Stylinidis, Efstrtios USING HOUGH TRANSFORM IN LINE EXTRACTION Efstrtios STYLIANIDIS, Petros PATIAS The Aristotle University of Thessloniki, Deprtment of Cdstre Photogrmmetry nd Crtogrphy Univ. Box 473, GR-54006, Thessloniki, Greece sstyl@topo.uth.gr, ptis@topo.uth.gr Working Group V/5 KEY WORDS: Hough trnsform, Line extrction, Algorithm ABSTRACT In close-rnge imges, normlly lrge number of geometricl fetures is vilble. For photogrmmetrists, the detection of shpes such s stright lines is very useful. These fetures re very helpful for further photogrmmetric work, such s sensor clibrtion, imge orienttion, DTM genertion etc. Hough Trnsform (HT), is such powerful tool for detecting predefined shpes (i.e. lines, ellipses). HT hs been used for more thn three decdes in the res of imge processing, pttern recognition nd computer vision. However, in digitl close rnge photogrmmetry HT hs only rrely been used. This pper is contribution on how HT cn be used s powerful technique for line extrction in close rnge photogrmmetric problems.. INTRODUCTION In rchitecturl photogrmmetry where lrge number of structures is vilble in the imges, tools for detecting pressigned shpes such s stright lines re very useful. These fetures re very useful for further photogrmmetric work, such s sensor clibrtion, imge orienttion, DTM genertion etc. Hough Trnsform (HT), is such tool for detecting predefined fetures (i.e. lines, ellipses) in imges nd hs been used for more thn three decdes in the res of imge processing, pttern recognition nd computer vision. However, in digitl close rnge photogrmmetry HT hs only rrely been used. In this pper HT focuses in problems of rchitecturl photogrmmetry. More specificlly, HT is used for line extrction from close rnge imges. An lgorithm hs been creted nd softwre in Microsoft Visul Bsic hs been developed. It must be cler from the beginning tht there re two wys in line extrction using the HT. It depends on the kind of work tht the user wnts to use the extrcted lines. If the mjority of lines is the subject of reserch then the whole imge must be exmined. This is slow process nd rther suffers from the disdvntge tht both useful nd useless dt re simultneously extrcted from the imge. On the other hnd, if only specific lines re the subject of reserch then the lgorithm is executed in specific prt of the imge which is defined by the user. Surely in this cse the process is much quicker. The uthors pproch ims to the second one, which mens tht HT is used s tool to extrct not ll the lines from the imge but only those tht re useful for further process. The im of this extrction process is the further use of lines such s in vnishing point computtion, single photo resection nd sensor clibrtion. Sttisticl tests re shown in rel test imges supporting the pproch.. WHAT IS HOUGH TRANSFORM - HOW DOES IT WORKS HT ws first proposed nd ptented by Pul Hough in 96 (Hough, 96) s technique for detecting curves in imges. The clssicl HT is technique for curve detection tht cn be described s prmetric curve (Bllrd nd Brown, 98). Previously, HT hs been expnded to detect rbitrry shpes (Bllrd, 98). Using n edge detector to locte points tht my consist n edge, the method exmines whether the points re components of specific type of prmetric curve. For instnce, such curve my be stright line or n ellipse. 9 Interntionl Archives of Photogrmmetry nd Remote Sensing. Vol. XXXIII, Supplement B5. Amsterdm 000.
