35
Building Detection by Markov Object processes and a MCMC Algorithm Laurent Garcin, Xavier Descombes, Josiane Zerubia, Herv´ e Le Men To cite this version: Laurent Garcin, Xavier Descombes, Josiane Zerubia, Herv´ e Le Men. Building Detection by Markov Object processes and a MCMC Algorithm. RR-4206, INRIA. 2001. <inria-00072416> HAL Id: inria-00072416 https://hal.inria.fr/inria-00072416 Submitted on 24 May 2006 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destin´ ee au d´ epˆ ot et ` a la diffusion de documents scientifiques de niveau recherche, publi´ es ou non, ´ emanant des ´ etablissements d’enseignement et de recherche fran¸cais ou ´ etrangers, des laboratoires publics ou priv´ es. brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by HAL-UNICE

Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

  • Upload
    others

  • View
    2

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

Building Detection by Markov Object processes and a

MCMC Algorithm

Laurent Garcin, Xavier Descombes, Josiane Zerubia, Herve Le Men

To cite this version:

Laurent Garcin, Xavier Descombes, Josiane Zerubia, Herve Le Men. Building Detection byMarkov Object processes and a MCMC Algorithm. RR-4206, INRIA. 2001. <inria-00072416>

HAL Id: inria-00072416

https://hal.inria.fr/inria-00072416

Submitted on 24 May 2006

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinee au depot et a la diffusion de documentsscientifiques de niveau recherche, publies ou non,emanant des etablissements d’enseignement et derecherche francais ou etrangers, des laboratoirespublics ou prives.

brought to you by COREView metadata, citation and similar papers at core.ac.uk

provided by HAL-UNICE

Page 2: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

ISS

N 0

249-

6399

ISR

N IN

RIA

/RR

--42

06--

FR

+E

NG

ap por t de r ech er ch e

THÈME 3

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Building Detection by Markov Object processes anda MCMC algorithm

Laurent Garcin — Xavier Descombes — Josiane Zerubia — Hervé Le Men

N° 4206

Juin 2001

Page 3: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE
Page 4: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

Unité de recherche INRIA Sophia Antipolis2004, route des Lucioles, B.P. 93, 06902 Sophia Antipolis Cedex (France)

Téléphone : 04 92 38 77 77 - International : +33 4 92 38 77 77 — Fax : 04 92 38 77 65 - International : +33 4 92 38 77 65

�������������� ���������������������! #"�$%�'&)(*�,+-�����/.�"��,����0101��02 �3�4 � 56� 5 #���7�#"��8��9�:

;=<?>�@BADC-E�FG<?@BHJIKCMLGNPOQ<SR1ITAD@3U�ADVWHDXZY\[]AJV^N�_?XZVWI`<aCPA\b�AD@B>�[PI`<cNMd3AD@WR?e^;�A\fgAJCMhikjmlonGp3q�rtsvuxw�poy�zS{ow8|~}Su�jm}SnQnGpB��n�zS{�j-|�ump��

|�n�zD��p����1�-}Su-um��p����m{�}Su-u1zD|~����zDum{�p����y�}D�8pow#��y8|TzDu1z

��zD�-�P}Sy8w7�-p,y�p�{�jmpoy�{�jmp�u��]�x������r����-|�u������Z��r�qZ�,�1zD��p��

�\ �¡�¢�£J¤-¥�¢�¦ ikj-|~�Q§¨}Sy8©ªzD|�nG�GzDwG�-pow�p�{ow8|�u-�c«-�-|�¬~�Z|�u-���Q|�u­�Z|���|�w�zD¬#zSpoy8|TzD¬%�-jm}Sw�}S��y�zD�-jm��®¯�poy�pQ§°pQnG}a�-po¬°z���pow±}D²%«-�-|�¬~�Z|�u-���±«a³´zµ{�}SuZ¶m���-y�zDw8|~}Su·}D²%}S«Z�¸p�{ow��¹®GºcpG�-pB¶mump�z���}S|�uaw�-y�}?{�p����7}Su�w8jmp3��pow7}D²»{�}SuZ¶m���-y�zDw8|~}Sum�¹�m§%j-|~{�j¼�8�-¬�|�w��%|�uaw�}Qw½§°}G�1zDy8w��3¾

¿ w8jmp¼¶my��8w�}SumpÀ|~��z·�-y8|~}SyµnG}?�-po¬±}Su*w8jmp´{�}SuZ¶m���-y�zDw8|~}Sum��§%j-|~{�j/�m��pÀ|�uxw�poy�zS{ow8|~}Sum�«�powv§¨p�pou�}S«Z�8p�{ow����

¿ w8jmp,��p�{�}Sum�µ}Sump,|~�#z�mzDw�zQnG}a�-po¬Á§%j-|~{�j�pouZ²Â}Sy�{�p��7w8jmp±{�}Sjmpoy�poum{�p3§%|�w8j�w8jmp,|�n�zD��p�®ikja�m�%§¨pÃj1z�Ä�p±z���}���w�poy8|~}Sy7�Z|~�8w8y8|�«-�-w8|~}Su�§%jm}���pÃn�zJÅZ|�n3�-nÆj1zS�kw�}«Pp�²Ç}S�-um�M®�svu�}Sy��-poy7w�}zS{�j-|~poÄ�pQw8j-|~�,n�zJÅZ|�n3�-nµ��§¨p�m��pGz^È´É°ÈÀÉÊ�8|�n��-¬TzDw8|~}Su´��zËȼpow8y�}S��}S¬�|~�¸�½¯ÃzS�8w8|�u-���¸�ÍÌÃy�p�pouzD¬���}Sy8|�w8j-nÎ�7nQ|ÏÅZp��À§%|�w8j·zË�8|�n3�-¬TzDw�p��·zDu-ump�zD¬�|�u-�m®�ikjmpouc§°pQw�p��8w,w8j-|~�,nGpow8jm}?�c}Suc«P}Sw8j��³auaw8jmpow8|~{3zDum��y�p�zD¬��8w�poy�p�}D��|�n�zD��p��¹®ÐµÑ�ÒPÓ�Ô�Õ £JÖ�¡�¦ ��}S|�uxw��-y�}a{�p�����p����-�#��È´É°È´É��-�8w�poy�p�}�Ä?|~�8|~}SuÁ�-«-�-|�¬~�Z|�u-�^pBÅ?w8y�zS{ow8|~}Su

×�Ø`Ù]Ú]Ø`ÛµÜvÝ]ØKÞDßÇÝ�àáÝ�âJÝ]ã�äÍåBæWç½è�éDêJàìë�âJÜ�Ù»è�Ý�àíåWÞSèWîï Ø`ÞJßÇÝ�àíÝ�â¹Ý�ã�ä¸åWæWç½èWéJêDàðë�âDÜ=Ù»è�Ý�àíåBÞSè�î�ñ�ò�Ý]óÃèWÞSô¹ä

Page 5: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

��������Á�����#���� ���k�P��: �=#��0 .� 7"/�� .�"��,����010��302��� �! 7"�$%�=&�7�,+-��� ���/�� #���7�7"P�¸��9�: �������a�,.�� � 56� 5

��� ¡�� � ¦ � p�«-�-w��-p\{�p�w8y�z�Ä�zD|�¬°p��8w��-p\�-�ow�p�{ow�poy�¬~p���« �Dw8|�nGpouxw������1zDy8w8|�y�-p\�-jm}Sw�}D���y�zD�-j-|~p���zSpoy8|~pou-ump��7ua�-nG�oy8|��x�mp���®���}S�m�%nG}?�-�o¬�|~��}Sum�#�-uµpoum��pon3«-¬~p��-pë �Dw8|�nGpouxw����1zDy%�-ump{�}SuZ¶m���-y�zDw8|~}Su­���á}S«Z�8pow���®���}S�m��-�B¶mu-|~����}Sum���-u �-y�}a{�p����8�m����}Sum{ow8�mpo¬%�8�-y¬��ápoum��pon�«-¬~p��-p��{�}SuZ¶m���-y�zDw8|~}Sum���a�-|Á��p,�-��{�}SnQ��}���p±pou��-po�ZÅË�1zDy8w8|~p��3¾

¿ ¬Tz �-y�ponQ|~loy�p p��8w��-u nG}a�-lo¬~pcz·�-y8|~}Sy8|±�8�-yˬ~p��µ{�}SuZ¶m���-y�zDw8|~}Sum���x�-|,{�}Sum�8|~�-loy�p �-p��|�uxw�poy�zS{ow8|~}Sum��pouxw8y�p,¬~p���}S«Z�¸pow����

¿ ¬Tz´��p�{�}Sum�-pµp��8w��-u­nG}a�-lo¬~p����ízDw8w�zS{�jmpÀzD�ZŪ�-}Su-um��p����a�-|%|�um�Z�-|�w�¬Tz´{�}Sjm�oy�poum{�p��Z�y����8�-¬�w�zDw�z�Ä�p�{±¬�� |�n�zD��p±w8y�zD|�w���p�®

��}S�m�'z�Ä�}Sum�°zD|�um�8|-�-ump#�Z|~�8w8y8|�«-�-w8|~}Su^zÃ�P}��8w�poy8|~}Sy8|1�-}Suaw'um}S�m�'y�p�{�jmpoy�{�jm}Sum�°¬Tz,{�}SuZ¶m���-y�zDw8|~}Sun�zJÅZ|�n�zD¬~p�®���}S�-y7}S«-w�pou-|�y°{�p�n�zJÅ?|�n��-nµ�Zum}S�m�°�-w8|�¬�|~��}Sum�°�-ump��8|�n��-¬TzDw8|~}Suµ�-p#wv³a�Pp�ÈÀÉ°È´É�G�-u zD¬���}Sy8|�w8j-nGpg�-pcȼpow8y�}S��}S¬�|~�¸�½¯ÃzS�8w8|�u-�S�ÍÌ�y�p�pouZ�^{�}S�-�-¬~��pgz�Ä�p�{c�-u*��{�jm�on�zª�-pcy�p�{o�-|�w��|�n3�-¬~��®���}S�m�=w�p��8w�}Sum�¨¬TzÃnG�ow8jm}?�-p��-��{oy8|�w�p��,¬Tz�²Â}S|~�'�8�-y°�-p��'�-}Su-um��p��°�8³?uxw8jm�ow8|��a�mp��¨pow°�-p��|�n�zD��p����8w��oy���}���{�}S�-|��a�mp��%y���po¬�¬~p���®�ÊÕ ¢�¡ Ó ¥�� � ¡�¦ �=y�}a{�p������m�=�P}Sum{ow8�mpo¬~���a����È´É°ÈÀÉ�����w��oy���}�Ä?|~�8|~}SuÁ�apBÅZw8y�zS{ow8|~}SuË�-p%« �Dw8|�nGpouxw��

Page 6: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

����������� ������������������������! "$#%�&(')��*+�,���.-/",�+�0�$1$1��$1 q

56��7���=7��0

2 3�4 ¢�£ Õ Ö �]¥�¢65 Õ 4 7

8 9;: Ñ £ : 5 ÑxÔ 7

< = ÑxÕ Ñ ¢�£5`¥�¤ � 9  .> Ñ ¥�¢ �ÊÕ Ö Ñ � ?

@ A Õ 5 4 ¢ A £ Õ ¥ Ñ ¡�¡ ?�m®�� BÃpB¶mu-|�w8|~}Su�}D²=z���}S|�uaw7�-y�}?{�p�����®,®3®,®±®,®±®±®,®±®,®3®±®,®±®,®±®,®±®3®,®±®,® C�m®í� ��uµpBÅ-zDnQ�-¬~p±}D²»�P}S|�uxw7�-y�}?{�p����±¾=ÈÀzDy8©�}�ÄË�-y�}?{�p����3®3®±®,®±®,®±®,®±®3®,®±®,® C

7 A £%5 Õ £ �/Õ Ö Ñ � DE ®�� �#po¬TzDw8|~}Sum� ®,®±®3®,®±®,®±®,®±®±®,®3®,®±®,®±®±®,®±®,®3®±®,®±®,®±®,®±®3®,®±®,® FE ®í� svuxw�poy�zS{ow8|~}Sum��®±®3®,®±®,®±®,®±®±®,®3®,®±®,®±®±®,®±®,®3®±®,®±®,®±®,®±®3®,®±®,® F

? G�¤Z¢�¤ Õ Ö Ñ � 2 H�Z®�� É°}SnQ�-�-w�zDw8|~}SuÀ}D²�w8jmp,�mzDw�znG}?�-po¬Áw�poy8nG� ®±®,®±®,®3®±®,®±®,®±®,®±®3®,®±®,® ����Z®í� È��-¬�w8|�Äa|~po§ ®,®±®3®,®±®,®±®,®±®±®,®3®,®±®,®±®±®,®±®,®3®±®,®±®,®±®,®±®3®,®±®,® �o�

I J�K]ÕMÕ ¡L5 4NM ¢ K]ÑPO=Õ ¢ Ñ 4 ¢65`¤ �`¡ 2Q@C?®�� ��}Sw�pouxw8|TzD¬�w½³?��p�� ®,®±®,®±®,®±®±®,®3®,®±®,®±®±®,®±®,®3®±®,®±®,®±®,®±®3®,®±®,® �o�C?®í� R�umpoy8��³Ë�1zDy�zDnGpow�poy�� ®,®±®,®±®±®,®3®,®±®,®±®±®,®±®,®3®±®,®±®,®±®,®±®3®,®±®,® � E

D ST5 ��`¤Z¢65 Õ 4 2 ?U ®�� V°�-|�¬~�Z|�u-�3z�ȼzDy8©�}¹Ä�{�j1zD|�uµ¾��#poÄ�poy��8|�«-¬~pk���-nQ�Gȼ}Suxw�p#ÉkzDy8¬~}ÃÈÀzDy8©�}�Äɨj1zD|�um�6���U ®í� ȼ}�Ä�p�� ®,®±®,®±®3®,®±®,®±®,®±®±®,®3®,®±®,®±®±®,®±®,®3®±®,®±®,®±®,®±®3®,®±®,® � UU ®íq É°}SnQ�-�-w�zDw8|~}SuÀ}D²�w8jmp±zS{�{�po�-w�zDum{�p3y�zDw8|~}��7®±®±®,®±®,®3®±®,®±®,®±®,®±®3®,®±®,® ��q

U ®íqZ®�� W�w8jmpoy7nG}¹Ä�p��7w8j1zDuµ«-|�y8w8j�zDum���-p�zDw8j ®±®,®3®±®,®±®,®±®,®±®3®,®±®,® ��qU ®íqZ®í� Xa|�nQ�-¬~p,«-|�y8w8j�zDum���-p�zDw8jË®3®,®±®,®±®±®,®±®,®3®±®,®±®,®±®,®±®3®,®±®,® ��qU ®íqZ®íq V°|�y8w8j�zDum�µ�-p�zDw8j�}D²»umpo|���jx«P}S�-y8|�u-�\«-�-|�¬~�Z|�u-��� ®,®±®,®±®,®±®3®,®±®,® � E

U ® � svnQ��}Sy8w�zDuaw#y�pon�zDy8©�zD«�}S�-w7w8jmp3{�}SnQ�-�-w�zDw8|~}Su�}D²»w8jmp3zS{�{�po�-w�zDum{�p±y�zDw8|~} ®,® �YCZ �^Ñ ¡���K¢�¡ 8 I

