Image Recognition of Icing Thickness on Power Transmission Lines Based on a Least Squares Hough Transform

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1 energies Article Image Recognition Icg Thickness on Power Transmsion Les Based on a Least Squares Hough Transform Jgjg Wang 1, Junhua Wang 2, *, Jianwei Shao 2 Jiangui Li 3, * 1 School Geodesy Geomatics, Wuhan University, Wuhan , Cha; jgjgwang@whu.edu.cn 2 School Electrical Engeerg, Wuhan University, Wuhan , Cha; hitwhshao@sa.cn 3 School Mechanical Electronic Engeerg, Wuhan University Technology, Wuhan , Cha * Correspondence: junhuawang@whu.edu.cn (J.W.); jianguili@whut.edu.cn (J.L.); Tel.: (J.W.) Academic Editor: Fengshou Gu Received: 13 January 2017; Accepted: 18 March 2017; Publhed: 23 March 2017 Abstract: In view shortcomgs current detection methods for icg thickness on transmsion les, an measurg method for icg thickness based on remote onle monitorg was proposed. In th method, a Canny operator used to get, addition, a Hough transform least squares are combed to solve problems traditional Hough transform parameter space whereby it easily dturbed by background noes, eventually s iced transmsion les un-iced transmsion les are accurately detected s which have low contrast, complex grayscale, many noes. Furrmore, based on imagg prciple camera, a new geometric calculation model for icg thickness establhed by usg radius transmsion le as a reference, automatic calculation icg thickness achieved. results show that proposed recognition method rarely dturbed by noes background, recognition results show good agreement with real s iced transmsion les un-iced transmsion les, simple easy to program, which suggests that method can be used for recognition calculation icg thickness. Keywords: transmsion le; icg thickness; Hough transform; least squares; geometric calculation model 1. Introduction earliest reports icg accidents on transmsion les appeared 1932, sce n Norway, Canada, Brita, Russia, Japan or countries or regions have had serious icg dasters. With global abnormal wear occurrg frequently today s climate, icg dasters on transmsion les are growg frequency due to prevailg macroclimate, micrometeorological, microtopography conditions. se seriously threaten safe operation grid have caused huge losses to respective national economies. Power transmsion le breakage, transmsion tower topplg, ice flashover, transmsion le gallopg, etc., caused by icg, ten occurred Cha durg wter, [1 3]. In 2008 sourn snowstorm Cha, direct economic losses State Grid Cha Sourn Power Grid were 10.4 billion 5 billion RMB, direct economic losses social impact caused by outage were more difficult to estimate [4 6]. In order to ensure normal operation system, reduce prevent icg daster consequences on transmsion les, it necessary achieve real-time onle monitorg icg thickness on se les. Compared with weighg methods which are susceptible to wd magnetic fields, icg rate meter methods which cannot directly measure icg thickness on transmsion les, optical fiber Energies 2017, 10, 415; doi: /en

2 Energies 2017, 10, sensg methods which have charactertics zero drift non-learity, wire dip methods which are susceptible to stiffness on rotatg transmsion les, recognition methods which are real-time vible have been a recent trend direction research on icg monitorg methods. In current world, vast majority transmsion towers are equipped with remote onle monitorg termals, se could collect transfer real-time icg s to monitorg centers, so we can obta real-time icg status from icg s, n calculate icg thickness to furr assess icg harm potential on transmsion les. However, background environment transmsion les complex, imagg environment easily affected by light factors, lossy compression methods are applied to transmsion process, which leads to icg s havg charactertics low contrast, complex grayscale, all kds noes, etc. [7,8]. At present, recognition algorithms for icg thickness on transmsion les rarely take to account se aspects. For example, based on obtag all slopes transmsion le an, slope le searchg algorithm described [9] calculates mastream slope as iced transmsion le. In th method, some slopes which do not belong to transmsion le will affect calculation mastream slope. In addition, optimal threshold mamatical morphology algorithm from [10] can only get s iced transmsion le from s which have simple backgrounds. In fact, transmsion le icg s have very complex backgrounds. Similarly, automatic trackg algorithm from [11] simply averages vertical coordates upper outle lower outle iced transmsion le, without considerg impacts noes. To address above problems, th paper presents an recognition algorithm for icg thickness on transmsion lea based on a least squares Hough transform. Compared with shortcomgs traditional Hough transform which easily affected by background noes parameter space [12 15], th algorithm combes a Hough transform with least squares method, n accurately identifies s iced transmsion les un-iced transmsion les s which have low contrast, complex grayscale, many noes. In addition, a new geometric model icg thickness was establhed to automatically calculate icg thickness. An engeerg example was carried out to test verify th proposed recognition method. 2. Image Recognition Process Based on least squares Hough transform, th paper presents an recognition algorithm for icg thickness on transmsion le, which can be divided to four steps: acquition, preprocessg, transmsion le detection, calculation icg thickness. specific implementation process as shown 1 volves followg steps: 1. Th paper uses a remote camera mounted at a fixed position on tower to take color s un-iced iced transmsion les at a fixed angle. captured s are shown 2 [16]. 2. color s un-iced iced transmsion les should be respectively subjected to grayscale processg to obta grayscale s. After that, Canny operator used to detect s two s. By settg a self-adaptation dual threshold Canny operator, s un-iced transmsion les iced transmsion le are preserved to a certa extent n non- are removed to greatest degree. 3. In s two s, a Hough transform used to search for located on a straight le, n achieve a rough positiong un-iced iced transmsion le s. At same time, least squares fittg applied to pixel coordates rough positiong based on lear equation, we can get accurate un-iced iced transmsion le s. Fally, pixel coordate equations transmsion le s are obtaed.

