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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
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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» 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
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pV = L(pR) (2.1)
ì ��ðñ L ´ö�÷�Ú�ø Þ��ù�ú Ú â ã�û ��ü ý Ú�þ�� ÿ���� �����'��� ���4
� ������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! �%
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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
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R(pM)
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∈ δM(qM) (2.7)
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V ´�Ú��� ����� �#���� I $ � �! qI ��Ú����' ���
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pI = TR(pR)
= TR · L−1(pV ) (2.8)
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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
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��Ú�¸ (2.4) �"�#�� δM(qM) èw¬ "##º�±U¼å°#§��� Ú � ������$ ��Þ �U�#©ª «�¬� ¥ � ° ±w® � �P� ��� M Ü� �; P!P¯ � �;:P<�=°> δM(qM) � U−1
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I∈ δI(qM) (2.10)
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ñ �/æ ? °6±,��´�Ú ¸ (2.7)(2.10) è � & � ? A °6±�ç�è è %#±�¼$���é�ê�� ����ë�ì�í Enî F ë�ì�í � u�ï/ðnñ�ò�óDô î/ë�ì�õ 3 ö�õ ë�ì�÷
AR øù�ú�û ü�ý�þ�ÿ�����õ�������� �µõ�� ������� ø���������ø����������� �! �"�(2.6) �$#½í ü8ý þ8ÿ%�&�'�&)( UV í UR í S �+*&,.-rí+/)- UR 0 UV ·L ÷%1
24365 Pí7��ö S ÷98;: 375 ;<9=4>Pí p′M = q
M 0@? 9�BA4û 09C δM(qM) =
qM �<�D�û 0 -�E4/ � (2.4) ÷7FG#�H ö�I #½í � (2.7) (�F�H��B �"J A���í�K�õ 0�L ��(�í p
M = qM �<� 2�M í � (2.1)(2.2)(2.3) ��#½í
pV = L(pR)
= L · U−1
R· UV (qV )
(2.11)
? õ;�í UV = UR · L−1 ? AN>�íp
V = qV (2.12)
÷�F4H��! �"J A���í � (2.8)(2.9) ��#½íq
I = TV (qV )
= TV · L · T−1
R(pI)
(2.13)
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I = qI (2.14)
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25