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A Polyline Process for Unsupervised Line Network Extraction in Remote Sensing

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(1)A Polyline Process for Unsupervised Line Network Extraction in Remote Sensing Caroline Lacoste, Xavier Descombes, Josiane Zerubia. To cite this version: Caroline Lacoste, Xavier Descombes, Josiane Zerubia. A Polyline Process for Unsupervised Line Network Extraction in Remote Sensing. [Research Report] RR-5698, INRIA. 2006, pp.26. �inria00070317�. HAL Id: inria-00070317 https://hal.inria.fr/inria-00070317 Submitted on 19 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published 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 destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. A Polyline Process for Unsupervised Line Network Extraction in Remote Sensing Caroline Lacoste — Xavier Descombes — Josiane Zerubia. N° 5698 September 2005. N 0249-6399. ISRN INRIA/RR--5698--FR+ENG. Thème COG. apport de recherche.

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(61) c9zNh­Xuwƒˆ}yumuwdfh·©‰~‰|fh|fhu ¦z}ƒ‡°Â€ªƒ‡z}g,ˆ}|)~gˆŽ{Ph}²¾¦h·ˆŽ~‰gu‡zÂNJ|Š)ˆNyzP|tNJ{P«fƒ‡ˆŽuw~‰z}|"zŽ€#˜zP©rX©‰~|fhSs¦df~¥yd"gˆŽ­X~‰g~ÃEhEsmu‡dfh «f|Š|fz}ƒ‡gˆŽ©‰~ÃEhE fƒwzty hEs‡sfh |Šsw~Æu r h {}~‰¬}hE| —Xr . ± ™}›P´ h(C) ∝ h (C) h (C) ¦dfhEƒwh ˆŽ|Š ˆ}ƒwhxƒ‡hEsw˜hSy®uw~‰¬}hE©rÂ{P~¬Ph |_—XrNh P«˜ˆuw~‰z}| ± 7}´šˆ}|Š¹h Y«Šˆu‡~zP| ± 4S•P´³jc#df~¥s¨~‰sˆ |fz}|)yzP|X¬}h­Nfƒ‡z}—Š©hEg €ªz}ƒ ¦df~¥yd)hˆf~ƒ‡hEyumhzPtuw~‰g~ÃSˆu‡~zP|_~¥sm|fzŽu/zPs‡sv~‰—f©‰hx{P~¬Ph |_uwdfh©¥ˆŽƒ‡{}hsv~‰Ã hzŽ€¯uwdfhsvu‡ˆŽuwhsv˜ˆ}yhjuwd˜ˆu~‰s ∪ Ω ¦dfhEƒwh Ω ~¥su‡dfh[swhuzŽ€=y z}|tNJ{P«fƒˆuw~‰z}|˜sšz}€ N /z}©‰rX©~‰|fhSs ³È"hŠƒwzP˜zYsvhu‡zNhEsvuw~‰gˆŽuwhu‡df~¥sgˆ­t~gj«fg —YrÁˆNsv~‰g7«Š©‰ˆŽuwhE)ˆ}|f|fhEˆ}©~‰|f{ s‡ydfh ghP²¾¦df~¥yd)y z}|Šsw~¥s usšz}€#sw«ŠyEyhEs‡sw~¬Phxsw~gj«f©¥ˆuw~‰z}|˜sšz}€¯u‡dfhfƒ‡zXy hEs‡st~¥s u‡ƒw~‰—f«tu‡~zP| sv/hEy ~ÆNJhSÁ—Yr¹uwdfh·thE|Šsw~Æu r ² ¦~uwd T {}ƒˆ}t«˜ˆŽ©‰©r·tƒ‡z}Šf~|Š{ju‡z 0 ³8†‘fƒ‡zXzŽ€9z}€y z}|X¬}hEƒw{Ph |Šy hŒ~¥s{}~‰¬}hE| ~‰|,µ™Ž”¦dŠh |πuwdfhfhEyƒ‡hEˆPsvh¨zŽ€%uwhEg˜hEƒ‡ˆŽuw«fƒ‡h hT ~¥s ©‰z}{YˆŽƒ‡~Æu‡dfg~‰y}³%» |fƒˆ}yuw~¥yhP²Xuwh g/h ƒˆu‡«fƒwhthSyƒ‡hEˆPsvhSs^{Ph