3 Energies 2017, 10, Energies Energies 2017, 2017, 10, 10, transmsion le s. Fally, pixel coordate equations transmsion le transmsion le s. Fally, pixel coordate equations transmsion le s are obtaed. 4. s Basedare on obtaed. imagg prciple camera transmsion le detection 4. Based on imagg prciple camera transmsion le detection 4. Based results, on a geometrical imagg prciple calculation model camera for icg thickness transmsion establhedle with reference detection to results, a geometrical calculation model for icg thickness establhed with reference to results, radius a geometrical calculation transmsion model le. for icg n thickness we can achieve establhed automatic with reference calculation to radius transmsion le. n we can achieve automatic calculation icg radius icg thickness. transmsion le. n we can achieve automatic calculation icg thickness. thickness recognition process process for for icg icg thickness thickness on on transmsion les. les. 1. recognition process for icg thickness on transmsion les. 2. color s are captured from a fixed remote camera, whose size 640* color s are captured from a fixed remote camera, whose size 640*480. A 2. color color s an areun-iced captured from atransmsion fixed remote camera, le; whose A color size 640*480. an iced A A color an un-iced transmsion le; A color an iced color transmsion anle. un-iced transmsion le; A color an iced transmsion le. transmsion le. 3. Image 3. Image Preprocessg 3. Image Preprocessg color color s s are are taken taken usg usg a remote a remote camera camera mounted on on tower, tower, n n a lossy a lossy color s are taken usg remote camera mounted on tower, n lossy compression method method applied applied to to transmsion process, process, so so se se s s have have complex compression method applied to transmsion process, so se s have complex backgrounds, low low contrast, many many kds kds noes, noes, which which affect affect detection backgrounds, low contrast, many kds noes, which affect detection transmsion les, les, refore, refore, purposes purposes preprocessg preprocessg th paper th are paper to elimate are to elimate transmsion les, refore, purposes preprocessg th paper are to elimate noes, improve noes, improve contrast, obta contrast, obta s, s, make appropriate make appropriate preparations preparations for for noes, improve contrast, obta s, make appropriate preparations for transmsion transmsion le le detection. detection. transmsion le detection.

4 Energies 2017, 10, Energies 2017, 10, Grayscale Processg 3.1. Grayscale Processg Conversion formulas from color to grayscale are as follows: Conversion formulas { from color to grayscale are as follows: g = P.R P.G P.B g = PR PG PB (1) P.R = P.G = P.B g (1) PR. = PG. = PB. = g where where P pixel pixel,, R red red component, component, G green green component, component, B blue blue component. component. Based Based on on grayscale grayscale processg, processg, grayscale grayscale s s shown shown 3 are are obtaed. obtaed. 3. grayscale s 2. grayscale an un-iced transmsion 3. grayscale s 2. A grayscale an un-iced transmsion le; grayscale an iced transmsion le. le; A grayscale an iced transmsion le Image Edge Detection 3.2. Image Edge Detection Canny operator most effective detection algorithm, whose process can be divided Canny operator most effective detection algorithm, whose process can be divided to four steps: Gaussian filterg, gradient calculation, non-maximum suppression, dual to four steps: Gaussian filterg, gradient calculation, non-maximum suppression, dual threshold threshold detection. detection Gaussian Gaussian Filterg Filterg We We use use a remote remote camera camera mounted mounted on on tower tower to to take take s, s, so so imagg imagg environment environment easily easily affected affected by by light light tensity, tensity, light light uniformity uniformity or or factors, factors, thus thus Gaussian Gaussian noes noes are easily are easily produced produced s s affect affect detection. detection. However, However, Gaussian noes Gaussian can noes be elimated can be elimated by Gaussian by filterg. Gaussian filterg. weighted weighted average gray average gray target pixel target pixel neighborhood neighborhood re-assigned re-assigned to gray to gray target pixel, target that pixel,, that, scanned with scanned 3 with 3 template 3 3 template (refer to (2)), (refer to (2)), weighted average weighted gray average gray re-assigned re-assigned to gray to gray center pixel: center pixel: (2) 16 (2) Gaussian filterg performed on 3, results are as shown 4. To some Gaussian filterg performed on 3, results are as shown 4. To some extent, noes are elimated. extent, noes are elimated Gradient Calculation Gradient Calculation On s, gray s adjacent obviously change. refore, core On s, gray s adjacent obviously change. refore, problem detection to fd with jumpg gray. In digital core problem detection to fd with jumpg gray. In digital processg analys process, amplitude direction gradient are calculated by fite processg analys process, amplitude direction gradient are calculated by difference first-order partial derivative, which are used to describe degree direction fite difference first-order partial derivative, which are used to describe degree pixel gray changes, n determe s. direction pixel gray changes, n determe s.