FZ®�� Xa|�n3�-¬TzDw8|~}SuÀ}D²»w8jmpÃ�-y8|~}Sy7nG}a�-po¬­®3®,®±®,®±®±®,®±®,®3®±®,®±®,®±®,®±®3®,®±®,® �YCFZ®í� B,zDw�z�¶mw8w8|�u-�Gw�poy8n ®±®,®±®,®±®±®,®3®,®±®,®±®±®,®±®,®3®±®,®±®,®±®,®±®3®,®±®,® � U

FZ®í�Z®�� Xa³?uxw8jmpow8|~{,|�n�zD��p�� ®±®±®,®3®,®±®,®±®±®,®±®,®3®±®,®±®,®±®,®±®3®,®±®,® � UFZ®í�Z®í� �#p�zD¬M|�n�zD��p��g®,®±®,®±®±®,®3®,®±®,®±®±®,®±®,®3®±®,®±®,®±®,®±®3®,®±®,® � U

Ú]Ú Þ�[]\�^0_a`

Page 7: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

� �. � "��a ���� ",��������� &+� �a" � �$1��0��� ���$1����%1$� � � �a"a� ���� ������a"$&�� �.� � �a

2�HPA £ Õ ¡ O=Ñ ¥�¢�¡ 8 D���Z®��·��y8|~}Sy�nG}a�-po¬c®±®3®,®±®,®±®,®±®±®,®3®,®±®,®±®±®,®±®,®3®±®,®±®,®±®,®±®3®,®±®,® � U���Z®í� B,zDw�znG}?�-po¬�®±®3®,®±®,®±®,®±®±®,®3®,®±®,®±®±®,®±®,®3®±®,®±®,®±®,®±®3®,®±®,® ��F���Z®íq Xa|�n3�-¬TzDw8|~}Suª®,®±®3®,®±®,®±®,®±®±®,®3®,®±®,®±®±®,®±®,®3®±®,®±®,®±®,®±®3®,®±®,® ��F

Ø`Ù�Ú�ØÇÛ

Page 8: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

����������� ������������������������! "$#%�&(')��*+�,���.-/",�+�0�$1$1��$1 E

� � #��"��,��3��������

���-w�}Sn�zDw�p��Qw�p�{�j-u-|��x�mp��'²Ç}Sy�«-�-|�¬~�Z|�u-��y�p�{�}Sum�8w8y8�m{ow8|~}Su��-¬Tz�³Gz�¬~p�zS�Z|�u-�3y�}S¬~p%|�u�zç%|~�-p7y�zDu-��p}D²1�-}Sn�zD|�um�»�8�m{�j�zS�]w�po¬~p�{�}SnQn3�-u-|~{�zDw8|~}Su�}Sy��-y8«1zDu��-¬TzDu-u-|�u-�m�S§%j-|~{�j�-pon�zDum��«P}Sw8j3�-y�p�{o|~��pzDum�¼�-�Àw�}��mzDw�pQqB�{�zDy8w�}S��y�zD�-j-|~{G|�uZ²Ç}Sy8n�zDw8|~}Su zD«P}S�-w,«-�-|�¬~�Z|�u-����®3��{o¬TzS���8|~{�zD¬=zD�-�-y�}�zS{�j}D²»w8j-|~�%©?|�um��}D²��-y�}S«-¬~ponG��{�zDu�«Pp�²Ç}S�-um��|�u���� U�� �?²Ç}Sy#pBÅmzDnQ�-¬~p�®

s½u w8j-|~��§°}Sy8©ª§¨p��m��pµ�-y�}S«1zD«-|�¬�|~�8w8|~{¼nGpow8jm}?�-��®*��y�}S«1zD«-|�¬�|~��w8|~{�w�p�{�j-u-|��x�mp��Ë|�u |�n�zD��p��po��nGpouxw�zDw8|~}Su¼��poumpoy�zD¬�¬�³�zS�-}S�-w�z�-|ÏÅ-po¬�zD�-�-y�}�zS{�jÁ®��'pow7w8jmp3|�um{oy�p�zS�8|�u-��y�p���}S¬��-w8|~}Su�}D²»w8jmp}S«m��poy8Ä�p���|�n�zD��p��¨¬~p�zS�-�°�m�'w�}3w�zD©�p#|�uaw�}�zS{�{�}S�-uaw°w8jmp#��p�}SnGpow8y8|~{�zD¬P|�uZ²Ç}Sy8n�zDw8|~}Su�{�}Suxw�zD|�ump��|�uQ|�n�zD��p��¹®�ikjx�m���x|�um�8w�p�zS�G}D²M�-p�zD¬�|�u-�3§%|�w8jG�-|ÏÅ-po¬~����§°p7�-pB¶mump7��p�}SnGpow8y8|~{�zD¬�}S«Z�¸p�{ow��'y�po¬TzDw�p��w�}�w8jmpÃ|�n�zD��p�Ç��p�pÃ��p�{ow8|~}Su�q�B®'ikj-|~�k|~�k§%j1zDw7�8w�}a{�j1zS�8w8|~{Ã��p�}SnGpow8y8³^|~�7zD«�}S�-w���� � ®�svu�}Sy��-poyw�} �m��pµw8j-|~�^{�}Sum{�po�-w�}D²� v}S«Z�¸p�{ow����%§°p�§%|�¬�¬�ump�p�����}SnGpµum}Sw8|~}Sum��zD«P}S�-w��P}S|�uxw^�-y�}a{�p�����p���Ç��p�p^��p�{ow8|~}Su·��B® ikjmpouª§¨pË«-�-|�¬~� ȼzDy8©�}¹Äg�-y�}?{�p�����p��}Su w8jmp^��p�}SnGpow8y8|~{�zD¬#}S«Z�8p�{ow�������� � �|�u6w8jmp���zDnGp�§°z�³ªw8j1zDw^}Sumpµ«-�-|�¬~�-�^ȼzDy8©�}¹Äªy�zDum�-}Sn)¶1po¬~�-�^}Su­�-|ÏÅ-po¬~��® ¯�poum{�p�§¨p¼zDy�pzD«-¬~p�w�}·�-p��8|���u |�uaw�poy�zS{ow8|~}Sum��«Ppow½§¨p�pou*}S«Z�8p�{ow���zDwËz ¬TzDy8��poy^y�zDu-��p�w8j1zDu�«x³ zc{o¬TzS����|~{�zD¬�-|ÏÅ-po¬=zD�-�-y�}�zS{�jÁ®�º�j-|�¬~pzË��w�zDum�mzDy��À«-�-|�¬~�Z|�u-��y�p�{�}Sum�8w8y8�m{ow8|~}Su �-p�zD¬~�ç%|�w8jcp�zS{�j´«-�-|�¬~�Z|�u-���po�1zDy�zDw�po¬�³��-w8jmp,�-y�}S�P}���p��µzD�-�-y�}�zS{�j�«�poumpB¶mw��7²`y�}Sn w8jmp,�-y8|~}Sy%©?um}�§%¬~p��Z��p3§¨p,j1z�Ä�p3zD«P}S�-ww8jmp�y�po¬TzDw8|~}Sum�k«Ppow½§°p�pou�«-�-|�¬~�Z|�u-�����Çp�® �m®=zD¬�|���u-nGpouxw���B®¨ikj1zDw°|~�°§%ja³�§¨p��m��p�w8jm}���pÃÈÀzDy8©�}�Ä}S«Z�8p�{ow°�-y�}a{�p�����p��=²Â}Sy'«-�-|�¬~�Z|�u-�Q�-pow�p�{ow8|~}SuË|�u^�-poum��p#�-y8«1zDuµzDy�p�zS��® V°³G�-}S|�u-���}-�x§°pÃpBÅ?�Pp�{oww8jmp'|�uZ²Ç}Sy8n�zDw8|~}Su�¬~}��8w��Z�mp'w�}#}?{�{o¬��m�8|~}Su�}Sy��8j1zS�Z|�u-�#w�}#«�p=y�po�-¬TzS{�p��3«a³,w8jmp=�-y8|~}Sy�©?um}�§%¬~p��Z��pzD«P}S�-w%w8jmp,y�po¬TzDw8|~}Sum�#«�powv§¨p�pou�«-�-|�¬~�Z|�u-���¹®

ikjmpou�z%�-y�}S«-¬~pon zDy8|~��p��]§%j-|~{�j�|~��w8jmp¨�8|�n3�-¬TzDw8|~}Su}D²1�8�m{�j3�-y�}?{�p�����p���®]���]��}SnGp=�-y�}S��y�p����j1zS�ky�p�{�pouaw8¬�³\«Pp�pouËn�zS�-pÃ|�uËw8j-|~�k¶1po¬~�M�Z§¨pÃj1z�Ä�p,�-p�{o|~�-p��Ëw�}���|�n3�-¬TzDw�p±}S�-yk�-y�}?{�p����k§%|�w8j�zȼ}Suxw�p�ÉkzDy8¬~}GȼzDy8©�}¹Ä�ɨj1zD|�uµnGpow8jm}a���Ç�#poÄ�poy��8|�«-¬~p±���-nQ��ÈÀÉ°È´É�� E�� B®

� (2&7��"1&±�����

ºcp#{�zD¬�¬1z� v{�}SuZ¶m���-y�zDw8|~}Su���z,��pow=}D²M}S«Z�¸p�{ow��������! #"!$&%&%&%' )(+*#}D²PÄSzDy8|TzD«-¬~p7��|-,�p��`w8j-|~�=§%|�¬�¬m«Pp�-pB¶mump���nG}Sy�pkzS{�{o�-y�zDw�po¬�³3|�u���p�{ow8|~}Su���B®�s½u�w8jmp'�-y�p���pouxw�{�zS��p��Dw8jm}���p'}S«Z�8p�{ow���zDy�p'«-�-|�¬~�Z|�u-���¹®

ikjmpou·§°pË�-pB¶mumpµz��Z|~�8w8y8|�«-�-w8|~}Su/.�}Su w8jmpË{�}SuZ¶m���-y�zDw8|~}Su­��pow���§%j-|~{�jª��zDw8|~�8¶1p��Q��}SnGp��|�Ä�pou´{oy8|�w�poy8|Tz\y�po¬TzDw�p��¼w�}�w8jmp��-y8|~}SyÃnG}a�-po¬0�Ç��p�p���p�{ow8|~}Su E #zDum�¼w�}\w8jmp�mzDw�zGnG}?�-po¬0�Ç��p�p��p�{ow8|~}Su���B®

Ú]Ú Þ�[]\�^0_a`

Page 9: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

� �. � "��a ���� ",��������� &+� �a" � �$1��0��� ���$1����%1$� � � �a"a� ���� ������a"$&�� �.� � �a

length

width

(X,Y,Z)

roof angle

orientation

��|����-y�pG��¾ V°�-|�¬~�Z|�u-�GnG}?�-po¬

� � ����: ����"P���� #��(2�,+-����� �!�,���=�

����§¨pË��zD|~�g²Ç}Sy8nGpoy8¬�³·zDu }S«Z�8p�{owQ�8w�zDum�-��²Ç}SyQz�«-�-|�¬~�Z|�u-�m®���|�y��8w§¨p^j1z�Ä�p^w�}À�-p��8|���u·w8jmp��p�}SnGpow8y8|~{�zD¬�nG}?�-po¬�}D²]zDu\}S«Z�8p�{ow'|�u^}Sy��-poy'w�}3«�p�zD«-¬~p7w�}3�-pB¶mump#w8jmp#{�}SuZ¶m���-y�zDw8|~}SuËnG}?�-po¬�®ikja�m�7§°p,y�po�-y�p���pouxwÃz�«-�-|�¬~�Z|�u-�G«x³Ë|�w��%y�}?}D²0�Ç��p�p���|��m®Á� B®

ikjmp±}S«Z�¸p�{ow%�1zDy�zDnGpow�poy��ÃzDy�pG¾¿ w8jmp±qB {�}a}Sy��Z|�u1zDw�p���}D²�w8jmp±{�pouaw�poy#}D²»w8jmp,y�}a}D²���� $�$��� ¿ w8jmpç%|~�Zw8j¼zDum�ˬ~pou-��w8j�}D²»w8jmpë-�-|�¬~�Z|�u-����� $�� ¿ w8jmp±zDu-��¬~p3�-pB¶mump���«a³\w8jmp,wv§¨}\�8|~�-p��7}D²»w8jmp,y�}a}D²��¿ w8jmp,}Sy8|~pouxw�zDw8|~}SuÀ}D²�w8jmp,«-�-|�¬~�Z|�u-������ �� "$#�� ���]� -] �" �� ������"01 � ��� � ��L� ���+�Q�a�T1�� ���� ��! � �� �!� 1�� 1����a",���%1����a-/�#"

$ % �#�W7� % "��,����010

ºcp��-y�p���pouawë-y8|~p'&m³�w8jmp�um}Sw8|~}Su´}D²'�P}S|�uxw,�-y�}?{�p�����®,svum�-p�p��M�Pw8j-|~�éa|�um�¼}D²¨�-y�}?{�p�����|~�,zS�mzJ��1zDw�p��cw�}�w8jmpG{�}Sum{�po�-w3}D²%{�}SuZ¶m���-y�zDw8|~}Sug|�uaw8y�}a�Z�m{�p�� |�u ��p�{ow8|~}Sug�Z�Á«�p�{�zD�m��pG|�w�zD¬�¬~}�§7�3�m�w�}��-pB¶mump^zËnGp�zS���-y�p�}Su·zµ��pow3}D²%uZ��w8�-�-¬~p�����|�®áp�®^w8jmp�{�}SuZ¶m���-y�zDw8|~}Su ��pow���nG}Sy�p��-y�p�{o|~��po¬�³�-pB¶mump��µum}�§±®'¯�}�§°poÄ�poy�}Sump,{�zDuµy�p�zS� �í� � ²Ç}Syk²Ç�-y8w8jmpoy#�-pow�zD|�¬~��®

Ø`Ù�Ú�ØÇÛ

Page 10: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

����������� ������������������������! "$#%�&(')��*+�,���.-/",�+�0�$1$1��$1 C

����� ����� ������������������������� ��� �!�#"$"� pow&% «Pp�z�«�}S�-um�-p��!Vk}Sy�po¬���pow�}D²�'&(��*) w8jmp�Vk}Sy�po¬�zD¬���po«-y�z^}D²�%�zDum�,+�w8jmp � po«�p������mpnGp�zS���-y�p±}Su-'&(�®

��� �� "$# �*.a" ��� ���" -]��� � �/.�&+� �' �0% � 1)��� �)1����N�� �Q� �'�����]� �Q��*��,�+�/-] ", �� �����a"$1 � %#���� �a��" &% � � �$1 "

ikjmpouµ§¨p±�-pB¶mump�znGp�zS�8�-y�p��µ�8�1zS{�p ��1 $/2 $43 °«x³^w8jmpòÂ}S¬�¬~}�§%|�u-��§kz�³´¾1 � 56(87*9 1 ( $ 1 ( ��� �&�#" $&%&%&%#$ � ( *;:<% * �¸� 1­|~�°w8jmpÃ{�}SuZ¶m���-y�zDw8|~}Suµ�8�1zS{�p�®»ºcp��-poum}Sw�p=2 w8jmp?>��vzD¬���po«-y�z�zS����}a{o|TzDw�p��^w�}@1 zDum�\²Â}SyACBD2 ¾3���A �FEHGJILKNMPO�Q�R ��STB-A VU 5W($7 "DXY[Z�\ %&%&% \ R ���&� " $&%&%&%#$ � ( *;B-A ]+ ��^ � " )%&%&%_+ ��^ � ( �`

