Improved Jitter Elimination and Topology Correction Method for the Split Line of Narrow and Long Patches

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1 International Journal Geo-Information Article Improved Jitter Elimation Topology Correction Method for Split Le Narrow Long Patches Chengmg Li 1, Yong Y 1,2, *, Pengda Wu 1, Xiaoli Liu 1 Peipei Guo 1 1 Chese Academy Surveyg Mappg, Beijg , Cha; licm@cm.ac.cn (C.L.); wupd@cm.ac.cn (P.W.); liuxl@cm.ac.cn (X.L.); guopp@cm.ac.cn (P.G.) 2 College Geomatics, Shong University Science Technology, Qgdao , Cha * Correspondence: yyong@cm.ac.cn; Tel.: Received: 10 August 2018; Accepted: 30 September 2018; Published: 11 Ocber 2018 Abstract: Extractg le narrow long patches is important for generalization l-use matic data. There two commonly used methods for extractg les: One is bed on Delaunay triangulation or is bed on skelens. However, it is difficult for skelen method preserve geometric structure pological consistency with origal data when dealg with polygons that have irregularity complexity junctions. Therefore, we propose an improved jitter elimation pology correction method for les bed on a constraed Delaunay triangulation. First, a le adjustment algorithm bed on geometric structure polygon is proposed elimate jitters. Second, a le pology correction algorithm is proposed for nodes with degree 1 or degree 2, considerg boundary pological constrat. The reliability proposed method is verified by comparg it with skelen method usg sample data superiority proposed method is verified by usg actual data from Cha s al conditions census Guizhou provce. Keywords: narrow long patches; le; constraed Delaunay triangulation; jitter elimation; le pology correction 1. Introduction Accordg Van Oosterom [1] Beard Mackaness [2], le plays an important role matag complete coverage non-overlappg spatial characteristics patch data before after ir generalization, because it is key element collapse dissolve operars for patch polygons. However, extractg patch le accurately effectively is still a difficult problem [3], especially ce irregularly shaped patches, such small patches well long narrow patches. This study focuses on extraction, jitter elimation, pology correction algorithms for le long narrow patches. A long narrow patch refers a polygon object with a rar large length small width, such slender rivers, low-grade roads highways, ridges ditches. In general, a long narrow patch connects patches different l feature types is an important map element for matag ensurg connectivity among patches. Accordg defition fe bendg given by Mitropoulos et al. [4], width long narrow patches can be calculated by followg equation: W = S/BL, where W is approximate average width patch, S is patch a, BL is lengthwise bele determed by longest skelen le patch. Accordg roughness drawg pen resolution human eye, Muller [5] defes 0.4 mm mimum distance visual resolution on map, so when width W a long narrow ISPRS Int. J. Geo-Inf. 2018, 7, 402; doi: /ijgi

2 ISPRS Int. J. Geo-Inf. 2018, 7, patch, such a road, river, canal, or trench, is under 0.4 mm, planar patch can be treated a long narrow patch. Splittg a long narrow patch h been studied when generalizg l use data, with skelen le patch primary le. There many research works on generation skelen les, skelen le calculation algorithms bed on bic geometric shapes, such Voronoi diagram Delaunay triangulation, very effective. However, although a le is constructed bed on skelen le, it is different from a skelen le because it not only expresses ma shape objects but also takes account spatial structure pological relations objects. As such, this paper proposes an improved jitter removal pology correction method for le long narrow patches. Our method optimizes consistency structural characteristics pological relationship produce les accordance with a human s cognition. The remader this paper is organized follows. Section 2 reviews related works on le extraction. Section 3 analyzes advantages disadvantages skelen method its optimization. Section 4 describes our improved le extraction method with constraed Delaunay triangulation (CDT), achievg le jitter removal pology correction. Section 5 demonstrates experiments analyses. Section 6 presents discussion conclusions. 2. Related Works Skelen extraction operars may be divided two types accordg different source data: Rter-bed vecr-bed skelen extraction methods. This study falls latter category. At present, three methods used extract les long narrow patch, namely rounded skelen les, skelen les, triangulation-bed skelen les. Rounded skelen les. Lee [6] Montanari [7] proposed rounded skelen le methods, i.e., medial axis tg methods. These rounded skelen les calculated usg a Voronoi diagram polygon boundary its vertices. Rounded skelen les consist two parts, namely parabol les. The parabol make les smoor at polygon bends. However, this algorithm is considerably complex design. Consequently, it is difficult optimize structural characteristics features furr. Triangulation-bed skelen les. Owg excellent properties Delaunay triangulation, such proximity, optimality, regionality, convexity polygons [8,9], scholars have performed considerable research [10 12] on extraction polygon skelen les bed on Delaunay triangulation well practical applications. DeLucia Black [13] first proposed extraction polygon skelen les bed on a CDT clsified triangles triangular mesh three categories bed on number polygonal edges present at three sides a triangle. Skelen le extraction for each type triangle w described, this formed foundation for subsequent research. Li [14] clsified skelen nodes Delaunay triangulation, tracked ma skelen le polygon reflect representative shape features ma extension direction polygon. Zou Yan [15] used CDT construct skelen for polygons proved that method w effective. However, Morrison Zou [16] supposed that method proposed by Zou Yan [15] sometimes produces triangles that do not represent true nature underlyg shape; refore, y put forward an improved algorithm by sertg new triangulation pots strategic locations end, normal, junction triangles. As noted by Pennga et al. [17], direct extraction skelen les with boundary-cdt suffers from at let followg three drawbacks: (1) skelen les at branch junctions appear be sawoth-like; (2) ty bumps at boundary lead extraneous spiked skelen les; (3) fewer boundary nodes result elongation skewg skelen les. To solve third problem, Uitermark et al. [18] Pennga et al. [17] suggested constructg a conformal constraed Delaunay