5 Energies 2017, 10, Energies 2017, 10, Energies 2017, 10, Grayscale s after Gaussian filterg. A grayscale an un-iced 4. transmsion Grayscale le s after Gaussian filterg. A grayscale an un-iced after Gaussian filterg; A grayscale an iced transmsion le transmsion afterfilterg. Gaussian filterg; A grayscale an iced transmsion le afterle Gaussian after Gaussian filterg. Gaussian filterg can t remove all noes. To furr elimate effects noes on detection, asobel template operator used for convolution calculation: Gaussian filterg can t remove all noes. To furr elimate effects 1 0 A 1grayscale 4. Grayscale s after Gaussian filterg. an un-iced noes on detection, a Sobel template operator used for convolution calculation: an iced transmsion le transmsion le after Gaussian filterg; G = APgrayscale x (3) , 1noes. Gaussian filterg can t remove all To furr elimate effects G = P x G = P y used noes on detection, a Sobel for convolution calculation: template operator , x, Gy) a gradient vector. where P pixel matrix, (G = P G = direction P x 0 O are0also obtaed 0 by (4): n gradient amplitude Gy G , 1 (3) after Gaussian filterg. (3) 1 x +2G y 1 G = G G 0G 0, y = P 0 (4) y ) a gradient where P pixel matrix, (Gx, G vector. y O = arctan G n gradient amplitude G direction O are xalso obtaed by (4): where P pixel matrix, (G x, Gy) a gradient vector. Based on Pi.g = 255 Gi / Gmax, we assignq gradient amplitude Gi directly to pixel gray n gradient amplitude G direction O are also obtaed by (4): G maximum Pi.g by scalg, where Gmax = Gx 2 + Gy2 gradient amplitude. n, 5, usg gradient (4) 2 grayscale s gradient amplitude As shown G =obtaed. G x 2 + GG are y y = arctan improve Gx contrast enhance features amplitude G as directly cano (4) Gy,, but not enough to determe. O s = arctan G x amplitude G directly to pixel gray Based on P.g = 255 G /Gmax, we assign gradient i i i Pi.g by scalg, where Gi.gmax maximum gradient amplitude. n grayscale = 255 Gi / G Based on P max, we assign gradient amplitude Gi directly to pixel gray s gradient amplitude are obtaed. As shown usg gradient amplitude G as 5,gradient amplitude. n Pi.g by scalg, where Gmax maximum s can gradient amplitude are obtaed. shown usgfeatures gradient grayscale directly improve contrastas enhance 5,, amplitude G as directly can improve contrast enhance features but not enough to determe s., but not enough to determe s. 5. grayscale s based on gradient amplitude. Gradient an un-iced transmsion le; Gradient an iced transmsion le Non-Maximum Suppression A number non- are cluded 5, so we can elimate with small with local largest gradient s to elimate non-. gradient s preserve 5. grayscale s based on gradient amplitude. Gradient an un-iced 5. transmsion grayscale based ongradient amplitude. le. Gradient an un-iced le; s Gradient an iced transmsion transmsion le; Gradient an iced transmsion le Non-Maximum Suppression A number Suppression non- are cluded 5, so we can elimate with small Non-Maximum gradient s preserve with local largest gradient s to elimate non-. A number non- are cluded 5, so we can elimate with small gradient s preserve with local largest gradient s to elimate non-. That method non-maximum suppression. Non-maximum suppression performed gradient