Stylinidis, Efstrtios Ech edge point is trnsformed from imge spce to prmeter spce by incresing the elements of n rry clled ccumultor, using the line prmeters s rry indices. The cells of the rry which hve the lrgest vlues indicte the possible loctions of lines in the imge (Figure c). Initilly ccumultor is set to zero. At first HT ws used to detect stright lines presented by the slopeintercept form (Eqution ). y = m x + b () For every edge point in the imge plne (xy plne), the ccumultor (bm plne, Figure c) is incresed using vlues for the slope nd y-intercept tht stisfies the Eqution s indices: A (m,b) = A(m, b) + () F Figure. Imge points (), prmeter lines (b), ccumultor cells (c) Ech edge point hs n ssocited prmeter line in the ccumultor (Figure b). The existence nd the position of colliner points re been indicted from the intersection of prmeter lines. The higher the number of colliner points the greter the possibility tht line is been detected in the imge. HT complexity depends on the number of increments required for the slope. For instnce, hving k increments of m, there re km number of computtions. In 97, Dud nd Hrt (Dud nd Hrt, 97) proposed tht the prmeters for line would be better described by the length! nd orienttion (Eqution 3) of norml vector to the line from the origin of the imge (Figure ).! = x cos + ysin (3) In the sme wy, following the steps of originl HT, for every edge point in the imge plne (xy plne), the ccumultor (! plne) (initilly set to zero) is incresed using vlues for the ngle nd rdius! tht stisfy Eqution 3 s indices: A (!,) = A(!,) + (4) Figure. Norml representtion of line Figure 3. Prmeter spce! Interntionl Archives of Photogrmmetry nd Remote Sensing. Vol. XXXIII, Supplement B5. Amsterdm 000. 0
Stylinidis, Efstrtios The ccumultor cells with the gretest number of votes correspond to lines in imge spce. This wy, the norml prmeteriztion gives sinusoidl curves in the ccumultor. The intersection of curves denote the possible loctions of lines in the imge nd the number found t the intersection shows the number of colliner points in the line. The rnge of! is D to + D, where D is the digonl size of the re serched in the imge spce. Additionlly, the rnge of is between 0 nd 00 grds. 3. GRADIENT IN HOUGH TRANSFORM The im is the detection of stright lines in close rnge imges. In order to mke the recognition of line esier the most common wy is the reduction of informtion which is included in the originl imge. To this end n edge opertor is used, like the grdient opertor, nd thus grdient imge is generted by this process. An imge cn be described s function f(x,y), where x,y re the spce indictors nd f the gry vlue for the specific imge pixel. The grdient of f t position (x,y) is the vector given by f x G x G [f (x, y)] = = (5) G f y y The mgnitude of the grdient t position (x,y) is given by y G [f (x, y)] = G x + G (6) When using 3x3 filter-msk such s 4 7 5 8 3 6 9 (7) the components G x nd G y for the center pixel of the msk (7) re given by (Sobel filter) G G x y = ( = ( 7 3 + + 8 6 + ) ( + 9 + ) ( + 9 4 + + 3 7 ) ) (8) Using formul (9) G [f (x, y)] > T (9) edge points re defined s these pixels tht the mgnitude of their grdient exceeds n initilly defined threshold vlue T. Interntionl Archives of Photogrmmetry nd Remote Sensing. Vol. XXXIII, Supplement B5. Amsterdm 000.
Stylinidis, Efstrtios 3. «Edge enhnced» imges () The edge detection process is gretly esed if, insted the originl imges, «edge enhnced» ones re used. This inevitbly leds to the use of some edge detector, like the ones presented next. 3.. Cnny edge detector. This is the work by John Cnny for his Msters degree t MIT in 983. He treted edge detection s signl processing problem nd imed to design the «optiml» edge detector. He formlly specified n objective function to be optimized nd used this to design the opertor. The objective function ws designed to chieve the following optimiztion constrins (Cnny, 986): (b) (c) Figure 4. Originl imge (), Cnny edge detector (b) imge, SUSAN imge (c). Mximize the signl to noise rtio in order to provide good detection.. Achieve good locliztion to ccurtely mrk edges. 3. Minimize the number of responses to single edge (nonedges re not mrked). 3.. SUSAN edge detector. SUSAN is n cronym for Smllest Univlue Segment Assimilting Nucleus. The SUSAN lgorithms cover imge noise filtering, edge finding nd corner finding. The edge detection lgorithm developed by Stephen M. Smith follows the usul method of tking n imge nd using predetermined window (circulr msk in this cse usul rdius is 3.4 pixels giving msk of 37 pixels) centered on ech pixel in the imge nd pplying loclly cting set of rules to give n edge response. This response is then processed to give s n output set of edges. (http://www.fmrib.ox.c.uk/~steve/susn/index.html) Figure 5. Finl line is shown overlid upon the «imge» line Figure 6. Finl line lignment fter best fitting process 4. IMPLEMENTATION - EXPERIMENTAL RESULTS The HT experiment implemented through softwre developed in Microsoft Visul Bsic environment. The user hs to select serch re for the lgorithm to serch, find nd locte the possible line. The softwre responses, showing the line loction (Figure 5). The extrcted line is shown overlid upon the «imge» line so s the user cn judge the effectiveness of the procedure. Additionlly, ll interesting pixels, tht hve distnce not greter thn pixel from the extrcted line, re recorded. Following best fitting procedure for ll the recorded interesting pixels, the best fitted line is clculted s well s its sttistics (Figure 6). In this process line form of Eqution ws used. Interntionl Archives of Photogrmmetry nd Remote Sensing. Vol. XXXIII, Supplement B5. Amsterdm 000.