3 ISPRS Int. J. Geo-Inf. 2018, 7, triangulation (CCDT) by addition Steer nodes boundary. Uitermark et al. [18] also tackled second problem by boundary simplification, however, this led pology error boundary tersection. Pennga et al. [17] stead tried solve second problem by settg a mimum a threshold for triangles remove ty bumps along boundary, y achieved good results. Regardg first problem, Jones et al. [19] study T -shaped junction, y noted that sar re is only one type III triangle present, this triangle can be adjusted by calculatg direction three sociated skelen le branches. However, this method cannot be used on + -shaped branches that have two adjacent type III triangles. On this issue, Pennga et al. [17] proposed connectg four skelen le branches midpot common edge two type III triangles for skelen adjustment, which better solves this type problem + -shaped junction. In addition, some research h focused on dealg with X - Y -shaped junction [20]. Neverless, existed research could only solve relatively simple problems skelen les extracted by Delaunay triangulation; re few methods for junctions with complex features, such multiple type III triangles or skelen le branches different directions. Straight skelen les. Aichholzer et al. [21] proposed a skelen le construction method; skelen les extracted usg this method structurally simple, contag only le segments. The itial algorithm is only applicable simple polygons. D et al. [22] extended scope algorithm monone polygon. A simple polygon P is said be monone with respect a le L if its tersection (if any) with any le perpendicular L is connected. Eppste Erickson [23] improved efficiency algorithm by usg a technique developed by Eppste for matag extreme bary functions. Haunert Sester [24] applied skelen algorithm solve problem a collapse generalization, which refers geometry type changes from a le for d multiple representation. The results ir study showed that skelen is a powerful ol for generalization. Furrmore, Haunert Sester [25] compd generation results three above-mentioned types skelen les highlighted advantages skelen les when treatg le jitter redundant le terference ir extraction. Straight skelens have good geometric properties computational efficiency. As such, skelen les better suited extraction a patch le. Furrmore, Haunert Sester [25] studied dimension-reduction long narrow patches usg skelen les, amended convergence multiple nodes roads, enablg application skelen les simple polygon tg. The triangulation-bed skelen le method skelen le method two commonly used methods for extractg les; Haunert Sester [25] suggested that latter method is better suited extraction a patch le. However, re still many complex situations that difficult deal with. To illustrate this, advantages disadvantages skelen le method its optimization furr analyzed Section 3. To alleviate limitations skelen le method, improved le extraction method with CDT is proposed Section Advantages Disadvantages Straight Skelens Straight skelen les a common method for extractg le narrow long polygons. Previous studies have that skelen is a powerful flexible ol for a collapse algorithm preserves pological relationships. However, this method leads accurate generalization results ce irregularity complexity junctions. In this section, we discuss systematic analysis advantages disadvantages skelen algorithm its improved version. The formation a skelen can be regarded an ward contraction process sides a polygon at a constant rate. Edge collisions durg contraction process treated by edge