6 Energies 2017, 10, direction, where local gradient amplitude largest are retaed. In order to simplify Energies Energies 2017, 10, 2017, comparon 41510, gradient amplitude, gradient angle O needs to be processed 6 15 as follows: That method non-maximum suppression. Non-maximum suppression performed gradient That method non-maximum suppression. Non-maximum suppression performed gradient Step 1: direction, range verse where trigonometric local gradient function amplitude ( π/2, largest π/2), are retaed. so In gradient order to angle O direction, where local gradient amplitude largest are retaed. In order to simplify comparon gradient amplitude, gradient angle O needs to be processed as obtaed simplify by (4) can plus a constant π/2, n range becomes (0, π). follows: comparon gradient amplitude, gradient angle O needs to be processed as Step follows: 2: Based on Table 1 6, gradient angles O are divided to four sectors Step 1: range verse trigonometric function ( π /2, π /2), so gradient angle O circumference, n gradient angles O are reset. Step obtaed 1: by range (4) can plus verse a constant trigonometric π /2, n function range becomes ( π /2, (0, π )/2)., so gradient angle O obtaed by Step (4) 2: can Based plus on a Table constant 1 6, gradient angles O are divided to four sectors Table π /2 1., Resettg n range gradient becomes (0, π ) angles.. Step circumference, 2: Based on Table n 1 gradient angles 6, O gradient are reset. angles O are divided to four sectors circumference, Sector n Gradient gradient Angle/Degree angles O are reset. Gradient Angle After Reset/Degree Table 1. Resettg gradient angles. 0 Sector (0, 22.5) Gradient Table (157.5, Angle/Degree 1. Resettg 180) Gradient gradient Angle angles. After Reset/Degree (0, (22.5, 22.5) 67.5) (157.5, 180) Sector 1 Gradient (67.5, Angle/Degree (22.5, 112.5) 67.5) Gradient Angle 45 After 90 Reset/Degree (0, (112.5, 22.5) (67.5, 157.5) (157.5, 112.5) 180) (22.5, (112.5, 67.5) 157.5) (67.5, 112.5) 90 3 (112.5, 157.5) four sectors circumference. 6. four1 sectors 3 circumference. Based on gradient angle O each pixel 2after resettg, we traverse two adjacent gradient direction n compare gradient amplitude G: If gradient amplitude target 6. four sectors circumference. pixel greater than gradient amplitudes adjacent two, gradient amplitude target pixel maximum, n its gradient amplitude scaled by (5). Orwe, Based on gradient angle O each pixel after resettg, we traverse two adjacent gradient amplitude target pixel will be reset to zero: gradient direction n compare gradient amplitude G: If gradient amplitude target pixel greater than gradient amplitudes Gi G i = adjacent 255 two, gradient amplitude (5) target pixel maximum, n its gradient G max amplitude scaled by (5). Orwe, gradient where amplitude Gmax maximum target pixel will be reset to gradient amplitude Gi gradient amplitude target pixel. After non-maximum suppression, G i = G zero: i gradient amplitudes G have been a certa Gi degree shrkage. Meanwhile, Gwith largest local gradient amplitude are retaed, i = 255 (5) whose gradient amplitudes are scaled to ir gray G maxs, n gray s or are reset to zero, as shown 7. where Gmax maximum gradient amplitude Gi gradient amplitude target pixel. After non-maximum suppression, gradient amplitudes G have been a certa degree shrkage. Meanwhile, with largest local gradient amplitude are retaed, whose gradient amplitudes are scaled to ir gray s, n gray s or are reset to zero, as shown 7. Based on gradient angle O each pixel after resettg, we traverse two adjacent gradient direction n compare gradient amplitude G: If gradient amplitude target pixel greater than gradient amplitudes adjacent two, gradient amplitude target pixel maximum, n its gradient amplitude scaled by (5). Orwe, gradient amplitude target pixel will be reset to zero: G max 255 (5) where G max maximum gradient amplitude G i gradient amplitude target pixel. After non-maximum suppression, gradient amplitudes G have been a certa degree shrkage. Meanwhile, with largest local gradient amplitude are retaed, whose gradient amplitudes are scaled to ir gray s, n gray s or are reset to zero, as shown grayscale s after non-maximum suppression. grayscale an uniced transmsion le after non-maximum suppression; grayscale an iced transmsion le after non-maximum suppression. 7. grayscale s after non-maximum suppression. grayscale an uniced transmsion le after non-maximum suppression; grayscale an iced 7. grayscale s after non-maximum suppression. grayscale an un-iced transmsion transmsion le le after after non-maximum non-maximum suppression. suppression; grayscale an iced transmsion le after non-maximum suppression.

7 Energies 2017, 10, Energies 2017, 10, Dual Threshold Edge Detection Dual purpose Threshold Edge Detection detection th paper to better identify s un-iced transmsion les iced transmsion les, which tries to keep foreground purpose detection th paper to better identify s un-iced remove background. However, purpose traditional Canny operator for transmsion les iced transmsion les, which tries to keep foreground detection to obta optimal s, which does not consider removg remove background. However, purpose traditional Canny operator for background. detection to obta optimal s, which does not consider removg background. In order to reta transmsion le s remove non- transmsion le s, In order to reta transmsion le s remove non- transmsion le s, we can set a dynamic dual threshold based on gradient amplitude transmsion le we can set a dynamic dual threshold based on gradient amplitude transmsion le s. high threshold H very obvious gradient amplitude transmsion le s, s. high threshold very obvious gradient amplitude transmsion le s, n low threshold L gradient demarcation pot transmsion le s n low threshold L gradient demarcation pot transmsion le s non- transmsion le s. When Gi > H, we thk that target pixel must be non- transmsion le s. When G i H, we thk that target pixel must be. When Gi < L, we thk that target pixel must not be. pixel whose gradient. When G i L, we thk that target pixel must not be. pixel whose gradient amplitude between L H furr verified as pendg : If gradient amplitude amplitude between L furr verified as pendg : If gradient amplitude pixel smaller than high threshold H range 3 3 neighborhood, pixel not pixel smaller than high threshold H range 3 neighborhood, pixel. In fal obtaed s, transmsion le s are preserved to a not. In fal obtaed s, transmsion le s are preserved certa extent n non- transmsion le s are removed on greatest degree. to a certa extent n non- transmsion le s are removed on greatest degree. three-dimensional dplay gradient amplitude (or gray ) 7 obtaed as three-dimensional dplay gradient amplitude (or gray ) 7 obtaed shown 8. as shown three-dimensional dplay gradient amplitude, among m, pixel 8. three-dimensional dplay gradient amplitude, among m, pixel coordates are used as x-ax y-ax, gradient amplitude (or gray ) coordates are used as x-ax y-ax, gradient amplitude (or gray ) pixel used as z-ax. gradient amplitudes 7a; gradient pixel used as z-ax. gradient amplitudes 7a; gradient amplitudes amplitudes 7b. 7b. As can be seen from 8, gradient amplitudes only change significantly at As can be seen from 8, gradient amplitudes only change significantly at transmsion le reach a peak ; what s more, changes or transmsion le reach a peak ; what s more, changes or locations are small. locations Moreover, are small. it observed that with gradient amplitude greater than 50 8 are substantially Moreover, located it observed at that with transmsion gradient amplitude le, n greater parts than 50 with gradient 8 are substantially amplitude greater located at than 25 are also located transmsion at s, le, so n parts high threshold with gradient amplitude 8a,b greater can be than 50, 25 are n also located low at threshold s, so high threshold 8a,b can be 25. Based 8a,b on dual can be threshold, 50, n we furr low determe threshold s. 8a,b Fallly, can be after 25. determg Based on dual threshold, s, we furr we set determe gray s s. Fallly, to after 255 determg gray s s, non- we set gray to s 0 to get bary s to 255, as shown gray s 9. non- As can be seen from to 0 to th get figure, bary while s carryg, on as shown detection, we 9. have As can retaed be seen from s th figure, while carryg transmsion on le to detection, greatest we extent have retaed possible, s removed some non-s transmsion le to transmsion greatest le. extent possible, removed some non-s transmsion le.