�Â��ºcp={�zD¬�¬� ½��}S|�uawÁ�-y�}?{�p������=z°nGp�zS�8�-y�zD«-¬~p¨zD�-�-¬�|~{�zDw8|~}Su3²`y�}Sn zk�-y�}S«1zD«-|�¬�|~��w���powMw�}���1 $/2�$43 �®

��}�§ §°pÃzDy�p,zD¬�¬~}¹§¨p���w�}�-p�zD¬P§%|�w8jËw8jmp��-poum��|�w½³\}D²�z ½�P}S|�uxw%�-y�}?{�p�������§%|�w8j^y�p�����p�{owkw�}�w8jmpnGp�zS���-y�p;3�®

X?}\w8jmpQ�Z|~��w8y8|�«-�-w8|~}Su . }D²°��p�{ow8|~}Su �^{�zDu´«Pp�§%y8|�w8w�pou·zS�Q¾�.���^�� �ba � � �3���^ � �®ikjmp�-poum��|�w½³�a��8�-¬�|�w��%|�uxw�}�w½§°}��1zDy8w��ca � � ��Fd � � �e � � ���§%jmpoy�p�dÀ�8w�zDum�-�7²Ç}Sy%w8jmp3�-y8|~}Sy7nG}?�-po¬zDum�fe\�8w�zDum�-�%²Â}Sy%w8jmp,�mzDw�znG}?�-po¬�®���hg i,j�k �Plm� n��o������������-� ��� �!�#"$"�prqs�*��t��#uj����� �!�#"$"� pow?v�«�p�z���³anQnGpow8y8|~{�y�po¬TzDw8|~}Su´}Suw%®#ikjmpou¼§¨p��-pB¶mump�w8jmp�umpo|���jx«P}S�-y8jm}?}a�À}D²�xC:j%«a³\w8jmp,²Ç}S¬�¬~}¹§%|�u-��§°z�³´¾�y

��x ���! zB{%T| fv<} $4}~B-x $ ��B-x * �Âq��Ê��pow �����&� " $&%&%&% $ � ( *3|~�%{�zD¬�¬~p���z{o¬�|��a�mp,|ϲ�zD¬�¬Mw8jmp±��}S|�uaw��7}D²��´zDy�pÃumpo|���jx«P}S�-y���®

��� �� "$# � � �� 1�� ���&� ���]� �Q� � ������� ��.P���]� 1a� �$1+�����/.!���]�! �a��� �]���� "$1��/. 1+���xj:<% � ���x� ���! zB�x@| fv<})$4}�B-x * �`��

ºcp���z�³µw8j1zDw;do�#1F� � � $�U;� %|~�,z�ÈÀzDy8©�}�ĵ²`�-um{ow8|~}SuÀ§%|�w8jÀy�p��8�Pp�{ow�w�}\w8jmp�y�po¬TzDw8|~}Suv |ϲ]²Â}Sy0 �B�1�¾¿ d � � ����&��d ��� ���� $]�*�~: �

Ú]Ú Þ�[]\�^0_a`

Page 11: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

U �. � "��a ���� ",��������� &+� �a" � �$1��0��� ���$1����%1$� � � �a"a� ���� ������a"$&�� �.� � �a

¿ |ϲ?d � � ~� �´zDum� jB % w8jmpou ¾ � � � $ ��� K�����HO� K��LO }Su-¬�³·�-po�Ppoum�-�G}Su �zDum�ª}Suy� � �]® � � � $ '|~�%w8jmp±��}Q{�zD¬�¬~p�����zD�1zDu-��po¬~}S�À{�}Sum�Z|�w8|~}Su1zD¬�|�uaw�poum�8|�w½³�®

�ÊÈÀzDy8©�}�ÄË��}S|�uaw7�-y�}?{�p����%|~�7z�P}S|�uxw7�-y�}?{�p����%§%jm}���p,�-poum�8|�w½³Ë|~�#zQÈÀzDy8©�}�Ä\²Ç�-um{ow8|~}SuÁ®��²Ç�-um{ow8|~}Su,e���1 � � � $�U;� #|~�3{�zD¬�¬~p�� ½|�uxw�poy�zS{ow8|~}Sug²`�-um{ow8|~}Su��Q|ϲ�e � � �� X |�nQ�-¬�|~p��w8j1zDw ��|~�#zG{o¬�|��x�mp�®¨ikjmpouµ§¨p3j1z�Ä�p±w8jmp,²Ç}S¬�¬~}¹§%|�u-�\p �a�-|�ÄSzD¬~poum{�pG¾�d�|~��zQÈÀzDy8©�}�Ä^²Ç�-um{ow8|~}Su

|ϲ=zDum��}Su-¬�³Ë|ϲ�w8jmpoy�p3pBÅ?|~�8w��7zDu�|�uxw�poy�zS{ow8|~}Suµ²Ç�-um{ow8|~}Su-e^�8�m{�jµw8j1zDw��-²Ç}Sy �{B-1 ¾d � � ������� � e ��� � E

ikj-|~��y�p��8�-¬�w�|~���8|�nQ|�¬TzDy�w�}µw8jmp^¯�zDnQnGpoy���¬~po³x�Íɨ¬�|��M}Sy�� w8jmp�}Sy�pon ²Â}Sy3w8jmp�ÈÀzDy8©�}�Ä y�zDum�-}Sn¶1po¬~�-�¹®2s½uª²�zS{ow��7zS�Q²Â}Sy�ÈÀzDy8©�}�Ä­y�zDum�-}Sn)¶1po¬~�-���k§¨p¼{�zDu �-pB¶mump�{o¬�|��x�mp���}Sw�pouaw8|TzD¬~��zDum�pBÅZ�-y�p����%w8jmp,�-poum��|�w½³-d¼w8j-y�}S�-��jµw8jmp���p,�P}Sw�pouxw8|TzD¬~��¾d � � ��FE �������� W

���! K��LO % �#" %$& ���

§%jmpoy�p(' � � 'y�po�-y�p���pouxw��#w8jmp±��pow7}D²=zD¬�¬Áw8jmp,{o¬�|��a�mp��7|�u��]®s�²=§°p�{�zD¬�¬�'*) � � %w8jmp���pow�}D²¨w8jmp�{o¬�|��a�mp���§%|�w8j,+Gpo¬~ponGpouaw����Pw8jmpouÀ§¨p�{�zDuÀzD¬~��}�§%y8|�w�pTd

zS�%²Ç}S¬�¬~}¹§7�3¾ d � � ��FE&�-� ���� W ) W���� /. K��LO % ) �#" $& � C

§%jmpoy�pT%0)�|~�#z���}Sw�pouaw8|TzD¬]�-pB¶mump��µ}Su�w8jmp±{o¬�|��x�mp��#}D²1+po¬~ponGpouxw��¹®2 % "����7" �!�,���=�

ºcp,{�jm}a}���p,w8jmp±�-poum�8|�wv³Ë}D²»w8jmpÃ�-y8|~}Sy7nG}?�-po¬]zS�k²Â}S¬�¬~}�§7��¾d � � ��43 ( K��LO � � � � U

¿�Y � � =|~�%w8jmp,ua�-n3«Ppoy�}D²�}S«Z�¸p�{ow��7|�uµw8jmp,{�}SuZ¶m���-y�zDw8|~}Su ���¿ w8jmpÃ�1zDy�zDnGpow�poy53c{�}Suaw8y�}S¬~�7w8jmp,|�uaw�poum�8|�w½³µ}D²»w8jmpÃ�P}S|�uxw7�-y�}?{�p������¿ w8jmp=²Ç�-um{ow8|~}Su �µnG}a�-po¬~�]w8jmp°|�uxw�poy�zS{ow8|~}Sum�»«Ppow½§°p�pouQw8jmp¨}S«Z�8p�{ow��»}D²mw8jmp¨{�}SuZ¶m���-y�zDw8|~}SuÁ®ºcp±}Su-¬�³\�m��pÃ�1zD|�y8§%|~��p,|�uxw�poy�zS{ow8|~}Su �Ç��p�p�²Ç�-y8w8jmpoy�B®

� � � � �6#798 :�;�<>=7@?�:BA� $4} � F�

Ø`Ù�Ú�ØÇÛ

Page 12: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

����������� ������������������������! "$#%�&(')��*+�,���.-/",�+�0�$1$1��$1 F

Dint

Dint

��|����-y�p3�Z¾���po¬TzDw8|~}Su v� ��� �{�#n��V�8�����"ºcp,�-pB¶mump3w½§°}Qw½³?��p��#}D²�y�po¬TzDw8|~}Sum��¾

��®#�#po¬TzDw8|~}Su~vʾ]ºcp%��z�³�w8j1zDw=w½§°}±}S«Z�¸p�{ow��=zDy�p7|�u�y�po¬TzDw8|~}SuDv�§%jmpouQw8jmp°²`y�zDnGp��¨zDy�}S�-um�w8jmponÆ|�uxw�poy���p�{ow �Ç��p�p���|��m®m��B®

�Z®#�#po¬TzDw8|~}Su���¾�s½²Á§¨pÃ{�zD¬�¬�� "!$����#w8jmp�{�pouaw�poy��7}D²�w½§°}«-�-|�¬~�Z|�u-����� � "!$��7w8jmpo|�yky�p��8�Pp�{B�w8|�Ä�p3¬~pou-��w8jm���� zDum� �2�-pB¶mump��´zS��|�u�w8jmp ��|��m®�qZ®�ºcp���z�³µw8j1zDw�w8jmp�w½§°}\«-�-|�¬~�Z|�u-���zDy�pÃumpo|���jx«P}S�-y��#§%|�w8jµy�p�����p�{ow%w�}Qw8jmpÃy�po¬TzDw8|~}Su��Ê|ϲ%¾����^ ��� "!$���� � ���0"0U ��� ]������^��� �|�[|���� ����� � $ | � |��������� � �¸����

ikj-|~��y�po¬TzDw8|~}Suª|~��-p��8|���ump��·²Â}Sy�«-�-|�¬~�Z|�u-���umpo|���jx«P}S�-y8|�u-�gzD¬~}Su-�Àw8jmpo|�y�§%|~�Zw8j­��}�§°p�-pB¶mump3z�8|�nQ|�¬TzDy7y�po¬TzDw8|~}Su�²Ç}Sy%«-�-|�¬~�Z|�u-���#umpo|���jx«P}S�-y8|�u-�^zD¬~}Su-�Gw8jmpo|�y7¬~pou-��w8jÁ®

� �hg �H��$�#���P� �8�����"ikjmpoy�p�zDy�pömÄ�péa|�um�-�#}D²��1zD|�y8§%|~��p±|�uxw�poy�zS{ow8|~}Su ¾

¿ ²Ç}Sy%w8jmp,y�po¬TzDw8|~}Su{v ¾

Ú]Ú Þ�[]\�^0_a`

Page 13: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

��� �. � "��a ���� ",��������� &+� �a" � �$1��0��� ���$1����%1$� � � �a"a� ���� ������a"$&�� �.� � �a

φ ψ C2

C1

d(C1,C2)

��|����-y�p3qZ¾���po¬TzDw8|~}Su �

� z�w�poy8nƲÂz�Ä�}S�-y��7|~�-pouxw8|~{�zD¬�}Sy8|~pouxw�zDw8|~}Sum� �Ç��p�p���|��m®-��B®� z�w�poy8n ��pou1zD¬�|-,�p��#|�uxw�poy���p�{ow8|~}Sum��®

¿ ²Ç}Sy%w8jmp,y�po¬TzDw8|~}Su � ¾

� z�w�poy8nƲÂz�Ä�}S�-y��7w8jmp,{o¬~}���poump�����}D²�w8jmpë-�-|�¬~�Z|�u-����{�pouxw�poy�� �Ç��p�p���|��m® E B®� z�w�poy8nƲÂz�Ä�}S�-y��#p �a�1zD¬Á�8|-,�p��7}D²»w½§¨}�«-�-|�¬~�Z|�u-���%²�zS{o|�u-��p��Z��p���®� z�w�poy8nƲÂz�Ä�}S�-y��#p �a�1zD¬My�}a}¹Ä�p���zDu-��¬~p���®� z�w�poy8nƲÂz�Ä�}S�-y��#p �a�1zD¬My�}a}¹Ä�p��7jmpo|���jxw��¹®

�*�P}Sw�pouxw8|TzD¬Á|~�7zS����}a{o|TzDw�p��Ëw�}Qp�zS{�j�©a|�um��}D²�|�uxw�poy�zS{ow8|~}Su �Ç��p�p��]|��m®m��B®�ikjmpÃ�1zDy�zDnGpow�poyn�z�³3«Pp'w8jmp°}Sy8|~pouxw�zDw8|~}Su\�Z|��Ppoy�poum{�p���w8jmp¨|�uxw�poy���p�{ow8|~}Su�zDy�p�zZ��w8jmp¨�Z|~��w�zDum{�pk«�powv§¨p�pouG{�pouxw�poy��¹�w8jmp,�Z|��Mpoy�poum{�p±«Ppow½§°p�pou�¬~pou-��w8jm���m§%|~�Zw8jm�#}Sy%y�}?}�Ä�p���zDu-��¬~p��¹®

ikjmpò`�-um{ow8|~}Su µ|~�#�-p��8|���ump���zS�k²Â}S¬�¬~}�§7��¾ � #$4} 1�FE&�-� � �c% � � #$4} �¸���

§%jmpoy�p #$4}�B % zDum� % � |~��w8jmp\���-n }D²7w8jmp^poumpoy8��³cw�poy8nG��y�po¬TzDw�p�� w�}�w8jmp\��|ÏÅ´�Z|��Mpoy�pouxw©?|�um�-�7}D²»|�uxw�poy�zS{ow8|~}SuÁ®

� � k�� : �,���=�

� ��� ����lm��� �8�V����������&�������V�$�mlm����#n �8� � l<"ºcp,���-�-��}���pÃw8j1zDw#§¨p,©?um}�§/zD¬�¬�w8jmp,Äa|~po§%�P}S|�uxw#�1zDy�zDnGpow�poy��#|�®áp�®M¾

Ø`Ù�Ú�ØÇÛ

Page 14: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

����������� ������������������������! "$#%�&(')��*+�,���.-/",�+�0�$1$1��$1 ���

θ1

θ2

∆θ

�]|����-y�p±�m¾ W�y8|~pouxw�zDw8|~}Su¼�Z|��Ppoy�poum{�p

C1

C2

��|����-y�p E ¾ V°y8|�u-��|�u-�Gw8jmp3{�pouxw�poy���{o¬~}���poy

Ú]Ú Þ�[]\�^0_a`

Page 15: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

��� �. � "��a ���� ",��������� &+� �a" � �$1��0��� ���$1����%1$� � � �a"a� ���� ������a"$&�� �.� � �a

0 10 20 30 40 50 60 70 80 90 100

-1.0

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0Potential

Parameter

0 10 20 30 40 50 60 70 80 90 100

-1.0

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50 60 70 80 90 100

-1.0

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

��|����-y�p3�Z¾��]}Sw�pouaw8|TzD¬

¿ w8jmpÃ|�uxw8y8|�um�8|�um{3�1zDy�zDnGpow�poy���¾

� w8jmp�²Â}?{�zD¬Á�Z|~�8w�zDum{�p� w8jmpÃ�-|ÏÅ-po¬��8|-,�p

¿ w8jmp,pBÅ?w8y8|�um�8|�um{±�1zDy�zDnGpow�poy���¾

� w8jmp,{�zDnGpoy�zG��}���|�w8|~}Su� w8jmp,{�zDnGpoy�z�}Sy8|~pouxw�zDw8|~}Su

ikja�m��§¨pË{�zDug�-y�}D�8p�{oww8jmp\{�}SuZ¶m���-y�zDw8|~}Su­}Suaw�}¼w8jmp�|�n�zD��p^y�pB²Âpoy�pouxw8|TzD¬��Ç��p�p��]|��m® C �zDum�{�}SnQ�-�-w�p±w8jmp±�mzDw�z�¶mw8w8|�u-�Gw�poy8nµ®