z}gh uwƒ‡~‰yEˆŽ©‰©r~‰|Âz}ƒth ƒuwzƒ‡hEf«Šyh¨uwdŠhyz}gf«fu‡ˆu‡~zP|[u‡~ghP³ ) 9          ,       DC c#dfhˆŽ©‰{}zPƒw~uwdfg ydfzPswh |Áu‡z_sv~‰g7«Š©‰ˆŽuwhu‡dfh·«f|f|Šz}ƒ‡gˆ}©~‰Ã hSÁgxhSˆ}sw«fƒ‡h π ~¥sxˆN‹h ¬Ph ƒsv~‰—f©‰h·Ä}«fgUÅ_ˆŽƒ‡°}z¬Ái¯dŠˆ}~| Źz}|Yuwh iˆ}ƒw©‰z ± ‹=ÄYÅ"iÅ"i#´8ˆŽ©‰{}z}ƒ‡~uwdfg  4E›f²C44)I³» u¯y z}|Šsw~‰svu‡sz}€¾sv~‰g7«f©¥ˆu‡~|Š{ˆt~‰s‡yƒ‡hu‡h=ŹˆŽƒ‡°}z¬ji¯d˜ˆŽ~‰|zŽ€Ô~|X¬ˆŽƒ‡~¥ˆŽ|YuÉgxhSˆ}sw«fƒ‡h ¦df~¥yd7/h ƒw€ªz}ƒ‡gs9swgˆŽ©‰© „ «Šgx˜s9—/hu ¦h hE|u‡dfhswŠˆPyhEs Ω ³%c#df~¥s9~uwhEƒ‡ˆŽuw~‰¬}hˆŽ©‰{}z}ƒ‡~uwdfgtzXhEs9|fzŽuɏthE˜hE|ŠzP|uwdŠh¯~‰|f~uw~¥ˆŽ©Xs uˆπuwhP³ †uÉhEˆPyd7svuwh ²Žˆ=u‡ƒ‡ˆ}|Šsv~uw~‰z}|€ªƒwzPg§u‡dfhy«fƒ‡ƒ‡h |Yu%svu‡ˆŽuwh S uwzmˆŒ|Šh ¦Usvu‡ˆŽuwh S ~¥s%fƒ‡z}/zPswhEˆPy yzPƒ‡f~|f{=uwzmˆ=fƒ‡z}/zPsw~Æu‡~zP|°}hEƒw|Šh © ³c#dŠh^u‡ƒ‡ˆ}|Šsv~uw~‰z}|x~¥s%ˆPy y h tu‡hEj¦~Æu‡dˆšfƒ‡z}—Šˆ}—f~‰©~u r S ) {P~¬Ph |j—Yruwdfh=l¨ƒ‡h h |jƒ‡ˆŽuw~‰zŠ³%c#df~‰sɈPy y h tuˆŽ|Šy h¯ƒˆu‡~z Q(S → .) ~¥sšy z}gf«tu‡hENswzuwd˜ˆuŒu‡dfhjfhu‡ˆ}~©‰hEÂ—˜ˆŽ©¥ˆŽ|Šy h7yzP|Št~uw~‰z}|N~¥s=¬}hEα(S, ƒw~NJhSÔ²˜y z}|Št~uw~‰z}|N«Š|Šth ƒ¨¦df~¥ydÂuwdf~¥s¨ˆŽ©‰{}z}ƒ‡~uwdfgyz}|X¬Ph ƒ‡{}hEs u‡z π ³8c#dŠ~‰s=svuwƒ‡z}|Š{xy z}|Št~uw~‰z}|~¥s{}~‰¬}hE| —Xr . Z Z Z Z ± ™ 4S´ π (dC) P (C, dC ) = π (dC ) P (C , dC) ¦dfhEƒwh A ˆ}|Š B ˆ}ƒwh=u ¦¯z7swhus^z}€Ôuwdfhšuwƒ‡~‰—f«[ˆ}s‡swzXy ~‰ˆŽuwhSxuwz Ω ²tˆ}|Š P ~¥s8u‡dfhŒu‡ƒ‡ˆ}|Šsw~Æu‡~zP|°}h ƒ‡|fhE©ŠzŽ€Ôu‡dfhmŹˆŽƒ‡°}z¬xydŠˆŽ~‰| C ³ pX«Šf˜zYsv~‰|f{xuwd˜ˆu dŠˆPs#ˆNJ|Š~Æu‡hth |Šsw~u r}² D ²t¦~uwdƒwhSsv/hEyuu‡zˆjswrXgxgh uwƒ‡~‰yEˆŽ©GghEˆ}sw«fƒ‡h ψ zP| Ω × Ω ²Xuwdfh y z}|Št~uw~‰z}| ± >™ 4E´~¥sπswˆŽ(.)uw~¥s Q(C ǘhE ~ƀ→. .) ± ™P™}´ α(C, C ) D(C, C ) = α(C , C) D(C , C) †šsšswdfz¦|N~‰|- 4E•%€ªz}ƒŒuwdfh7NJ|f~uwhs uˆuwhjsvŠˆPyh7yEˆ}swh}²/~Æu¨~‰sšz}fuw~‰gˆ}©u‡z[gˆŽ°PhuwdŠh7fƒ‡z}—Šˆ}—f~‰©~u r α ˆ}sŒ©‰ˆ}ƒw{Ph7ˆ}sŒ˜zYswsw~‰—f©huwz ƒ‡hEt«˜yh¨uwdfhˆ}«tuwzty z}ƒ‡ƒwhE©‰ˆŽuw~‰z}|[z}€u‡dfhŹˆŽƒ‡°}z¬ydŠˆ}~|³8c#dY«˜s ²t¦h¨u‡ˆŽ°Ph . ± ™ "P´ α(C, C ) = min {1, R(C, C )} 46H5 G7498 i h. h. h. i. 2. i h. h. i h. h. h. I−1. I. d. h. i h. i h. h. h. i+1. c. c. h. h. i=1. i=1. c. c. h. h. d. d. c∈C. d. p. p. d. d. ∞ N =0. T. N. N. 1/T. T. T. i. 0. 0. T. 0. T. A. B. 0. T. B. 0. A. t. T. 0. 0. 0. 0. 0. 0.

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