Stylinidis, Efstrtios The experiment took plce in n indoor imge (Figure 8) cquired with Kodk DCS 40 still video cmer with super wide ngle lens 7 mm (Figure 7). Four horizontl nd four verticl lines hve been extrcted from the imge nd their sttistics re shown in Tble. The results tht presented in Tble, re derived from the ppliction of HT technique in the indoor imge. Formerly, the originl imge ws pre-processed with the SUSAN edge detector (Figure 4c). Figure 7. DCS 40 A globl relibility test took plce, using the sttisticl test of vrince weight unit. An onesided F-test is defined s: o : H = / : H < () In this cse, the zero hypothesis H o is being ccepted if ^. F f, () Figure 8. Extrcted lines from the experimentl test where f re the degrees of freedom nd. is the significnce level. In the experiment where ws set equl to one pixel nd ³ clculted below unit (0.4.0) (Tble ), it is cler tht the lterntive hypothesis H is being ccepted. These leds to the conclusion tht mesurements in the imge were tken with n ccurcy lower thn one pixel. A Line No. Hough Trnsform Results in SUSAN Edge Imge No. of Points ^ o ^ (grd) ^ b (pixels) (H) 07 0.94 0.0 0.05 (H) 077 0.99 0.04 0.09 3 (H) 58 0.89 0.09 0.08 Figure 9. Extrcted lines were plotted in 4 (H) 36 0.74 0.3 0.08 Autocd environment using ActiveX technology 5 (V) 3 0.90 0.7 0.7 6 (V) 53 0.89 0.4 0.76 7 (V) 33 0.75 0.7 0.63 4. Model cretion -ActiveX technology 8 (V) 5 0.37 0.07 0.04 During best fitting process, mong the other prmeters, line s endpoints coordintes re clculted nd recorded s well. A very useful tech- Tble. Line sttistics nique for dt utiliztion hs been developed using ActiveX technology in CAD environment. AutoCd is such CAD pckge tht provides the bility to use this technology. Extrcted lines from HT process were plotted in AutoCd environment (Figure 9). Through the softwre developed it is possible to use ll possible AutoCd bilities. 5. CONCLUSIONS HT is technique for detecting rbitrry shpes nd predefined shpes, such s lines, s well. Even if it is not widely used in close rnge pplictions, HT remins powerful tool nd must be used in line extrction. In this pper HT ws exmined from the point of view of line extrction. 3 Interntionl Archives of Photogrmmetry nd Remote Sensing. Vol. XXXIII, Supplement B5. Amsterdm 000.
Stylinidis, Efstrtios Experimentl results proved tht using n edge imge, quickly nd ccurtely lines cn be detected nd locted in close rnge imges. More specificlly, the vlue of -posteriori vrince of weight unit reched 0.4 pixel nd lower thn pixel. Finlly, new softwre module ws creted turning to dvntge of ActiveX technology in CAD environment. Using this technology in AutoCd environment, extrcted lines where plotted, hving s result the imge model cretion. All AutoCd utilities nd commnds cn now be ccessed nd used from the developed module. REFERENCES Admos, C., Fig W., 99. Hough Trnsform in Digitl Photogrmmetry. In: Interntionl Archives of Photogrmmetry nd Remote Sensing, Wshington, USA, Vol. 9, Prt B3, pp. 50-54. Bllrd, D. H., 98. Generlizing the Hough Trnsform to detect rbitrry shpes. Pttern Recognition, 3(), pp. -. Bllrd, D. H., Brown C. M., 98. Computer Vision. Prentice-Hll Inc., Englewood Cliffs, New Jersey, pp. 3-3. Cnny, J., 986. A computtionl pproch to edge detection. IEEE Trnsctions on Pttern Anlysis nd Mchine Intelligence, 8(6), pp. 679-698. Dud, R. D., Hrt P. E., 97. Use of the Hough Trnsform to detect lines nd curves in pictures. Communiction of the ACM, 5(), pp. -5. Hough, P.V.C, 96. Method nd Mens for Recognizing Complex Ptterns. U.S. Ptent 3,069,654. Stylinidis, E., Ptis P., 999. Semi-utomtic «interest line» extrction in close rnge imges. In: Interntionl Archives of Photogrmmetry nd Remote Sensing, Thessloniki, Greece, Vol. XXXII, Prt 5W, pp. 37-4. Interntionl Archives of Photogrmmetry nd Remote Sensing. Vol. XXXIII, Supplement B5. Amsterdm 000. 4