ºcp,�m��pÃw8jmp�²Â}S¬�¬~}�§%|�u-�\�mzDw�zQnG}a�-po¬'¾e � � � �� � � � � �¸����

svw%nGp�zDum�7w8j1zDw#w8jmp±�mzDw�zQnG}?�-po¬Á|~�7{�}SnQ�-�-w�p�����po�1zDy�zDw�po¬�³^²Ç}Sy#p�zS{�j�}S«Z�8p�{ow�®�ºcp,�m��p±w8j-y�p�p©?|�um�-�7}D²��mzDw�z�¶mw8w8|�u-�Gw�poy8nG��¾

¿ w8jmp�¶my��8w#}Sumpò�z�Ä�}S�-y��%¬~}¹§ Ä�zDy8|TzDum{�p±}Suµp�zS{�j�y�}a}D²��8|~�-p�®

Ø`Ù�Ú�ØÇÛ

Page 16: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

����������� ������������������������! "$#%�&(')��*+�,���.-/",�+�0�$1$1��$1 ��q

��|����-y�p�C?¾��=y�}D�¸p�{ow8|�u-�Ëz�y�}a}D²�}Suxw�}Qw8jmp±|�n�zD��p

Ú]Ú Þ�[]\�^0_a`

Page 17: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

�o� �. � "��a ���� ",��������� &+� �a" � �$1��0��� ���$1����%1$� � � �a"a� ���� ������a"$&�� �.� � �a

¿ w8jmp,��p�{�}Sum�µ}Sumpò�z�Ä�}S�-y��#j-|���jµ��y�zS�Z|~pouxw�}Su�w8jmp,y�}a}D²�p��Z��p���®¿ w8jmpÃw8j-|�y��µ}Sumpò�z�Ä�}S�-y��7j-|���j�{�}Suxw8y�zS�8w�«�powv§¨p�pou�w8jmpÃwv§¨}�y�}a}D²��8|~�-p���®ºcpòÇ}Sy8n��-¬TzDw�p3zD�xzD|�uµw8jmp±�mzDw�z¶mw8w8|�u-�Gw�poy8nƧ%|�w8j�zDu�poumpoy8��³ËpBÅZ�-y�p����8|~}Su ¾

� � �FE ��� � �c% � � �¸��q�§%jmpoy�p �B{% zDum�{% �3|~�%w8jmp,�8�-n }D²»w8jmpÃw8j-y�p�p±poumpoy8��³Ëw�poy8nG�#�-pB¶mump���zD«P}�Ä�p�®

� �hg q ��n�����u ��� �s½²=§¨pj1z�Ä�p��poÄ�poy�zD¬»|�n�zD��p����Pw8jmpouÀw8jmp�{�}SuZ¶m���-y�zDw8|~}Suc{�zDuÀ«Pp3�-y�}D�8p�{ow�p��À|�uxw�}Ëp�zS{�j´|�n�zD��pzDum�6w8jmp��mzDw�zc¶mw8w8|�u-�·w�poy8n4{�zDu�«�p�{�}SnQ�-�-w�p��­²Â}Sy\p�zS{�j |�n�zD��p�® V¨³ªw8jmp�§°z�³��7w8j-|~�\|~�p�����pouxw8|TzD¬Á|ϲ»§¨p±§°zDuxw�w�}«-�-|�¬~��qB }S«Z�8p�{ow��±¾�}Su-¬�³��8w�poy�p�}���{�}S�x³�{�zDuµw8jmp�}Sy�pow8|~{�zD¬�¬�³µpoum���-y�p��w8jmp^�-u-|��a�mpoump����Q}D²�p�zS{�j6qB }S«Z�8p�{ow�® ikjmpË}S«Z�8p�{owQn3�m�8wQ{�}Sy8y�p��8�P}Sum� w�}´z�nQ|�u-|�n3�-n)}D²w8jmp\�mzDw�zµ�P}Sw�pouxw8|TzD¬¨²Â}Sy�p�zS{�j·|�n�zD��p�®!X?}�w8j-|~��zD�-�-y�}�zS{�j |~���Z|��Mpoy�pouxw�²`y�}Sn w8jmp�{o¬TzS����|~{�zD¬{�}Sy8y�po¬TzDw8|~}SuZ��«1zS��p��´�8w�poy�p�}���{�}S�x³�®�ikjmp���y�p�zDw�poy�w8jmp�ux�-n�«�poy,}D²'|�n�zD��p��¹�1w8jmp�nG}Sy�p�y�po¬�|TzD«-¬~pzDum��zS{�{o�-y�zDw�p,w8jmp,y�p��8�-¬�w�®

� 5 93�,�#0����� ��93� .\�k���=#���� ���0

� ��� �@�P�8�#������Pn ��� ���#"ºcp,�Z|~��w8|�u-���-|~�8jµw8j-y�p�p,wv³a�Pp��#}D²»��}Sw�pouaw8|TzD¬��Ç��p�p���|��m® U þ

¿ �kw8w8y�zS{ow8|�Ä�p±�P}Sw�pouxw8|TzD¬'¾ % ���¿ �#po�-�-¬~�8|�Ä�pÃ�P}Sw�pouxw8|TzD¬°¾�% ���¿ È�|ÏÅ-p��Ë��}Sw�pouaw8|TzD¬�m}Sy#p�zS{�j�©a|�um�µ}D²»|�uxw�poy�zS{ow8|~}Su¼}Sy#�mzDw�z�¶mw8w8|�u-�Gw�poy8nµ�m§¨p±{�jm}a}���p�z���}Sw�pouaw8|TzD¬�w½³?�PpQ¾¿ �#u�zDw8w8y�zS{ow8|�Ä�p3��}Sw�pouaw8|TzD¬Áw�}Q«-y8|�u-��{o¬~}���poy#w8jmpë-�-|�¬~�Z|�u-�\{�pouxw�poy��¿ � y�po�-�-¬~�8|�Ä�p±��}Sw�pouaw8|TzD¬�w�}�Ppou1zD¬�|-,�p,w8jmp,«-�-|�¬~�Z|�u-���7|�uaw�poy���p�{ow8|~}Sum�¿ �/È�|ÏÅZp��Ë�P}Sw�pouxw8|TzD¬�²Ç}Sy%w8jmp,}Sw8jmpoy#©a|�um�-�7}D²»|�uxw�poy�zS{ow8|~}Su ¾

� W�y8|~pouaw�zDw8|~}Su��Z|��Mpoy�poum{�p� º�|~�Zw8jµ}Sy7¬~pou-��w8j��Z|��Mpoy�poum{�p

Ø`Ù�Ú�ØÇÛ

Page 18: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

����������� ������������������������! "$#%�&(')��*+�,���.-/",�+�0�$1$1��$1 � E

0 10 20 30 40 50 60 70 80 90100

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0Potential

Parameter

Repulsive

0 10 20 30 40 50 60 70 80 90100

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0Potential

Parameter

Mixed

0 10 20 30 40 50 60 70 80 90100

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0Potential

Parameter

Repulsive

��|����-y�p U ¾=��}Sw�pouxw8|TzD¬�w½³?��p��

� ��}a}D²�zDu-��¬~p±�Z|��Mpoy�poum{�p¿ �/È�|ÏÅZp��Ë�P}Sw�pouxw8|TzD¬�²Ç}Sy%w8jmp,�mzDw�z¶mw8w8|�u-��w�poy8nG�±¾

��� zDy8|TzDum{�p� ÌÃy�zS�Z|~pouxw� É°}Suaw8y�zS�8w

ikjmp���¬~}S��p��,{�jm}���pouÀ²Ç}SyÃw8jmp��P}Sw�pouxw8|TzD¬~�,�-¬Tz�³Àz\��y�p�zDw,y�}S¬~p �Ç��p�p ��|��m® F�3¾�w8jmpQ�8w�p�po�Ppoyw8jmp��8¬~}S�Pp±|~���1w8jmp±nG}Sy�p�w8jmp�zS����}?{o|TzDw�p��µ�P}Sw�pouxw8|TzD¬�j1zS�Ãz ½w8j-y�p��8jm}S¬~� �3«Ppoj1z�Ä?|~}S�-y�® W�u�w8jmp{�}Suaw8y�zDy8³���z�¬~p����#�8w�p�po���8¬~}S�Pp±zD¬�¬~}�§7��z�nG}Sy�p &1pBÅ?|�«-¬~p±«�poj1z�Äa|~}S�-y�®

B��-y8|�u-� w8jmpc�8|�n��-¬TzDw8|~}SuÁ�3�8w�p�po�Ê�8¬~}S��p��µ���1zDy�zDuxw�p�p zS{�{o�-y�zS{o³2«-�-w�um}Sw�pBÅZj1zD�m�8w8|�Ä?|�w½³§%jmpoy�p�zS�%��}D²`wk�8¬~}S�Pp��¨���1zDy�zDuaw�p�p±z�«�pow8w�poykpBÅ?j1zD�m��w8|�Äa|�wv³�«-�-wkum}Sw7zS{�{o�-y�zS{o³�®=s½u^«P}Sw8jË{�zS��p����w8jmp���}S¬��-w8|~}Su¼w�}�}¹Ä�poy�{�}SnGpw8jmp3�-y�}S«-¬~pon�}D²'pBÅ?j1zD�m��w8|�Äa|�wv³�}SyÃzS{�{o�-y�zS{o³�|~�#w�}\|�um{oy�p�zS��p�w8jmp��|�n3�-¬TzDw8|~}Su�w8|�nGp�®

� �hg �T�� ��� � � �*���Pl � �$�#� "ºcp\um}Sy8n�zD¬�|-,�p�zD¬�¬¨�P}Sw�pouxw8|TzD¬~��«Ppow½§°p�pou � X zDum� �Z� ��zDum� X }Sy � X zDum� X §%jmpow8jmpoy�w8jmp�P}Sw�pouxw8|TzD¬�|~��zDw8w8y�zS{ow8|�Ä�p���y�po�-�-¬~�8|�Ä�p�}Sy#nQ|ÏÅ-p��M®%ikjmpou¼§¨p3{�zDuÀpBÅZ�-y�p����7w8jmp3w�}Sw�zD¬�poumpoy8��³µ}D²

Ú]Ú Þ�[]\�^0_a`

Page 19: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

��� �. � "��a ���� ",��������� &+� �a" � �$1��0��� ���$1����%1$� � � �a"a� ���� ������a"$&�� �.� � �a

Parameter

Potential

Potential

Parameter

��|����-y�p FZ¾=��}Sw�pouxw8|TzD¬»�8¬~}S��p

w8jmp�{�}SuZ¶m���-y�zDw8|~}SuczS��% � � ���������%�� � � k§%jmpoy�p3w8jmpr%��'zDy�p�w8jmp3um}Sy8n�zD¬�|-,�p��À�P}Sw�pouxw8|TzD¬~�¹®ikjmp��1zDy�zDnGpow�poy���� � zDy�pÃ{�jm}���pou�zS{�{�}Sy��Z|�u-�Qw�}w8jmp�y�po¬TzDw8|�Ä�pÃ|�nQ�P}Sy8w�zDum{�pç¨p�§%|~�8jËw�}���y�zDuxww�}Qp�zS{�j�wv³a�Pp,}D²�|�uaw�poy�zS{ow8|~}Su¼}Sy7�mzDw�z¶mw8w8|�u-�Gw�poy8nµ®

�W: ���� k�P���#

� ��� � � ��n ��� �D�Dq �V� t��#uw� � �P���p � � u�� � "$�� �n�������lm�oqs����8� ���V� n��-qs�*��t��Ju� � �P�� "

ikjmp��8|�n��-¬TzDw8|~}Suc{�}Sum�8|~�8w���|�u�«-�-|�¬~�Z|�u-�µz\ȼzDy8©�}¹Ä�{�j1zD|�u¼§%j-|~{�j´{�}SuxÄ�poy8��p��,w�}\w8jmp��Z|~��w8y8|�«Z��-w8|~}Su .�® X?}�§°p3j1z�Ä�p�w�}^�-pB¶mumpzGw8y�zDum�8|�w8|~}SuÀ©�poy8umpo¬�� §%j-|~{�jÀ|~��zD�Ppoy8|~}?�Z|~{���|�y8y�p��Z�m{ow8|�«-¬~pzDum� .���|�uxÄ�zDy8|TzDuxw�®3s½u�²ÂzS{ow���§¨p�y�po�-¬TzS{�p�w8jmp�|�uxÄ�zDy8|TzDum{�p�{�}Sum�Z|�w8|~}Su´«a³�z�y�poÄ�poy��8|�«-|�¬�|�w½³¼{�}SuZ��Z|�w8|~}Su�§%j-|~{�j�|~�#�8w8y�}Su-��poy�zDum��p�zS�8|~poy7w�}QÄ�poy8|ϲdz�®°ikjmp±y�poÄ�poy��8|�«-|�¬�|�wv³µ{�}Sum�Z|�w8|~}Su�nGp�zDum�#w8j1zDw��� .���^�� �� � � $��� ¨n3�m��w7«�p,��³anQnGpow8y8|~{,§%|�w8j�y�p��8��p�{ow#w�} xÊzDum���\®�svum�-p�p��M�m«a³\y�po�-¬TzS{o|�u-�� «x³-1,�Z§°p±}S«-w�zD|�uµw8jmp,|�uaÄSzDy8|TzDum{�p�{�}Sum�Z|�w8|~}SuÁ®

� pow�� � � $ ^�� =«�p,z�w8y�zDum�8|�w8|~}Su�©�poy8umpo¬�®�ºcpÃ�-pB¶mump±zDum}Sw8jmpoy7©�poy8umpo¬��ʧ%j-|~{�j�|~�%�-pB¶mump��zS��²Â}S¬�¬~}�§7��¾�§°p�{�jm}?}���pµz�umpo§Æ�8w�zDw�pD�´²Çy�}Sn�w8jmp�{o�-y8y�pouxw��8w�zDw�p � zDum� w8jmpËw8y�zDum��|�w8|~}Su©�poy8umpo¬���zDum�g§¨pËzS{�{�po�-w�w8j-|~���-y�}S�P}���zD¬¨§%|�w8jªz��-y�}S«1zD«-|�¬�|�w½³ + � � $4� ,}Sy�§°p\��w�z�³gzDw�w8jmp

Ø`Ù�Ú�ØÇÛ

Page 20: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

����������� ������������������������! "$#%�&(')��*+�,���.-/",�+�0�$1$1��$1 �6C

��w�zDw�p ��}Sw8jmpoy8§%|~��p�® X?}§¨p±{�zDuµ§%y8|�w�p�¾

� � � $��� � \�� � � � $ ^�� %+ � � $4� PU��#� � ]R�� �zB �� �¸�o��

� � � � \�� � � � $ ^�� � X � + � � $4� �¸� E

É°}Sum��p �x�mpouaw8¬�³��-w8jmp�y�poÄ�poy��8|�«-|�¬�|�w½³�{�}Sum�Z|�w8|~}Suµ{�zDuË«�p�§%y8|�w8w�pou˲Â}Sy7zD¬�¬ Vk}Sy�po¬Á��pow�� x $�� B�1 ¾