8 Energies 2017, 10, Energies 2017, 10, Energies 2017, 10, bary s after dual threshold detection. 9. bary s after dual threshold detection. bary bary s s an an un-iced un-iced 9. bary transmsion transmsion s le; le; after dual bary bary threshold s s detection. an an iced iced bary transmsion transmsion s le. le. an un-iced transmsion le; bary s an iced transmsion le. 4. Power Transmsion Le Edge Detection Based on Least Squares Hough Transform 4. Power Transmsion Le Edge Detection Based on Least Squares Hough Transform 4. Power In order Transmsion to furr identify Le Edge Detection s Based on Least transmsion Squares le Hough from Transform s, th In order to furr identify s transmsion le from s, paper presents a new algorithm based on a least squares Hough transform. Hough transform th paper In order presents to furr a newidentify algorithm based s on a least squares transmsion Hough transform. le from Houghs, transform th used paper to locate s un-iced transmsion les iced transmsion les usedpresents to locatea new s algorithm un-iced based on a least transmsion squares Hough les transform. iced Hough transmsion transform les roughly, used n least squares method used to locate m accurately. roughly, to locate n s least squares un-iced method transmsion used to locateles m accurately. iced transmsion les roughly, n least squares method used to locate m accurately Rough Positiong 4.1. Rough Positiong prciple Hough transform to transform straightle detection problem space toprciple parameter space Hough by by usg transform mappg to transform relation between straight le space detection space problem parameter space. space. n space we we to determe determe parameter space by located usg located on mappg on same same le relation byle fdg between by fdg cumulative space cumulative peak parameter peak parameter space. parameter n space we [17 23]. determe space refore, [17 23]. refore, Hough located transform Hough on can transform same be le usedcan by forbe fdg rough used positiong for rough cumulative positiong un-iced peak uniced parameter transmsion space transmsion le[17 23]. le refore, iced iced transmsion Hough transform transmsion le. can be le used. for rough positiong un- iced In In transmsion space i-j, le all collear iced pots can be transmsion representedle by a. straight le equation: In space i-j, all collear pots can j = be ki+ represented b by a straight le equation: (6) j = ki + b (6) where k slope straight le b j tercept. ki b (6) where Takg (i, slope j) as parameter, straight le (k, b) as variable, tercept. where k slope straight le b tercept. we can get (7): Takg (i, j) as parameter, (k, b) as variable, we can get (7): Takg (i, j) as parameter, (k, b) as b = variable, ik+ j we can get (7): (7) where i slope straight le j b = b tercept. ik ik+ j j So (7) can be regarded as a lear equation (7) parameter space k-b. where i slope straight le j tercept. So (7) can be regarded as a lear equation Thus, a pot space corresponds to a straight le parameter space, pots parameter space k-b. collear Thus, space tersect at same pot parameter space, as shown 10. a pot space corresponds to a straight le parameter space, pots collear space tersect at same pot parameter space, as shown 10. j b j b i Image space i Image space k Parameter space k Parameter space 10. Correspondence between space i-j parameter space k-b. If slope straight le space fite ( lear equation x = a), above correspondg relationship Correspondence Correspondence will not be expressed. between between In order space space to be i-j i-j able to parameter express parameter any space space slopes k-b. k-b. straight le detection, parameter coordate (k, b) should be expressed as polar coordates ( ρ, θ ): If slope straight le space fite ( lear equation x = a), above correspondg relationship will not be expressed. In order to be able to express any slopes straight le detection, parameter coordate (k, b) should be expressed as polar coordates (, ):

