú;q�s � }�~ ��þ�a�± � ��  ´�Ú� ¬�B�x�� ����� ÛU§�±�¼S���t�uO��� ¬�B�x�­�´�Ú �����#� R Ü ������� ­�y�z}òU� R

����ñ í'î W����� ������� �� @/� #��#ë � ÛUÚN�����#� V Ü � ! í �#���� ����� ���± V

� ��ñ � 2 µ�ß�����$�­ � ? °@±�¼ ì � ����� “ � ? ��ñ ��� ” Û���ÿ�Ú 2

µ ß�à�á�â ã �8� I ­N����° ±U¼N������� R Ü � � © ª «�¬ �w P! pR ´�Ú �8�� y�z ����� Ú I $ � 2 µ�ß �! p

I ��Ú ��� è ��© ª6«�¬ ­ ¥ �}ò�'¶Û�òU�#�±U��������$ ��Þ q

V ´�Ú��� ����� �#���� I $ � �! qI ��Ú����' ���

� �2� ±�¼ R Ü ������� þ��ÿ V Ü � ��� ����� ����±�y�z�²�³@� �å��',��ÚR í'î I Ú V í'î I ï ��ð ñ TR Ú TV �#�N� �,� °}Û/$ � ²�³#´�Ú�µ�¸#­ ��°'ìÛ è ­�º�±�¼

pI = TR(pR)

= TR · L−1(pV ) (2.8)

qI = TV (qV ) (2.9)

S#��t�u���� ¬ B�x����,����Ú ��� è ��������$ ��Þ ����©ª@«�¬ ­ ^�ò�_¥ � òO�P##±�� ¶F§w� ? ��ñ è J}î%� ±���0�� ´�Ú pI Û q

I è ��6 P! ��§�_U�´�§ îU§P# ¼#ì � Û�º Ú p

I Û qI è �76 P! ­P%#±�í'¨#¶ í#�4����°'± � ´�Ú �� ­�´�§n_ Ú � ? ��ñ�� L�� � ­�%�± è Ú�� � ´�Ú�� ñ ���ò������ � ��  ��nC « ��þ�a�±¡�¢ � £ @ £ Û[¤Da £���ôõ ��% @ Ú��D6[¥�¦6�§�¨�ò���#�±� ­�Ú��n6[©�ª�­ Þ�� « �������°6±#Û`��·°6±�¼ òU� è ����Ú�ì � ©�ª�Û�ò

��Ú�¸ (2.4) ­�"�#�� δM(qM) èw¬ "#­#º�±U¼å°#§���­ Ú � ������$ ��Þ �U�#©ª «�¬�­ ¥ � ° ±w® � �P� ��� M Ü�­ �; P!P¯ � �;:P<�=°> δM(qM) � U−1

V�

�(� � ð ñ òO� �����#� V Ü ��±�² � δV (qM) ÚZ� �'�#��îU� TV �#�N� � ð ñ6

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V

pM

pR

M

UR

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( ³µ´µ¶Z· ) R(̧µ¹µ¶Z· )

( ºµ»�¶Z· )

( ¸µ¹µ¶Z·µ¼½ºµ» )

³µ´¾µ¿

¹ZÀµÁZ½Ã( ³µ´µ¶Z·µ¼½ºµ» )UV

I(ÄÆÅKÇÉÈ )

qV

T R(ÊZ˵̵͵ÎϵнѵÒ

)

pI

T V(ÓµÔZ˵̵ÍÎ ÏµÐ½ÑµÒ )

qI

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L(RÕ�Ö V×ZؽٵÚ

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» 2.2: ��������®�¯ � y�z�²�³òU� I $ ��±�² � δI(qM) ÛF°'±#Û p

I Û qI�� �! � ô °'±/Û8Ü#´ µ�¸#­ ���}�

�6±U¼p

I∈ δI(qM) (2.10)

2.3 ÝRÞdo7ßRàdá7âRã)�$ � ·,¸�¹���� @ Ú AR ��©�ä�#��å�������@��®�¯ ò ��#�± ��� �åÚ S��t�u��#� ¬ B�x���� ����y�z�ò�Ú ��� Û`������� è ^}ò�_2��å ��� � î2�����

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25