\ � .���^ � \�� � � � $ ^ � %+ � � $4� *U \ � � � .���^ � �� � � � \ � .���^�� \ � � ���+$ ^ � %+ ���+$ � *U \ � � � .���^�� �� ��� �¸����

s½u¼}Sy��-poy�w�}�Ä�poy8|ϲ`³�w8jmp3y�poÄ�poy��8|�«-|�¬�|�wv³�{�}Sum�Z|�w8|~}SuÁ�P|�w�|~�������{o|~pouxwÃw�}GÄ�poy8|ϲdzµw8j1zDw�²Ç}SyÃzD¬�¬x $�� ¾ \ � .���^�� \� � � � $ ^ � %+ � � $4� � \�� .���^�� \ � � ���+$ ^ � %+ ���+$ � �¸�6C

s�²3§°pÀ�8�-�-��}���p�w8j1zDw�.���^�� � � � $ ^�� �j1zS�µz·�-poum�8|�w½³ §%|�w8j y�p��8��p�{owËw�}ªz·�8³?nQnGpow8y8|~{nGp�zS���-y�p��Q}Su�1� �1,�Z§°p±{�zDuµ§%y8|�w�pG¾

\ � .���^ � \ � � � � $ ^�� %+ � � $4� � \ � \ � � ��^ � $ ^�� d � � $4� %+ � � $4� �¸� U

\� .���^ � \ � � ���+$ ^ � %+ ��� $ � � \��~\ � � ��^��+$ ^ � d ��� $ � %+ ���+$ � �¸�+F�

¯�poum{�pÃw8jmp,y�poÄ�poy��8|�«-|�¬�|�wv³µ{�}Sum�Z|�w8|~}Su�|~�7�WzDw8|~�¸¶1p��µzS�7��}?}Su�zS�±¾d � � $4� %+ � � $4� � d ���+$ � %+ ���+$ � �Â����ºcpçkzDuxw�w�}Qn�zJÅ?|�nQ|-,�p±w8jmp3zS{�{�po�-w�zDw8|~}Su�y�zDw8|~} + � � $4� ¨��}§¨p,w�zD©�pQ¾

+ � � $4� ������ Y�� X $ d ��� $ � d � � $4� �� ��Z�

Xa�-�-��}���p�§¨p\j1z�Ä�pË�-pB¶mump��·��poÄ�poy�zD¬¨©�poy8umpo¬~� � � «a³cw8jmp��WzDnGp�§kz�³��»w8j1zDw�|~�3§°p�j1z�Ä�p{�jm}���pouc©�poy8umpo¬~� � � zDum�czS{�{�po�-w�zDum{�p�y�zDw8|~} + � ��}Ëw8j1zDw±p�zS{�j ©�poy8umpo¬ � � Ä�poy8|϶1p��3w8jmpy�pB�Ä�poy���|�«-|�¬�|�w½³6{�}Sum�Z|�w8|~}SuÁ® W�«xÄ?|~}S�m�8¬�³�� � � � � � � ��� � � � � � � X GzD¬~��}gÄ�poy8|϶1p��^w8j-|~�{�}Sum�Z|�w8|~}SuÁ®

��}¹§*§¨p±�-pB¶mump±w8jmpòÇ}S¬�¬~}¹§%|�u-�\zD¬���}Sy8|�w8j-n ¾

Ú]Ú Þ�[]\�^0_a`

Page 21: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

� U �. � "��a ���� ",��������� &+� �a" � �$1��0��� ���$1����%1$� � � �a"a� ���� ������a"$&�� �.� � �a

¿ ɨjm}a}���p±z�©�poy8umpo¬ � � zS{�{�}Sy��Z|�u-�\w�}Qw8jmpÃ�-y�}S«1zD«-|�¬�|�w8|~p�� � � ®¿ ɨjm}a}���p�zQumpo§/{�}SuZ¶m���-y�zDw8|~}Su{�^²Çy�}Sn�� � � � $�� ¨§%jmpoy�p �¼|~�7w8jmp3{o�-y8y�pouaw�{�}SuZ¶m���-y�zJ�w8|~}SuÁ®

¿ ÉkzD¬~{o�-¬TzDw�p±w8jmpÃy�zDw8|~} + � � � $4� � ��� K ��� �LO� � K�� � � O ®¿ �%{�{�po�-wQw8jmpËumpo§Æ{�}SuZ¶m���-y�zDw8|~}Su �c§%|�w8j6�-y�}S«1zD«-|�¬�|�w½³ ��� Y � X $ + � � � $4� ��¨}Sw8jmpoy8§%|~��p�8w�z�³�zDw7w8jmp,{o�-y8y�pouxw�{�}SuZ¶m���-y�zDw8|~}Su ��®ikjx�m�°w8jmpÃȼzDy8©�}¹Ä�{�j1zD|�u��-pB¶mump��^«x³Gw8j-|~�%zD¬���}Sy8|�w8j-n {�}SuxÄ�poy8��p��kw�}�w8jmpÃ�Z|~�8w8y8|�«-�-w8|~}Su�.

�`�-y�}¹Äa|~�-p���|�w%|~�#zD¬~��}GzD�Ppoy8|~}a�Z|~{�zDum��|�y8y�p��Z�m{ow8|�«-¬~p � §%j-|~{�j�|~�%w8jmp±{�zS��pÃ|�u��-y�zS{ow8|~{�p B®

� �hg q �#u��J"��}�§ §¨pG�-pB¶mump�§%j1zDw±w8jm}���pQ©�poy8umpo¬~��{�}Sum{oy�pow�po¬�³Ày�po�-y�p���pouxw�®^s½um�-p�p�� w8jmpQ©�poy8umpo¬~��zDy�p\zS�¸���}a{o|TzDw�p���w�} ½nG}¹Ä�p����3§%j-|~{�j¼§%|�¬�¬»«Pp±¬�|~�8w�p���²Ç�-y8w8jmpoy�®�svu��-y�zS{ow8|~{�p��Pw8jmp��-y�}S�P}��8|�w8|~}Su´}D²=w8jmp©�poy8umpo¬�|~�%n�zS�-p3zS�k²Â}S¬�¬~}�§7��¾

¿ �]|�y���w%�-u-|ϲÇ}Sy8nQ¬�³�{�jm}?}���p3z��1zDy�zDnGpow�poyc>¼|�u�z���|�Ä�pou���pow�� B-'¿ �-y�}Sn w8jmp�{o�-y8y�pouxwÃ{�}SuZ¶m���-y�zDw8|~}Su �´zDum�µw8jmp3�1zDy�zDnGpow�poyc>»�1�-y�}S��}���p3zQumpo§Ê{�}SuZ¶m�S��-y�zDw8|~}Su���®

�my�}SnÆum}�§ }SuÁ�m§¨p±{�zD¬�¬�� w8jmp±zD�ZÅ?|�¬�|TzDy8³Ë�-y�}S«1zD«-|�¬�|~�8w8|~{3�1zDy�zDnGpow�poy���pow�®¯�poy�pÃ|~�%w8jmp±¬�|~�8w7}D²�w8jmp±nG}�Ä�p��3¾

��®�� 5`£J¢ K ¤ 4 Ö6Ö Ñ ¤Z¢ Kikjmp3«-|�y8w8jÀ{�}Sum�8|~�8w���|�u´zS�-�Z|�u-�\w�}\w8jmp�{o�-y8y�pouaw,{�}SuZ¶m���-y�zDw8|~}Su zDu¼}S«Z�8p�{ow��-u-|ϲÂ}Sy8nQ¬�³{�jm}���pou |�um% zDum�·w8jmpË�-p�zDw8j­{�}Sum�8|~�8w���|�u y�ponG}�Ä?|�u-� zDu·�-u-|ϲÂ}Sy8nQ¬�³ {�jm}���pouª}S«Z�8p�{ow²`y�}Sn w8jmp±{o�-y8y�pouaw�{�}SuZ¶m���-y�zDw8|~}SuÁ®

�Z®� £D¤ 4 ¡��K¤Z¢65 Õ 4ºcp��-u-|ϲÂ}Sy8nQ¬�³ {�jm}?}���pËz�«-�-|�¬~�Z|�u-�À|�u·w8jmp\{o�-y8y�pouaw{�}SuZ¶m���-y�zDw8|~}Su6zDum� zµ�Z|�y�p�{ow8|~}SuzDnG}Su-�Gw8jmp,w8j-y�p�p±}Sump��±¾¿ �Z|�y�p�{ow8|~}Su�}D²�w8jmp,«-�-|�¬~�Z|�u-� �á�#¬~pou-��w8j¿ �Z|�y�p�{ow8|~}Su�}D²�w8jmp,«-�-¬�|~�Z|�u-� �á�#§%|~�Zw8j¿ �Z|�y�p�{ow8|~}Su�}D²�w8jmp,Ä�poy8w8|~{�zD¬�zJÅ?|~�

Ø`Ù�Ú�ØÇÛ

Page 22: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

����������� ������������������������! "$#%�&(')��*+�,���.-/",�+�0�$1$1��$1 �+F

��|����-y�pG���Z¾=i�y�zDum�8¬TzDw8|~}Su

ikjmpou*§¨p´nG}¹Ä�pcw8jmp´y�}?}D²Q{�pouxw�poy�}D²w8jmpc{�jm}���pou*«-�-|�¬~�Z|�u-�6|�u w8jmp´{�jm}���pouÊ�Z|�y�p�{B�w8|~}SuË}D²�z�{�poy8w�zD|�uµ�Z|~�8w�zDum{�pÃ�-u-|ϲÇ}Sy8nQ¬�³^{�jm}���pou�y�p�����p�{ow8|�Ä�po¬�³^}Su�� ��� � ��� ��� U�� � ��� ��� �� ��� � ��� ��� U�� � ��� �� }Sy�� ���� �� ��� U��� �� �� ®

qZ® �\Õ ¢�¤Z¢65 Õ 4ºcpQ�-u-|ϲÇ}Sy8nQ¬�³´{�jm}a}���p\zË«-�-|�¬~�Z|�u-��|�ucw8jmp�{o�-y8y�pouxw�{�}SuZ¶m���-y�zDw8|~}SuªzDum� zDugzDu-��¬~p�|�u� ��� � ��� � $�U�� � �� � � ®=ikjmpouµ§°p,y�}Sw�zDw�p,w8jmp±{�jm}���pouµ«-�-|�¬~�Z|�u-�\§%|�w8jµw8jmp,{�jm}���pouÀzDu-��¬~p�®

��|����-y�pG����¾=��}Sw�zDw8|~}Su

�m® G 5 �`¤Z¢65 Õ 4ºcp��-u-|ϲÂ}Sy8nQ¬�³ {�jm}?}���pËzµ«-�-|�¬~�Z|�u-�À|�u·w8jmp\{o�-y8y�pouawQ{�}SuZ¶m���-y�zDw8|~}Suªw8jmpou·§°p\{�jm}a}���p}SumpQ}D²°|�w���²Â}S�-y±p��Z��p��3zDum�´§°pnG}�Ä�pQ|�w,§%|�w8jgzË�Z|~��w�zDum{�pQ{�jm}���pougzD�xzD|�u |�u z^��|�Ä�pou|�uxw�poy8Ä�zD¬�®

Ú]Ú Þ�[]\�^0_a`

Page 23: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

��� �. � "��a ���� ",��������� &+� �a" � �$1��0��� ���$1����%1$� � � �a"a� ���� ������a"$&�� �.� � �a

E ®�� 5`£J¢ K ¤ 4 Ö6Ö Ñ ¤Z¢ K�Õ�� 4 Ñ 5 M K   Õ �]£5 4NM   � 5 �`Ö 5 4NM ¡ikj-|~�M©a|�um�3}D²?nG}¹Ä�p=|~�Á�-p��8|���ump��3w�}k¶mwMw8jmp��-y8|~}Sy]nG}a�-po¬�®]s½um�-p�p��M�SzS�Áw8jmp�umpo|���ja«�}S�-y8|�u-�«-�-|�¬~�Z|�u-���GzDy�p^{�}SnQnG}Su |�u �-y8«1zDu­zDy�p�zS�QzDum� zS��w8jmpo³gzDy�p\²�z�Ä�}S�-y�p�� «a³cw8jmp^�-y8|~}SynG}a�-po¬���|�w±|~�,�m��pB²Ç�-¬=w�}��-y�}S�P}���pQw8j-|~�,©?|�um�c}D²%nG}�Ä�p��8|�um{�pQw8jmpoy�pG|~��zË��}a}?�´{�j1zDum{�pw8j1zDw7|�w7|~�#zS{�{�po�-w�p��M® W�ump±{�zDuµy�pB²Âpoy7w�} ��� E � w�}���p�p,}Sw8jmpoy�pBÅmzDnQ�-¬~p��#}D²»�-y8|~}Sy7nG}?�-po¬¶mw8w8|�u-�GnG}�Ä�p��7²Ç}Sy%y�}�zS�µ�-pow�p�{ow8|~}SuÁ®ikjmp7«-|�y8w8jË{�}Sum�8|~�8w��¨|�u��-u-|ϲÂ}Sy8nQ¬�³G{�jm}?}��8|�u-�z±«-�-|�¬~�Z|�u-��|�u^w8jmp#{�}SuZ¶m���-y�zDw8|~}SuµzDum�\w�}zS�-��z�«-�-|�¬~�Z|�u-�G|�uµ|�w��%umpo|���ja«�}S�-y8jm}?}?�µ«x³^w8jmpòÂ}S¬�¬~}�§%|�u-�\§°z�³´¾¿ ɨjm}?}���p±z�¬~pou-��w8j ��Bo� � � � ( � � ��� ��� ®¿ ɨjm}?}���p±z�Z|~�8w�zDum{�p�^rBo� � � ^ ��� �� ®¿ ɨjm}?}���pÃwv§¨}\zDu-��¬~p�� ÀzDum� �­|�u � ��� � ��� � � U�� � ��� � � ®¿ ɨjm}?}���p � �[Bo� ��� � �� ��� U�� � �� ��� ®¿ ɨjm}?}���p�� Bo� ��� � ( � ����� �� ®¿ R=Ä�pouxw8�1zD¬�¬�³��1{�jm}a}���p ��Bo� � ��� Y � � ����� � ®

ºcp,�-pB¶mump±w8jmpÃumpo§*«-�-|�¬~�Z|�u-�ËzS�7�8jm}�§%u�|�u �]|��m®����Z¾���� � � � � � " U � �� �0� � � � � ��"0U @U �^ ��� "!$���� � �0"�U ���

� U ^ � � � �

W�ump�{�zDu�um}Sw8|~{�p¼w8j1zDw\w8jmp¼umpo|���jx«P}S�-y8|�u-� «-�-|�¬~�Z|�u-�ª�1zDy�zDnGpow�poy��ËÄ�poy8|ϲ`³ªw8jmp¼p �a�1zJ�w8|~}Sum� �¸����°§%j-|~{�j¼�-pB¶mump,w8jmp,y�po¬TzDw8|~}Su �Q®ikjmpoy�p�zJ²`w�poy�§¨p°{�zD¬�¬��±w8jmp¨zD�-�-¬�|~{�zDw8|~}SuQ§%j-|~{�jQzS����}?{o|TzDw�p��»z%umpo|���jx«P}S�-y8|�u-�,«-�-|�¬~�Z|�u-�Ãw�}zDum}Sw8jmpoy�}Sump'zDum�±��}SnGp=zD�ZÅZ|�¬�|TzDy8³Ã�-y�}S«1zD«-|�¬�|~�8w8|~{=�1zDy�zDnGpow�poy��0> � ���0$ ^)$� $ �0$ � � $ � $��� �®