9 Energies 2017, 10, Energies 2017, 10, ρ = i cosθ + j sθ, (8) Energies 2017, 10, where ρ dtance from coordate orig to straight le, θ angle between vertical If le slope passg straight through le orig space positive fite direction ( lear i ax. equation x = a), above correspondg We assume relationship straight les will not n directions be expressed. for each In order pixel topot be able P(i, to j), express (n = 180, any slopes angular accuracy straight le detection, le parameter 1 ) coordate n calculate (k, b) should ( ρ, be θ ) expressed coordates as polar n coordates straight les (ρ, separately, θ): as shown 11. Fally, we can get correspondg polar coordates n straight les all pixel pots. refore, a pot ρ = i cos θ + space j scorresponds θ, to a susoidal curve (8) parameter space, while collear pots space tersect at same pot parameter where ρ dtance from coordate orig to straight le, θ angle between space. vertical le passg through orig positive direction i ax. We assume straight les n directions for each pixel pot P(i, j), (n = 180, angular accuracy detection le 1 ) n calculate (ρ, θ) coordates n straight les separately, as shown 11. Fally, we can get correspondg polar coordates n straight les all pixel pots. refore, a pot space corresponds to a susoidal curve parameter space, while collear pots 10. Correspondence between space tersect space at i-j same parameter pot space parameter k-b. space. 11. correspondence between space i-j parameter space ρ -θ. Based on mappg relationship between space i-j parameter space ρ -θ, we detect s 9, n calculate ρ under all θ, at same time, accumulate occurrence number ρ under θ. results are shown 12. When cumulative number greater than threshold PL, are on a straight le whose pixel 11. length correspondence greater than between threshold space PL. In i-j order to parameter accurately space detect -. s on 11. correspondence between space i-j parameter space ρ-θ. both sides transmsion le, selected threshold PL should be significantly larger than cumulative Based on number mappg relationship or non- between les. By observg space i-j 12, parameter occurrence space number -, we Based on mappg relationship between space i-j parameter space ρ-θ, detect ρ under θ transmsion s le s 9, n significantly calculate larger under than all non-, at les, same so time, we detect s 9, n calculate ρ under all θ, at same time, optimum threshold can be chosen accumulate occurrence number as 100. ρ under under θ.. results results are shown are shown When cumulative number greater than threshold PL, are on a straight le whose pixel length greater than threshold PL. In order to accurately detect s on both sides transmsion le, selected threshold PL should be significantly larger than cumulative number or non- les. By observg 12, occurrence number under transmsion le s significantly larger than non- les, so optimum threshold can be chosen as Accumulated stattical results after Hough transform. accumulated results 12. Accumulated stattical results after Hough transform. accumulated results 9a after Hough transform; accumulated results 9b after Hough transform. 9a after Hough transform; accumulated results 9b after Hough transform. We set color detected transmsion le to red by settg PL = 100. When cumulative number greater than threshold P rough positiong results transmsion le after L, are on a straight Hough transform are shown le whose pixel length greater than threshold P 13 with red color. L. In order to accurately detect s on both sides transmsion le, selected threshold P L should be significantly larger than cumulative number or non- les. By observg 12, occurrence number

10 optimal sgle pixel s transmsion le are as shown 14. As shown 14, detection algorithm based on least squares Hough transform less sensitive to non- noes, n can accurately identify s un-iced Energies 2017, 10, ρ under θ transmsion le s significantly larger than non- les, so optimum threshold can be chosen as 100. We set color detected transmsion le to red by settg P L = 100. rough positiong results transmsion le after Hough transform are shown 13 with red color. Energies 2017, 10, rough rough positiong positiong results results transmsion transmsion le le s s after after Hough Hough transform. transform. rough rough positiong positiong results results an un-iced an un-iced transmsion transmsion le s; le s; rough positiong rough positiong results an results iced an transmsion iced transmsion le s. le s Accurate Positiong 4.2. Accurate Positiong transmsion le detected by Hough transform may be located on transmsion le detected by Hough transform may be located on a number straight les whose pixel length are greater than PL, because Hough transform a number straight les whose pixel length are greater than P L, because Hough transform easily affected by background noes. In order to obta optimal sgle pixel easily affected by background noes. In order to obta optimal sgle pixel transmsion le s from transmsion le s, it necessary to carry out pixel transmsion le s from transmsion le s, it necessary to carry out a pixel coordate fittg transmsion le s by least square function. coordate fittg transmsion le s by least square function. First all, we can determe center pixel coordate equation transmsion le First all, we can determe center pixel coordate equation transmsion to split transmsion le both sides. Based on (6), coordates all le to split transmsion le both sides. Based on (6), coordates all transmsion le are regressed by least squares to calculate center pixel coordate transmsion le are regressed by least squares to calculate center pixel coordate equation transmsion le calculated: equation transmsion le calculated: j = kmi+ bm (9) j = k m i + b m (9) Secondly, transmsion le s are divided to two groups based on (10): Secondly, transmsion ki le m + b s m j> 0 are divided to two groups based on (10): { (10) ki m + bm j< k m i + b m j > 0 (10) Each group located on one kside m i + b m j < 0 transmsion le. Once aga, least square fittg performed usg (6) for each group pixel coordates to obta optimal sgle pixel Each group on both sides located transmsion on one side le: transmsion le. Once aga, least square fittg performed usg (6) for each group pixel coordates to obta optimal sgle pixel on both sides transmsion le: j = ki 1 + b1 (11) { j = k2i + b2 j = k 1 i + b 1 Fally, grayscale obtaed by optimal set to 255, that, pixel (11) j = k 2 i + b 2 color set to white, so we can obta accurate positiong results transmsion le. Fally, Based on rough grayscale transmsion obtaed le s by (see optimal 13), we set can to get 255, pixel that, coordate pixel equations color set tooptimal white, so s we can on obta both sides accurate positiong transmsion resultsle after accurate transmsion positiong: le. j = i (12) j = i j = i j = i (13)