� �!% ��� %� #$ > � } �����

ikjmpQ�-p�zDw8jc{�}Sum�8|~�8w��Ã|�u´y�ponG}�Ä?|�u-��z^«-�-|�¬~�Z|�u-���-u-|ϲÂ}Sy8nQ¬�³´{�jm}���pou´|�u´w8jmpQ��pow,}D²°w8jmpumpo|���jx«P}S�-y8|�u-��«-�-|�¬~�Z|�u-���#}D²»w8jmp±{o�-y8y�pouaw�{�}SuZ¶m���-y�zDw8|~}SuÁ®��� �� "$# � ���.� Q�������]�a"�� �",�T.����" ���$- �$1��/. �a� � �]�,���"$�� � �a��"a����� �Q�, ���� � � � - �a"�a� ���������(���+�Q� "

Ø`Ù�Ú�ØÇÛ

Page 24: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

����������� ������������������������! "$#%�&(')��*+�,���.-/",�+�0�$1$1��$1 �Z�

φ ψ

l2

l1

d(C1,C2)

L1

L2

C1

C2θ1

θ2

��|����-y�pG���Z¾ V¨|�y8w8j�}D²�z�umpo§*«-�-|�¬~�Z|�u-�

α

α+δα

��|����-y�pG��qZ¾��#}?}D²»zDu-��¬~p,nG}?�Z|϶1{�zDw8|~}Su

�Z® �\ÕMÕ � ¤ 4.M � Ñ Õ Ö 5 � ¥�¤Z¢65 Õ 4ºcp±zS�-��w�}Qw8jmpÃy�}?}D²�zDu-��¬~p3zQÄSzD¬��mp,{�jm}���pouµ|�u � �=^ ���� ��� U?^ ���� ��� ®

C?® S Ô ¤ ONO 5 4.M � Ñ 4.M ¢ K ¤ 4 Ö Ô 5`Ö]¢ Kikj-|~�%nG}�Ä�p,|~�k�m��pB²`�-¬M§%jmpou�z�«-�-|�¬~�Z|�u-�Gj1zS�7«�p�pou��-pow�p�{ow�p��µ«-�-w%j1zS�7z�§%y�}Su-�\}Sy8|~pouZ�w�zDw8|~}SuÁ®=ikjmp,Ä�zDy8|TzDum{�p,w�poy8n ²�z�Ä�}S�-y��7w8jmp±«�p��8w%}D²»w8jmp,w½§°}G�P}����8|�«-|�¬�|�w8|~p���®

U ® 9�� ¡ Ñ ¢ Õ�� ¤ K ¤ � � £ ÕMÕ���/j1zD¬Ï²�y�}?}D²=}D²=zQ«-�-|�¬~�Z|�u-��n�z�³µ{�}Sy8y�p�����}Sum��w�}Gw8jmp,§%y�}Su-�^j1zD¬Ï²�y�}a}D²�|�uµw8jmp3|�n�zD��p�®�m}Sy'|�um�8w�zDum{�p��a|�w'|~�'w8jmp#{�zS��p7§%jmpouËzë-�-|�¬~�Z|�u-��|~�¨zD¬~}Su-�z±�8w8y�p�pow�®»svum�-p�p��M�a}Sump�}D²Mw8jmpj1zD¬Ï²»y�}?}D²={�}Sy8y�p��8�P}Sum�-�7w�}\zQy�p�zD¬Áj1zD¬Ï²=y�}a}D²»|�u�w8jmp±|�n�zD��p±§%jmpoy�p�zS��w8jmp3}Sw8jmpoy#}Sump3|~�

Ú]Ú Þ�[]\�^0_a`

Page 25: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

��� �. � "��a ���� ",��������� &+� �a" � �$1��0��� ���$1����%1$� � � �a"a� ���� ������a"$&�� �.� � �a

��|����-y�pG�o�m¾ Xa§kzD�-�-|�u-��¬~pou-��w8jÀzDum�˧%|~�Zw8j

�-¬TzS{�p��\�-�P}SuËw8jmpÃ�8w8y�p�pow��`w8jmp�Ä�zDy8|TzDum{�p�|~�k�8n�zD¬�¬ÁzD¬�w8jm}S�-��j�w8jmpoy�pÃzDy�p�um}p��Z��p���B®���u} �P��pow7}D²=z�j1zD¬Ï²»y�}a}D²»�-¬TzS{�p��7w8jmp,«-�-|�¬~�Z|�u-��|�uµw8jmpÃy8|���jxw���}��8|�w8|~}SuÁ®

��|����-y�pG� E ¾ W �M��pow#}D²=z�j1zD¬Ï²»y�}a}D²FQADC�AD@o<���@BADY�<?@��ÀXZC´E���AGE����ADV3X�¨Y�X�R?ADVikjmpoy�p\|~�z�«-|��¼�Z|��Mpoy�poum{�p^«�powv§¨p�pouªw8jmp\«-|�y8w8j �D�-p�zDw8jªnG}�Ä�p��Q}Su }Sump�j1zDum�ªzDum�gw8jmp

nG}?�Z|϶1{�zDw8|~}Su2}D²�zDu }S«Z�¸p�{ow�}Su�w8jmp�}Sw8jmpoyËj1zDum�M® ikjmp�¶my��8w\wv³a�Pp¼}D²3nG}�Ä�p��µzD¬�¬~}¹§7�Ë�m�w�} {�}�zDy���po¬�³ �-¬TzS{�pµ��}SnGp�«-�-|�¬~�Z|�u-����§%jmpoy�p�zS��w8jmpµ��p�{�}Sum�­}Sump�y�pB¶mump��Gw8jmpµ��}��8|�w8|~}Su�zDum�w8jmp��8j1zD�Pp�}D²±w8jmp�{�}�zDy���po¬�³ª�-¬TzS{�p�� }S«Z�8p�{ow���®*svum�-p�p��M�%|�u6�-y�zS{ow8|~{�p�w8jmp���p�{�}Sum�6wv³a�Pp�}D²nG}¹Ä�p��,}Su-¬�³��-y�}S�P}���p�8n�zD¬�¬��Z|~�8�-¬TzS{�ponGpouxw��3}Sy�nG}?�Z|϶1{�zDw8|~}Sum�±}D²'w8jmp}S«Z�8p�{ow���®±ikj-|~�é?|�um�}D²�nG}�Ä�p���|~��p�����pouxw8|TzD¬Z«�p�{�zD�m��pkz��-�-y�p%�-p�zDw8j �J«-|�y8w8jG�-y�}?{�p�����|~�»|�y8y�p�zD¬�|~�8w8|~{,¾�w8jmp¨�-y�}S«1zD«-|�¬�|�wv³w�}�-y�}S�P}���p,w8jmpë-|�y8w8j�}D²�z§°po¬�¬Á�-¬TzS{�p���zDum�µ��j1zD��p���}S«Z�8p�{ow7|~�7pBÅZw8y�ponGpo¬�³Ë¬~}�§±®

Ø`Ù�Ú�ØÇÛ

Page 26: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

����������� ������������������������! "$#%�&(')��*+�,���.-/",�+�0�$1$1��$1 ��q

� ��� ����lm��� �8�V����������&����o�P��!� ���8�* �!� ���V�8����"D�� < � 2 9 ¢ K]Ñ £ Õ : Ñ ¡¢ K ¤ 4   5`£¹¢ K ¤ 4 Ö�Ö Ñ ¤Z¢ KW�ump3{�zDu˲Ç}Sy8n�zD¬�|-,�p3w8jmp���pÃnG}�Ä�p��#«x³Ëw8jmpòÂ}S¬�¬~}�§%|�u-�G§kz�³c¾

� �!% ��� %� $ > [� } ���q�

§%jmpoy�p ��|~�#z�«P}S�-um�-p��µ�8�-«m��pow7}D² ' ®»ºcp,um}Sw�p��^w8jmp � po«�p��8���mp±nGp�zS�8�-y�p±}Su�' ®��� �� "$#�� ���]� 1+��� � �� ���;� � - ���( %1 �� ���]���� %1+�;�/. ���]� ��� 1���� �" �� &%��"01a��� ���&%� "ikjmp,©�poy8umpo¬�� {�}Sy8y�p�����}Sum�Z|�u-�Gw�}Gw8jm}���p,nG}�Ä�p��#|~�%§%y8|�w8w�pou�zS�±¾

� � � $4x � W� � � XY � � \�� �� �� ��� � ����K � � � O � ��� � ��^ > � � � ��D��

�1}Sy)Vk}Sy�po¬���pow���x $�� B�1,�?¬~pow7�m�7�-pB¶mump�¾� ��x �� �� \ � W� � � \��� �� O � ��� �!����K � � � O � � � 3���^ � �� ��^ > �Â� E

V°�-w��D|�u3�-y�zS{ow8|~{�p�� � |~���-p��8|���ump�����}7w8j1zDw�} � � � #$ > �� � � ��} $��=> ÁzDum� �7|~���8³?nQnGpow8y8|~{�®ikjmpouµ²Ç}Sy � B�1,� >{B �Ã� zB��¼zDum��� � ��� �� � � #$ > �¾

.���^ � � � � $ ^ � � a � � �3���^ � � � � $ ^�� ������ ��^ � $ ^�� � 3���^�� Y � � � � � $ ^ � �� � � ��YC d � � $4� � .���^�� � � � $ ^�� � ��^ � $ ^ � � XY � � a � � � � � �� U

É°}Sum��p �x�mpouaw8¬�³���zS{�{�}Sy��Z|�u-�\w�}Qp �x�1zDw8|~}Su��Â�Z� ,¾ + � � $4� ������ Y�� X $ � K � O� K �LO"! ®D�� < � 8 S 5 O � Ñ   5`£¹¢ K ¤ 4 Ö Ö Ñ ¤Z¢ Ksvuªw8j-|~�G{�zS��p��'w8jmpµ�8|-,�p�}D²Ãw8jmp�{�}SuZ¶m���-y�zDw8|~}Su6Ä�zDy8|~p���® ºcp�j1z�Ä�p�w�}À�m��pËw8jmp$#��� � �a 1$� ��� �� � �Q�����%%�-y8|�um{o|��-¬~pG|�uaw8y�}a�Z�m{�p��·«a³cÌÃy�p�pou |�u � E � ®Ëikjmp�©�poy8umpo¬ � �-y�}S��}���p��±w�}�zS�-�gzDu}S«Z�8p�{ow��-u-|ϲÇ}Sy8nQ¬�³·{�jm}���pou |�um%Ƨ%|�w8j �-y�}S«1zD«-|�¬�|�w½³ �'&zDum� w�}¼y�ponG}¹Ä�pµzDu·po¬~ponGpouawQ§%|�w8j�-y�}S«1zD«-|�¬�|�wv³ � ( � �'&�U � ( � X B®'ikjx�m�7§°p±{�zDuµ§%y8|�w�p � � ��& �(&�U � ( � ( §%|�w8j ¾

�(& � � $4x � \ � � M � ��� � � � + ��^� + �]% ���F�

� ( � � $4x � W� � � R�� �)� zB-x� XY � � �Âq���

Ú]Ú Þ�[]\�^0_a`

Page 27: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

�D� �. � "��a ���� ",��������� &+� �a" � �$1��0��� ���$1����%1$� � � �a"a� ���� ������a"$&�� �.� � �a

ºcp±�-pB¶mump,w8jmp,�8³?nQnGpow8y8|~{,nGp�zS�8�-y�p���²Â}Sy)Vk}Sy�po¬Á��pow�� x $�� B-1 ¾

� ��x �� �� \ � \� � � M � ��� � � � � + ��^� �3���^ � �U \ � W� � � R � �)� �B �� �3���^ � �ÂqZ�

� pow=x ( �<x�f1 ( zDum��� ( G " � �4f1 ( G " w8jmpou ¾� ��x ( ��( G "' �� E GJI KhMPOY[Z \ ��� W� � M R�� �zB-x�( $ ��� �B ��( G " ]+ ( ��^ � �Âq���

� E GJI KhMPOY[Z \ � � Y R ���&� " $&%&%&% $ � ( *�B-x ( $&�&� " $&%&%&% $ � ( G " *;B � ( G " ]+ ( ��^�� �Âq�q�

� E GJI KNMPO� Y � X Z \�� � ��� \ M R����~B ��( G "&$4� � zB-x�( ]+ ( G " ��^ � ]+ ��^� �ÂqD��

��� ��� ( G " -x ( �Âq E ikj1zDw#�-y�}�Ä�p��7w8j1zDw ��|~�#�8³anQnGpow8y8|~{�®

s�²[� � � � � �zB�1,� zB{% ¨w8jmpoug¾.���^�� � � � $ ^�� � a � � �3���^ � ���& + ��^� + �]% �Âq���� ��^�� $ ^ � � 3���^ � ]+ ��^ �ÂqYC d � � $4� � .���^ � � � � $ ^ � � ��^�� $ ^�� � ��& a � � + �]% �Âq U

�#um�˧°p3zD¬~��}Qj1z�Ä�pG¾

.���^�� � ���+$ ^ � � a ��� �3���^ � �� ( XY ��� �Âq�F�� ��^��+$ ^ � � 3���^ � �`�x��d ���+$ � � .���^ � � ��� $ ^�� � ��^ � $ ^�� � � ( a ��� Y ��� �`�m�

X?}w8jmp3zS{�{�po�-w�zDum{�p±y�zDw8|~}G}D²=z�«-|�y8w8j��-pB¶mump���«x³(R ��®��Z�Ã|~�±¾

+ � � $4� ����� Y � X $ � (��& a ��� a � � + �]% Y � � *U X � �`�x��

��um�^²Â}Sy#zQ�-p�zDw8j��`nG}�Ä�p,²`y�}Sn �\w�} � B�m|�w%|~�%w8jmp±{�}Suxw8y�zDy8³�®Ø`Ù�Ú�ØÇÛ

Page 28: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

����������� ������������������������! "$#%�&(')��*+�,���.-/",�+�0�$1$1��$1 � E

D�� < � < � 5K£J¢ K ¤ 4 Ö�Ö Ñ ¤Z¢ K6Õ � 4 Ñ 5 M K   Õ ��£5 4.M   �N5 �`Ö 5 4NM ¡ikjmp�©�poy8umpo¬ �Æ�-y�}S��}���p��3w�}�zS�-�·z�umpo|���ja«�}S�-y8|�u-�¼«-�-|�¬~�Z|�u-��§%|�w8jg�-y�}S«1zD«-|�¬�|�w½³ �'&3zDum� w�}y�ponG}¹Ä�p�}SumpË}D²#w8jmp^«-�-|�¬~�Z|�u-���Qj1z�Ä?|�u-�cz�umpo|���ja«�}S�-yQ|�u w8jmpË{o�-y8y�pouxwG{�}SuZ¶m���-y�zDw8|~}Su6§%|�w8j�-y�}S«1zD«-|�¬�|�wv³ � ( ®»ºcp,j1z�Ä�p3zD�xzD|�u � � ��&�� &�U � ( � ( §%|�w8jg¾