11 Energies 2017, 10, Based on rough transmsion le s (see 13), we can get pixel coordate equations optimal s on both sides transmsion le after accurate positiong: { { j = i j = i j = i j = i optimal sgle pixel s transmsion le are as shown 14. As shown 14, detection algorithm based on least squares Hough transform less sensitive to non- noes, n can accurately identify s un-iced transmsion le iced transmsion le s with complicated background various noes. Energies 2017, 10, Energies 2017, 10, (12) (13) 14. Accurate positiong results transmsion le accurate un-iced 14. Accurate positiong results transmsion le accurate un-iced transmsion 14. Accurate le positiong s; results accurate iced transmsion transmsion le le s. accurate un-iced transmsion le s; accurate iced transmsion le s. transmsion le s; accurate iced transmsion le s. We place accurate positiong results transmsion le to origal color s, We We as place place shown accurate accurate positiong positiong 15 with results results red color. transmsion transmsion Accurate positiong le le to to results origal origal color color transmsion s, s, as as shown shown le have a good with with agreement red red color color with.. s Accurate Accurate positiong positiong un-iced results results transmsion le transmsion transmsion iced le le transmsion have have a le good good agreement agreement origal with with color s. s s un-iced un-iced transmsion transmsion le le iced iced transmsion transmsion le le origal origal color color s. s. 15. Accurate positiong results are placed to origal color s. Accurate positiong 15. Accurate result an positiong un-iced results transmsion are placed le; to Accurate origal positiong color s. result Accurate an iced 15. Accurate positiong results are placed to origal color s. Accurate positiong transmsion result le. an un-iced transmsion le; Accurate positiong result an iced positiong result an un-iced transmsion le; Accurate positiong result an iced transmsion le. transmsion le. 5. Calculation Icg Thickness 5. Calculation Icg Thickness 5.1. Calculatg Icg Thickness Based on Least Squares Hough Transform 5.1. Calculatg Icg Thickness Based on Least Squares Hough Transform imagg prciple camera as shown 16. camera can be seen as a convex lens, f imagg focal length, prciple d object camera dtance, as shown v 16. dtance. camera can be seen as a convex lens, f focal length, d object dtance, v dtance. Camera Camera f Focus f Focus

12 15. Accurate positiong results are placed to origal color s. Accurate positiong result an un-iced transmsion le; Accurate positiong result an iced Energies 2017, 10, transmsion le. 5. Calculation Icg Thickness 5.1. Calculatg Icg Thickness Based on Least Squares Hough Transform imagg prciple camera as shown 16. camera can be seen as a convex lens, f focal length, d object dtance, v dtance. Camera R0 f Focus Image wire R P Wire d v Imagg Imagg prciple prciple camera. camera. Based on imagg prciple convex lens, we can get (14): Based on imagg prciple convex lens, we can get (14): R p = f v f R 0, (14) where R p size, R 0 radius transmsion le. We use a remote camera mounted at a fixed position on tower to take s un-iced transmsion les iced transmsion les at a fixed angle. refore, deformation ratio fixed same at same position. n we can get calculation formula icg thickness based on s un-iced transmsion les s iced transmsion les. D = x 2 x 1 R 0 R 0, (15) where D icg thickness, x 2 pixel radius icg transmsion le x 1 pixel radius un-icg transmsion le. To get x 2 /x 1, we need to do followg analys: At pot A 17a, pixel radius iced wire AB/2. Likewe, A B /2 pixel radius un-iced wire (see 17b). camera takes s from a fixed position at a fixed angle, so ABC A B C are similar, n: x 2 = AB/2 x 1 A B /2 = AB A B = AC A C (16) So geometrical calculation model icg thickness on transmsion le obtaed: D = AC A C R 0 R 0 (17) Accordg to detection results transmsion le (Equations (12) (13)), we substitute pixel height to equation unknown number j, n get A C = 8.46 pixel AC = pixel.

13 AC D = R R (17) ' ' AC 0 0 Accordg to detection results transmsion le (Equations (12) (13)), we substitute pixel height to equation unknown number j, n get A C = 8.46 pixel AC = pixel. Energies 2017, 10, Schematic Schematic diagram diagram transmsion transmsion les. les. Image Image schematic schematic diagram diagram an an iced iced transmsion transmsion le; le; Image Image schematic schematic diagram diagram an an un-iced un-iced transmsion transmsion le. le. Compared with manual count results transmsion le on origal, Compared with manual count results transmsion le on origal, recognition error <1 pixel, as shown Table 2. recognition error <1 pixel, as shown Table 2. Table 2. Power transmsion le detection results. Table 2. Power transmsion le detection results. Detection Results A C /Pixel AC/Pixel Least Detection squares Hough Results transform A C /Pixel 8.46 AC/Pixel Manual count Least squares Hough transform Manual count 8 28 refore, recognition algorithm based on least squares Hough transform can accurately detect transmsion le. known transmsion le ACSJ-400/50, refore, recognition algorithm based on least squares Hough transform can accurately whose diameter mm, so icg thickness D = mm can be calculated by (17). detect transmsion le. known transmsion le ACSJ-400/50, whose diameter mm, so icg thickness D = mm can be calculated by Equation (17) Comparon with Or Image Recognition Methods Although we do not know real icg thickness on monitorg pot, real average icg thickness entire transmsion le mm, so average icg thickness entire transmsion le can be used as a reference for icg thickness at monitorg pot to verify its correctness. We tested or recognition methods 2 calculate icg thickness. fal results are shown Table 3. Table 3. Calculated icg thickness based on different recognition methods. Image Recognition Method Real Icg Thickness/mm A/mm B/mm C/mm D/mm Icg thickness Notes: Method A least squares Hough transform method. When s are obtaed, method B simply averages vertical coordates upper outle lower outle transmsion le as transmsion le s dtance [10,24]; Method C searches for dtance between upper lower transmsion le to obta maximum dtance as transmsion le s dtance [25], n method D uses Hough transform to fit two rom pots on transmsion le s to calculate slope transmsion le s [16]. As can be seen from Table 3, error method D largest calculated icg thickness results. In th method, we have used 10 sets two rom pots on transmsion le s to calculate icg thickness. resultg icg thickness, which ranges from mm to mm, depends on accuracy two rom pots n produces very unstable results. Method C uses maximum dtance transmsion le s to calculate icg thickness, so resultg error largest methods A, B C. Obviously, calculated icg thickness from method A method B are closest to real icg thickness. Compared with method A, method B accumulates all pixel coordates to compute an average, which can require a large amount

14 Energies 2017, 10, calculation. In summary, recognition algorithm based on least squares Hough transform can accurately detect calculate icg thickness. Moreover, it s an easy stable algorithm. 6. Conclusions Aimg at shortcomgs current icg thickness detection methods for transmsion les, a new recognition method for icg thickness on transmsion les based on a least squares Hough transform proposed th paper. Firstly, grayscale s un-iced transmsion les iced transmsion les are obtaed by grayscale processg. Secondly, accordg to prciple preservg transmsion le s removg non-s, we set self-adaptation dual threshold based on gradient change n detect s by a Canny operator. Thirdly, Hough transform combed with least squares method to accurately detect transmsion le s get pixel coordate equations optimal sgle pixel s. Fally, accordg to imagg prciple camera real radius un-iced transmsion le, geometric calculation model for icg thickness establhed to achieve automatic calculation icg thickness. algorithm can be used to accurately extract transmsion le s s with complex backgrounds noe terference. It solves shortcomgs traditional Hough transform parameter space which easy to be dturbed by background noes, n realizes automatic calculation icg thickness. refore, th paper explores a new approach to recognition icg thickness. It proved that method sensitive to background noes, identification errors transmsion le s are less than 1 pixel. Furrmore, th method simple easy to program, has a certa practicality. Acknowledgments: Th work was supported part by National Natural Science Foundation Cha (Grant Number ) part by National Natural Science Foundation Cha (Grant Number ). Author Contributions: All authors conceived designed study. Under guidance Junhua Wang Jiangui Li, Jgjg Wang implemented methodology with asst Jianwei Shao. Jgjg Wang, Junhua Wang Jiangui Li wrote document, all authors read approved fal manuscript. Conflicts Interest: authors declare no conflict terest. References 1. Jiang, X.; Xiang, Z.; Zhang, Z.; Hu, J.; Hu, Q.; Shu, L. Predictive model for equivalent ice thickness load on overhead transmsion les based on measured sulator strg deviations. IEEE Trans. Power Deliv. 2014, 29, [CrossRef] 2. Hu, J.; Sun, C.; Jiang, X.; Xiao, D.; Zhang, Z.; Shu, L. DC flashover performance various types ice-covered sulator strgs under low air pressure. Energies 2012, 5, [CrossRef] 3. Hu, J.; Sun, C.; Jiang, X.; Yang, Q.; Zhang, Z.; Shu, L. Model for predictg DC flashover voltage pre-contamated ice-covered long sulator strgs under low air pressure. Energies 2011, 4, [CrossRef] 4. Hu, J.; Jiang, X.; Y, F.; Zhang, Z. DC flashover performance ice-covered composite sulators with parallel air gaps. Energies 2015, 8, [CrossRef] 5. Ma, T.; Niu, D. Icg forecastg high voltage transmsion le usg weighted least square support vector mache with fireworks algorithm for feature selection. Appl. Sci. 2016, 6, 438. [CrossRef] 6. Hou, H.; Y, X.; You, D.; Chen, Q.; Tong, G.; Zheng, Y.; Shao, D. Analys defects equipment 2008 snow daster sourn Cha area. High Volt. Eng. 2009, 35, X, G.; J, X.; Hu, X. On-le monitorg system transmsion le icg based on DSP. In Proceedgs th IEEE Conference on Industrial Electronics Applications (ICIEA), Taichung, Taiwan, June 2010; pp Qi, L.; Wang, J.; Chen, Y. Research on segmentation icg le based on NSCT 2-D OSTU. In Proceedgs th International Conference on Modellg, Identification Control, Sousse, Tunia, December 2015; pp. 1 5.

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