�(& � � $4x � W� � � XY � � \�� �� �� ����� K�� � � O � � � + ��^ > + � � �`�xq�

� ( � � $4x � W� ��� K��LO R � �)� zB-x XY } � � �`����

� pow=x $�� «PpÃw½§°} Vk}Sy�po¬���pow��7|�u�1 ¾� ��x �� � \ � \� � � M � � � � K�� � O � ��� � � � � + ��^� �3���^�� $U \ � W

� ��� K �LO R � � � B �� �3���^ � �`� E ºcp±�-pB¶mump;x�(^zDum� ��( G "7zS�7§¨p±�Z|~���-y�poÄ?|~}S�m�8¬�³Ë��}w8j1zDw3¾� ��x�( ��( G " � E GJILKNMPOY[Z \ ��� W

� ��� K��LO R�� �zB-x�( $ � � �B�� ( G " ]+ ( ��^ � �`�x��

� E GJILKNMPOY[Z \ � � W� � � R�� �zB-x�( $ � � zB�� ( G "&$ �B � � � ]+ ( ��^ � �`� C

� E GJILKNMPOY[Z \ � � Y R ���&� "!$&%&%&%#$ � ( *;B-x�( $&�&�#" $&%&%&%#$ � ( G "!*&B ��( G "' R � � ( B y ���&� " $&%&%&%#$ � ( G " * ]+ ( ��^�� �`� U

� E GJI KNMPO� Y � X Z \ � � ��� \ M R ���~B�� ( G "&$ zB

y��� $4�(� �B-x�( ]+ ( G " ��^�� ]+ ��^

�`�QF�� � ����( G " -x�( � E ��

���xzD|�u�w8jmp,nGp�zS�8�-y�p ��|~�#�8³anQnGpow8y8|~{�®� pow0�zBz1,� �B���� >,B �Ã�!} � � #$ > %zDum�f� � � ��}1®

.���^ � � � � $ ^�� � a � � �3���^�� ���& XY � � + ��^�} + � � ����

� �� � ���

� E �

� ��^ � $ ^�� � 3���^�� ]+ ��^�} � E ��d � � $4� � .���^�� � � � $ ^�� � ��^ � $ ^�� � �'& a � � + � � ���

� �� � ���

� E q�

Ú]Ú Þ�[]\�^0_a`

Page 29: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

��� �. � "��a ���� ",��������� &+� �a" � �$1��0��� ���$1����%1$� � � �a"a� ���� ������a"$&�� �.� � �a

��� �� "$# � ��� ��1 � � -]�"�� � � �(/�Y�����0������ �� � � #$�� =� � � % ��1 P�a� *+�,����� ��1�� ���� "a����� ���]� ����� � ����� �$1 �� &L��� &+�� � ���]� *� Q���Q�a� ���a" ��"�� 1�- �,��� ��� � � ���]� ������ � "a� -] ", �� �����a"$11+��� � /� ���]���Q�,��� ����"a� � -] ", �� �����a"$1�1������� &%� ���]��1� �� � �� � �a 1a��� "�� �� ��)� 1 �Q� ��0 !1 - �, # �/.�#��� � �a 1a��� �� �� �'�Q�� ��% "

Xa|�nQ|�¬TzDy8¬�³��m§¨p±j1z�Ä�pG¾.���^�� � ���+$ ^ � � a ��� �3���^�� �� � XY } ��� � E ��� ��^��+$ ^ � � 3���^�� � E�E d ��� $ � � .���^�� � ���+$ ^ � � ��^��+$ ^ � � ��� a ��� Y } ��� � E ��

¯�poum{�p,w8jmp±zS{�{�po�-w�zDw8|~}Su�y�zDw�p±�-pB¶mump��µ«a³ R���®1�Z�,}D²=z�umpo|���jx«P}S�-y8|�u-�^«-|�y8w8jµ|~�±¾

+ � � $4� ������ Y � X $ � �� ( a ��� a � � + � � Y � � Y } � � *U X ����

� �� > �

���� � E C

��um�^²Â}Sy#zQ�-p�zDw8j��`nG}�Ä�p,²`y�}Sn �\w�} � B�m|�w%|~�%w8jmp±{�}Suxw8y�zDy8³�® � Ñ ¥�¢65 : Ñ ¥ Õ O ��¢�¤Z¢65 Õ 4 Õ�� ¢ K]Ñ >�¤-¥ Õ   5`¤ 4

���0� � "0U � � " U �� U ^ �� ��� ��� "�U ��� � �

� � #"0U � � "�U �� U�^ � ����� ����"0U � �0� � "0U � �

� � � � � �0� � � � � ��"0U TU �

����

� �� > �

���

��������������

"� ��� ��� "0U "

� ����� ����"0U � X � � � ��� ��� "�U ����� ����"�U � � � � ������ ��� �� U�^�� ����� ��� "�U ��� ��� �� U�^�� ��� ��� "0U � � � X �� � � � � X �� � � � X � �� � � � � � X� � X � � � �

��������������

� ����

��� ��� "�U ����� ����"�U � � � ��� �� U�^ � ����� ��� "�U � � ��� �� U�^ � ��� ��� "0U ����

� � � " U �� U�^ � � ^ ��� � $�� ��}

§%jmpoy�p � � ¨zDum� � ��} °zDy�p,w8jmp±�B {�pouxw�poy���}D²�w8jmp3}S«Z�¸p�{ow��0 ¼zDum�-}1®Ø`Ù�Ú�ØÇÛ

Page 30: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

����������� ������������������������! "$#%�&(')��*+�,���.-/",�+�0�$1$1��$1 �YC

��|����-y�p����Z¾�i�§¨},{�}SuZ¶m���-y�zDw8|~}Sum��}S«-w�zD|�ump��§%|�w8j 3 � � � �8�8� X �`¬~pB²Çw]j1zDum�-��|~�-p �zDum� 3 � � � � X�`y8|���jaw7j1zDum�-�8|~�-p

� � � �Hlm�����8�8�P������#lm�*��t � �� � �j� � �s�!��lm��� �8�J������ ����� � � �P��!� � �8�P��!�� �J�����svw±|~��p�����pouxw8|TzD¬°w�}µum}Sw8|~{�p�w8j1zDw3w8jmp^{�}SnQ�-�-w�zDw8|~}Su·}D²7w8jmp�um}Sy8n�zD¬�|~��zDw8|~}Su {�}Sum�8w�zDuxw}D²%w8jmp�-poum��|�w½³�a�|~�Áum}Sw�ump�{�p�����zDy8³,w�}�zS{�j-|~poÄ�p¨w8jmp¨{�}SnQ�-�-w�zDw8|~}SuQ}D²mw8jmp°zS{�{�po�-w�zDum{�p¨y�zDw8|~}-®�svum�-p�p��M�§°p#{�zDu\Ä�poy8|ϲ`³Qw8jmp�pBÅ?�-y�p�����|~}Su\}D²Mw8jmp�zS{�{�po�-w�zDum{�p�y�zDw8|~}3}Su-¬�³Q|�uaÄ�}S¬�Ä�p��°y�zDw8|~}��¨�8�m{�j^zS� � K � O� K��LO ®È�}Sy�p�}¹Ä�poy���zS{�{�}Sy��Z|�u-�·w�} � F�B�kw8jmpÀzS{�{�po�-w�zDum{�p¼y�zDw8|~}g}Su-¬�³­�-po�Ppoum�-�Ë}Su6w8jmpÀzS�-�-p��M�y�ponG}¹Ä�p�� }Sy�nG}?�Z|϶1p��g}S«Z�8p�{owQzDum�g}Sugw8jmp\}S«Z�8p�{ow���|�u y�po¬TzDw8|~}Su §%|�w8jg|�wQzDum�gum}Sw�}Sugw8jmp§%jm}S¬~p�{�}SuZ¶m���-y�zDw8|~}SuÁ®=ikjx�m�¨w8jmp#{�}SnQ�-�-w�zDw8|~}SuË}D²Mw8jmp7y�zDw8|~} � K � O� K��LO |~�'�8|�nQ�-¬~p�zDum� �a�-|�w�pk²�zS�8w�®

� � ��0����8��0

� ��� � ��l � n��V������ ���?� � � � � ����� lm����#n��|�y��8w%§°p±}Su-¬�³Ë�8|�n3�-¬TzDw�p3w8jmp,�-y8|~}Sy7nG}?�-po¬M§%|�w8jm}S�-w#w8jmp±�mzDw�znG}?�-po¬ �Ç��p�p���|��m®M����B®

Ú]Ú Þ�[]\�^0_a`

Page 31: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

� U �. � "��a ���� ",��������� &+� �a" � �$1��0��� ���$1����%1$� � � �a"a� ���� ������a"$&�� �.� � �a

� pB²Çw±¾=�8³?uxw8jmpow8|~{,|�n�zD��p �7|���jaw3¾»y�p��8�-¬�w7}D²»w8jmp±�-pow�p�{ow8|~}Su��|����-y�pG�6C?¾ BÃpow�p�{ow8|�u-�G«-�-|�¬~�Z|�u-��|�u��8³auaw8jmpow8|~{,|�n�zD��p��

� �hg ���J�8�����$���� ���8� � lZ � 8 � 2 S Ò 4 ¢ K]Ñ ¢65`¥P5 ¤ M Ñ ¡ikjmpouÁ��§°p�§°}Sy8©c}Su·�8³?uxw8jmpow8|~{\�mzDw�z��Ç��p�p���|��m®'�6C B®µikj-|~��|�n�zD��pGj1zS��«Pp�poug}S«-w�zD|�ump��g«x³z��8|�n��-¬TzDw8|~}Su6}D²#w8jmp^�-y8|~}SyQnG}a�-po¬�®cºcpËzS�-�ªzÀÌ,zD�m���8|TzDu um}S|~��p^w�}¼w8jmp^y�}a}¹Ä�p��GzDum�·w8jmp��y�}S�-um�µ|~�%y�po�-y�p���pouxw�p���«x³µz��-u-|ϲÂ}Sy8nÆum}S|~��p±}Su�w8jmp,��y�z�³Ë¬~poÄ�po¬~��®

Z � 8 � 8 �\Ñ ¤ � 5 ¤ M Ñ ¡ikjmp�zSpoy8|TzD¬k�-jm}Sw�}���§¨poy�pË�-y�}¹Äa|~�-p�� «a³cw8jmp vs½um�8w8|�w8�-wGÌÃ��}S��y�zD�-j-|��a�mp ��zDw8|~}Su1zD¬ � � �-y�poum{�jÈÀzD�-�-|�u-�µsvum�8w8|�w8�-w�p ÃzDum�¼§¨poy�pG}S«-w�zD|�ump��À«a³Àz^�Z|���|�w�zD¬={�zDnGpoy�zµzDw±z^y�p���}S¬��-w8|~}Suc}D²%�Z®í�Dnµ®ikjmpÄ?|~po§%�P}S|�uxw±�1zDy�zDnGpow�poy���zDy�pQ��|�Ä�pouc§%|�w8jcp�zS{�j |�n�zD��p�®QikjmpQy�p��8�-¬�w±}D²��]|����-y�p�� U j1zS�«Pp�pouµ}S«-w�zD|�ump��µ§%|�w8j¼z�8w�poy�p�}���{�}S�-|~{±{�}S�-�-¬~p �`|�®áp�®�}Su-¬�³^wv§¨}�|�n�zD��p���B®

��� % "��701.\���Á��0��� ��� �r� �����zlm� �#nW�«aÄa|~}S�m��¬�³´w8jmpQ��p�}SnGpow8y8|~{�zD¬¨nG}?�-po¬¨�-}?p��±um}Sw3¶mw�zDux³´©?|�um�c}D²%«-�-|�¬~�Z|�u-�´zDum�c|�w±n��m�8w3«Ppy�pB¶mump�� ® �m}Sy^|�um�8w�zDum{�p��#}SumpÀ{�}S�-¬~���-pB¶mump¼��poÄ�poy�zD¬�wv³a�Pp��^}D²3«-�-|�¬~�Z|�u-���˧%|�w8j��Z|��Mpoy�pouxw

Ø`Ù�Ú�ØÇÛ

Page 32: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

����������� ������������������������! "$#%�&(')��*+�,���.-/",�+�0�$1$1��$1 ��F

��|����-y�p\� U ¾¨��p�zD¬�|�n�zD��p���¾¨}S«-w�zD|�ump��¼{�}SuZ¶m���-y�zDw8|~}Su��-y�}D�8p�{ow�p��¼}Su�w8jmp±¬~pB²Çw�zDum��w8jmp±y8|���jaw|�n�zD��p��

��p�}SnGpow8y8|~{�zD¬?nG}?�-po¬~�]zDum��zS�-��zknG}�Ä�p¨§%j-|~{�j�§¨}S�-¬~��zD¬�¬~}�§·w�}7�8§%|�w�{�j�«Ppow½§°p�pou�w8jmp=�Z|��Mpoy�pouxwnG}?�-po¬~� �ÂzDu�pBÅmzDnQ�-¬~p±}D²»w8j-|~�%©?|�um��|~�%�8jm}�§%u�|�u����o� � B®

�-�-y8w8jmpoy8nG}Sy�p��Sw8jmp=�-y8|~}Sy]nG}a�-po¬a|�uxÄ�}S¬�Ä�p��»}Su-¬�³Ã�1zD|�y8§%|~��p=|�uaw�poy�zS{ow8|~}Su�«-�-w�}Sump'{�}S�-¬~��zD¬~��}�m��p,�8|�u-��¬~po§%|~��pÃ�P}Sw�pouxw8|TzD¬�w�}�²�z�Ä�}S�-y#��|�Ä�pou��8j1zD�Pp��%}Sy��m}Su�w8jmp,{�}Suxw8y�zDy8³��1«-|�����poy#{o¬�|��x�mp��#w�}n�zDu1zD��p±¬~}Su-�\zD¬�|���u-nGpouxw���®��� �hg �,�V�$�mlm����#nikjmpoy�p±y�pon�zD|�u�z¬~}Sw7}D²»w8j-|�u-���7w�}Q�-}-® �m}Sy#|�um�8w�zDum{�pG¾

¿ }Sump,{�zDuµw�zD©�p,w8jmp±}?{�{o¬��m�8|~}Sum�%|�uaw�}\zS{�{�}S�-uxw��¿ }Sump,{�zDuµ�m��p±z¬�|���jaw7nG}a�-po¬�®��� ��� �[��l ��n��V������

ikjmp��-y�}S�P}���p���zD¬���}Sy8|�w8j-n�|~��y�zDw8jmpoyÃ��¬~}�§±®#ikjmpoy�pB²Â}Sy�p�|�w�|~��ump�{�p�����zDy8³�w�}�¶mum����}SnGp�§°z�³?�w�}GzS{�{�po¬~poy�zDw�p3w8jmp±{�}SuxÄ�poy8��poum{�p�®

ikjmp�¶my��8wk|~�-p�z�{�}S�-¬~�Ë«Pp�w�}��-y�}S��}���pÃnG}Sy�p�y�po¬~poÄ�zDuxw7nG}¹Ä�p���®=svum�-p�p��M�-}SumpÃ{�}S�-¬~�Ë���-|~�-pw8jmpc�-y�}S��}��8|�w8|~}Sum��w8j1zDu-©?�µw�}ªw8jmp´|�n�zD��p�® �1}Syµ|�um�8w�zDum{�p��Ã|�wµ|~��nG}Sy�p p �{o|~pouxw�w�}­�-y�}D��P}���p�«-�-|�¬~�Z|�u-���˧%j-|~{�j*zDy�p¼zD¬�y�p�zS�Z³6¬~}a{�zDw�p���}Su�p��Z��p��¹®/����§°p�j1z�Ä�p¼�-y�}S��}���p�� nG}�Ä�p��

Ú]Ú Þ�[]\�^0_a`

Page 33: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

q�� �. � "��a ���� ",��������� &+� �a" � �$1��0��� ���$1����%1$� � � �a"a� ���� ������a"$&�� �.� � �a

}D²7«-|�y8w8j �D�-p�zDw8j |�u z�umpo|���jx«P}S�-y8jm}?}a� }D²#zµ«-�-|�¬~�Z|�u-�¼w�}�¶mw�w8jmpG�-y8|~}Sy�nG}?�-po¬��]§°p\��jm}S�-¬~�zD¬~��}�-y�}S��}���p±nG}�Ä�p��7§%j-|~{�j�¶mw7w8jmp±�mzDw�zZ®

ºcpQ{�}S�-¬~� zD¬~��}^�m��pw8jmpQ�8|�n��-¬TzDw8|~}Su w�}�p��8w8|�n�zDw�pQ��}SnGp�1zDy�zDnGpow�poy��¹®Qs½um�-p�p��M��|�u´w8j-|~�§°}Sy8©��7zD¬�¬�w8jmpµ�1zDy�zDnGpow�poy�� �Çp��8�Pp�{o|TzD¬�¬�³ªw8jm}���p��-pB¶mu-|�u-�gw8jmpµ�P}Sw�pouxw8|TzD¬~��G§¨poy�p�²Ç}S�-um�­«x³w8y8|TzD¬ÃzDum�6poy8y�}Sy�®*ikjmp�p��8w8|�n�zDw8|~}Su {�}S�-¬~��zD¬�¬~}¹§ �m�\w�}´¶mum�6w8jmp�}S�-w8|�n�zD¬�ÄSzD¬��mp��^}D²,w8jmp�1zDy�zDnGpow�poy��nG}Sy�pËp �{o|~pouaw8¬�³�® W�ump^{�zDu·y�pB²Âpoy�w�} � � � �-���+F � ²Ç}Sy�nG}Sy�p^|�uZ²Ç}Sy8n�zDw8|~}Suª}Su·w8jmp���-«Z�¸p�{ow7}D²»�1zDy�zDnGpow�poy�p��8w8|�n�zDw8|~}SuÁ®

�#um}Sw8jmpoy°��}����8|�«-¬~p7|�nQ�-y�}¹Ä�ponGpouxw7{�}S�-¬~�\«�p#w8jmp7�m��p�}D²MnG}Sy�p���}S�-j-|~��w8|~{�zDw�p��\w�p�{�j-u-|��x�mp�����m{�j�zS�'w8jmp�}Sump#�-y�p���pouaw�p��^|�u �í��� � � �í�Z� � �x§%jmpoy�p�w8jmp#y�pÍ�8p�{ow8|~}SuË}D²Áw8jmp#�-y�}S�P}��8|�w8|~}Sum�°{�zDu\«Pp�-po¬Tz�³�p��M®

� ������"��=3����0

��� � B�®Xaw�}�³xzDuÁ��º ®%X�®��,poum�mzD¬�¬����m®Dȼp�{�©�p�� Xaw�}?{�j1zS�8w8|~{7ÌÃp�}SnGpow8y8³�zDum��|�w����#�-�-¬�|~{�zDw8|~}Sum�������}Sj-uµº�|�¬�¬~po³ËzDum� X?}Sum�¹�M�+F U C?®

�í� � B�® X�®ÉkzDy8w�poy��Ë�]®áÈ·®��=y�pouxw�poy�� R»ÅZ��}Sumpouaw8|TzD¬Ë���1zS{�p��·zDum� {�}S�-uxw8|�u-� �-y�}?{�p�����p������ � "� � " "N&%��"� !" �)�6� "1�Z�����B���+FZ���+FYCS�Z®

�íq � É�®��m®¨ÌÃpo³�poy��°�m®=ȼ}S¬�¬~poy�� Xa|�n��-¬TzDw8|~}Su zDum� ¬�|�©�po¬�|�jm}?}?�ª|�uZ²Çpoy�poum{�p�²Ç}SyG�8�1zDw8|TzD¬#��}S|�uaw�-y�}a{�p���� ����� �� /����/ �&+�� � ��� "a/ � �/.��/� �����1a��� �a1 ��� ��"$� �$1 �#�1�Z���mq E FJ�vqYCSqZ���+F�FD�m®

� � � É�®Q�m®\ÌÃpo³�poy��� � |�©�po¬�|�jm}a}?� svuZ²Âpoy�poum{�p ²Ç}Sy Xa�1zDw8|TzD¬¼�]}S|�uaw ��y�}?{�p�����p�� ��®Qs½u W�®�R#®VkzDy8um�-} ��� ��|~po¬~��pouÁ�ZºÊ® X�®�,poum�mzD¬�¬�zDum��Èg® ��®-È Ä�zDu � |~p��8jm}S�-w��mp��Z|�w�}Sy������ � �+�'�� %1�������)�,��� ����"a� ��� � #��a� � ���+�6� /�� ��� -/��� Y�������1ɨj1zD�-n�zDu-u¼zDum��¯ÃzD¬�¬�� � }Sum�-}SuÁ���+F�F U ®

� E � �]®]ÌÃy�p�pouÁ� v�#poÄ�poy���|�«-¬~pQ���-nQ�gÈ´É°ÈÀÉ É°}SnQ�-�-w�zDw8|~}Su zDum��V%z�³�p��8|TzDugÈ�}?�-po¬ BÃpow�poy¸�nQ|�u1zDw8|~}Su���� ������� ����"a��#% U �Z�/C?���B� CSq��Z�]�+F�F E ®

�í� � �]®kÌ�y�p�pouÁ� vÈÀÉ°È´ÉÆ|�u6|�n�zD��pÀzDu1zD¬�³?�8|~� ��®'svu6º ®'�3®°Ì�|�¬�©?�¹� X�®¨�7|~{�j1zDy��-��}Su zDum� B®�m®.Xa�-|~po��po¬�j1zD¬�w�poy���p��Z|�w�}Sy���� �! "$#%�&� �� �� �!�/��� "a� � ���� ", Y����� �0�o�]�-�Á®Pq U �B�vq�F�FZ�ɨj1zD�-n�zDu�zDum�µ¯ÃzD¬�¬�� � }Sum�-}SuÁ�Á�+F�F��Z®

� C � � ®¹ik|~poy8umpo³�� vÈÀzDy8©�}�Ä�ɨj1zD|�um��²Ç}Sy R»ÅZ�-¬~}Sy8|�u-����}��8w�poy8|~}Sy B�|~��w8y8|�«-�-w8|~}Sum����� �/���'� " ����-]�"�� "� �#"��������#u-|�Ä�poy���|�w½³�}D²»È�|�u-ump���}Sw�zZ�mÈÀzDy�{�jg� E �Á�+F�FD�m®

� U � É�®m�#}S«Ppoy8w�zDum��Ì®�ÉkzS��po¬�¬TzZ�� vȼ}Suxw�pÉkzDy8¬~} Xaw�zDw8|~�8w8|~{�zD¬�È�pow8jm}?�-�����/Xa�-y8|�u-��poy¸� � poy8¬TzD�m���po§ �'}Sy8©P�Á�+F�F�FZ®

� F � É�®��#}S«Ppoy8w��� vȼ�ow8jm}a�-p��¨�-p7È�}Suaw�p�ÉkzDy8¬~}3�1zDy°É¨j1z��~ump��'�-p�ȼzDy8©�}¹Ä ��� R=�M®QR={�}Sum}SnQ|~{�zZ��+F�F��Z®

Ø`Ù�Ú�ØÇÛ

Page 34: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

����������� ������������������������! "$#%�&(')��*+�,���.-/",�+�0�$1$1��$1 qZ�

����� � V�®/B®1�7|��-¬~po³��) vȼ}a�-po¬�¬�|�u-� Xa�1zDw8|TzD¬»�»zDw8w�poy8um����� ��� "a/ � �/.���� ��� ��Y � � � ���� 1������0 ���$��1a����������� ��� �a"$� �$1 ��q�FZ�-�-�Á®M�6CS�J�v�Z���Z���+F�FYC?®

����� � V�® B�®1�7|��-¬~po³�� �k®m��® �,po¬�¬�³�� vȼzDy8©�}¹Äµ�]}S|�uaw���y�}?{�p�����p�� ��� " �.�/�Y�� � ���� " � �6� "~��� E �� U�U ���+F��Z�Á�+FYC�C

����� � ��®=�1® V%zS�-�-po¬~po³��7È·® ��®'Èg®'ÄSzDu � |~p��8jm}S�-w�� v�#p�{�}S��u-|�w8|~}Su�}D²3}�Ä�poy8¬TzD�-�-|�u-�ª}S«Z�8p�{ow���m�8|�u-�GȼzDy8©�}¹Ä��8�1zDw8|TzD¬Á�-y�}?{�p�����p������ ������)��-]�"�� � ������� �����Á�+F�FZ��®

����q � � ®kik|~poy8umpo³��¸�+F�FD��B�0 v� um}Sw�pÀ}Su ȼpow8y�}S�P}S¬�|~��¯�zS�8w8|�u-���^©�poy8umpo¬~�^²Â}SyË��poumpoy�zD¬±�8w�zDw�p�8�1zS{�p������ � �,�'� " �)��- " � ��� ��� �'���6��N�/.��/� Y��� 1������a1 � � " �/. � �� �$1���� "~�P�+F�F E ®

���o� � ¯�®��#�mp��JÈ·®á��®¹¯��-y8uÁ�& V%z�³�p���|TzDu�}S«Z�8p�{ow�|~�-pouaw8|϶1{�zDw8|~}Su���� � � ��� ����"a� # U �Z�J�-�Á®J�D�QFJ�v�����Z��+F�F�FZ®

��� E � �3® Xaw�}S|~{�zZ���® B�p���{�}Sn3«Pp������m®���poy8�-«-|TzZ�� v�ÆÈÀzDy8©�}�Ä ��}S|�uxwG��y�}?{�p����3²Ç}Sy�#}�zS� R»Å?�w8y�zS{ow8|~}Suµ|�u��#ponG}Sw�p X?poum��p��µs½n�zD��p�� ����� � ����� ���$1+�, ",�'�P"���-]�"�� ��}Gq�F���qZ�1�������Z®

����� � Èg®�svn3«Ppoy8w½³����®+BÃp���{�}Sn3«Pp����! Xa|�n3�-¬TzDw8|~}Su�-p��-y�}a{�p����8�m�Á}S«Z�8pow��'¾ R�w8�m�-p¨�-p»²ÂzD|~�WzD«-|�¬�|�w����}S�-yQ�-ump�zD�-�-¬�|~{�zDw8|~}Su �¼¬Tz´��po��nGpouaw�zDw8|~}Su ��� |�n�zD��p ����� � ����� ���$1+�, ",�'� "���-]�"�� ��}q U�U ���1�������Z®

���6C � �3®Áº z�zD��po�Ppow�poy���pouÁ� ¸É°}Suaw8y8|�«-�-w8|~}Sum�Qw�}�w8jmp Xaw�zDw8|~�8w8|~{�zD¬kÈ�}?�-po¬�¬�|�u-�À}D²#s½n�zD��p B,zDw�zzDum�PXa�1zDw8|TzD¬]��}S|�uxw��»zDw8w�poy8um����� �!�� � �]�a1$��1 �N� � � � �. ��&%�a"$1$����� �/.��) "��Q�Q1o�Á�+F�FYC?®

��� U � W�® �1zD�-��poy�zS��� X�® � z�Ä�p�zD�Á� � ®M�#}S«Ppoy8w��]Ì®�É°���-y8©SzZ�»É�®���po¬�¬~poy�� ÍqJ��B �#p�{�}Sum��w8y8�m{ow8|~}Su}D² �#y8«1zDu�X?{�poump���²Çy�}Sn X?p �a�mpoum{�p��,}D²¨svn�zD��p�������|�u´�#�-w�}Sn�zDw8|~{�R»ÅZw8y�zS{ow8|~}Su´}D²¨ÈÀzDuZ�ȼzS�-p;W�«Z�¸p�{ow��7²`y�}Sn �%poy8|TzD¬»zDum� Xa�1zS{�p3svn�zD��p����/R'�Z|�w�p���«a³Ë��®�ÌÃy8�mpouÁ� W�® �Ã�mpo«-¬~poyzDum���]®��#��}S�-y8|~��� V°|�y8©?j��D�m��poy��Á�+F�F E

���+F � É�®?�1®1ÌÃpo³�poy�� R7®-��®-ikjm}SnQ�m��}SuÁ� ¸É°}Sum�8w8y�zD|�ump��µÈ¼}Suxw�p3ÉkzDy8¬~}QÈÀzJÅZ|�n3�-n � |�©�po¬�|�jm}?}?�²Ç}Sy BÃpo�Ppoum�-pouxw BÃzDw�z ��� ��� "a/ � �/.)���]��� ���� ���/� �����1a��� �� ���$ 1a����������� � � �a"a� �a1 � E �m����}-®qZ�Z�-�Á®í� E C¹�v��F�FZ���+F�F��Z®

�í��� � �]®��m®QÌ�y�p�pouÁ�Ë��®�È�|�y�zZ� BÃpo¬Tz�³�p�� �#pÍ�8p�{ow8|~}Su |�u ��poÄ�poy��8|�«-¬~p ���-nQ� ȼpow8y�}S��}S¬�|~�8�¯�zS�8w8|�u-��� ��� �! Y���]� �� ���� �a1��)�$1��, �" �'����� -]�"���uÁ® Xx�v�Z�B� F�FZ���u-|�Ä�poy��8|�w½³^}D²NV°y8|~�8w�}S¬��P�+F�F�FZ®

�í�Z� � � ®Pik|~poy8umpo³��M��®�È�|�y�zZ�+ X?}SnGpQzS�mzD�-w8|�Ä�pQȼ}Suxw�pGÉkzDy8¬~}ËnGpow8jm}?�-�#²Â}Sy V%z�³�p��8|TzDuÀ|�uZ²Âpoy¸�poum{�p ��� �/� �����1a��� �a1 �� � �,�� ���� �,� U �m�-�Á®m� E �YC¹�v� E � E ���+F�F�FZ®

Ú]Ú Þ�[]\�^0_a`

Page 35: Building Detection by Markov Object processes and a MCMC … · 2017. 1. 29. · ISSN 0249-6399 ISRN INRIA/RR--4206--FR+ENG apport de recherche THÈME 3 INSTITUT NATIONAL DE RECHERCHE

Unité de recherche INRIA Sophia Antipolis2004, route des Lucioles - B.P. 93 - 06902 Sophia Antipolis Cedex (France)

Unité de recherche INRIA Lorraine : Technopôle de Nancy-Brabois - Campus scientifique615, rue du Jardin Botanique - B.P. 101 - 54602 Villers lès Nancy Cedex (France)

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France)Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38330 Montbonnot St Martin (France)

Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt - B.P. 105 - 78153 Le Chesnay Cedex (France)

ÉditeurINRIA - Domaine de Voluceau - Rocquencourt, B.P. 105 - 78153 Le Chesnay Cedex (France)��������� ���� ���������� ��� ���

ISSN 0249-6399