4 ISPRS Int. J. Geo-Inf. 2018, 7, events segmentation events, eventually formg a skelen composed vertex angle bisecrs ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 4 17 ISPRS Int. J. Geo-Inf. 2018, 7, FOR PEER REVIEW 17 polygon, by thick le Origal Origal Method Method for for Straight Straight Skelens Skelens Advantages Advantages Split Split les les extracted extracted bed bed on on on skelen skelen method method have have have followg followg advantages: advantages: (1) (1) (1) each each each le le le segment segment skelen skelen is is is longest longest le le segment segment found found on on polygon polygon medial medial axis axis (2) (2) no no extraneous extraneous spikes spikes generated generated near near boundary boundary polygon polygon formation formation a a skelen. skelen. As As As Region Region A A 1, 1, 1, when when a light slight jitter jitter appears appears at at polygon polygon boundary, boundary, skelen skelen formed formed describes describes jitter jitter jitter well well well without without without producg producg extra extra extra spikes. spikes. spikes. The The two two The two advantages advantages noted noted noted above above above make make make skelen skelen les les les a agood good reflection reflection ma ma structural structural characteristics characteristics polygons, polygons, suitable suitable for for extractg extractg les les more more regular, regular, simple simple polygons. polygons. 1. Straight skelens Disadvantages Disadvantages The The extracted extracted skelen skelen les les cannot cannot be be directly directly used used les les for for actual actual objects, objects, cludg cludg roads roads river river river systems, systems, systems, which which which ten ten ten have complex have have complex complex structural structural structural characteristics, characteristics, characteristics, because because because se se se not visually not not visually visually pleg. pleg. pleg. Haunert Haunert Haunert Sester [25] Sester Sester discussed [25] [25] discussed discussed three key three three problems key key problems problems with with with skelens skelens skelens a detailed a manner. detailed detailed As manner. manner. As As 2, thicker 2, 2, le thicker thicker le le figure is figure figure is is le which le le is extracted which which is is from extracted extracted from from skelen les. skelen skelen First, les. les. re First, First, many re re branches many many branches branches at boundary at at boundary boundary between between between two two two objects. When objects. objects. two-dimensional When When two-dimensional two-dimensional (2D) long (2D) (2D) narrow long long a narrow narrow a a elements elements elements reduced 1D reduced reduced le elements 1D 1D with le le se elements elements primary with with se se primary primary skelens, pological skelens, skelens, relation between pological pological two neighborg adjacent objects (polygons) cannot be preserved, 2a. relation relation between between two two neighborg neighborg adjacent adjacent objects objects (polygons) (polygons) cannot cannot be be preserved, preserved, Second, multiple nodes present certa parts objects (such corners) at a close distance. 2a. 2a. Second, Second, multiple multiple nodes nodes present present certa certa parts parts objects objects (such (such corners) corners) The skelens extracted se regions will be considerably dense. As 2b, at at a close close distance. distance. The The skelens skelens extracted extracted se se regions regions will will be be considerably considerably dense. dense. As As re a large number skelens Box B at bend. Third, branches (three or more) 2b, 2b, re re a large large number number skelens skelens Box Box B at at bend. bend. Third, Third, branches branches multiple objects converge, more connectg nodes appear, leadg jitter (three (three or or more) more) multiple multiple objects objects converge, converge, more more connectg connectg nodes nodes appear, appear, leadg leadg skelen this region, which does not correspond primary shape actual jitter jitter skelen skelen this this region, region, which which does does not not correspond correspond primary primary shape shape objects, 2c. actual actual objects, objects, 2c. 2c. 2. Problems with extractg skelens: (a) (a) changes pological relation relation at end, 2. Problems with extractg skelens: (a) changes pological relation at end, (b) dense (b) dense skelens skelens (c) jitter (c) jitter at at branch branch junctions. junctions. end, (b) dense skelens (c) jitter at branch junctions Optimization Optimization Method Method for for Straight Straight Skelens Skelens A pologically pologically constraed constraed correctg correctg algorithm, algorithm, a skelen skelen elimation elimation algorithm, algorithm, a connection connection pot pot reconstruction reconstruction algorithm algorithm were were proposed proposed by by Haunert Haunert Sester Sester [25] [25] for for aforementioned aforementioned three three problems, problems, respectively, respectively, optimize optimize a skelen skelen le. le.

5 ISPRS Int. J. Geo-Inf. 2018, 7, Optimization Method for Straight Skelens ISPRS AInt. pologically J. Geo-Inf. 2018, 7, constraed x FOR PEER REVIEW correctg algorithm, a skelen elimation algorithm, 5 17 a connection pot reconstruction algorithm were proposed by Haunert Sester [25] for aforementioned Topologically threeconstraed problems, respectively, Correctg Algorithm optimize a skelen le Topologically Regardg Constraed difficulty Correctg pological Algorithm preservation at boundary between two adjacent objects with directly extracted skelens, Haunert Sester [25] proposed modifyg Regardg clations difficulty pological planes that defe preservation skelen at boundary optimize between skelen. two adjacent 3a is optimization objects with result directly extracted 2a. The optimized skelens, skelen Haunertguarantees Sester [25] uniqueness proposed modifyg tegrity clations le, planes also that defe same pological skelen relationship optimize between skelen. adjacent map 3a is objects. optimization result 2a. The optimized skelen guarantees uniqueness tegrity le, also same pological relationship between adjacent map objects Skelen Elimation Algorithm Skelen Elimation Algorithm The skelen elimation algorithm is essentially an iterative deletion leaf nodes (hangg nodes) The skelen skelen elimation les until algorithm remag is essentially an iterative skelen deletion is medial leaf axis nodes (hangg polygon. nodes) To avoid skelen excessive les or sufficient until remag removal nodes, skelen skelen is medial arcs sociated axis with polygon. nodes To avoid excessive constraed or sufficient terms removal length, width, nodes, angle. skelen arcs3b sociated shows with elimation nodes results constraed from dense termsskelen length, les width, angle. 2b. No redundant 3b shows hangg elimation arc exists results from skelen dense le after skelen this les elimation. 2b. No redundant hangg arc exists skelen le after this elimation Connection Pot Reconstruction Algorithm The The connection pot reconstruction algorithm optimizes skelen by byjog regions where three or or more skelen branches tersect aggregates se tersections a sgle connection pot. The summed squ horizontal distance distance between between this this connection connection pot pot or or tersects tersects must must not not exceed exceed 3 m 3 m [25]. [25]. 3c 3c shows shows adjustment complex mergg situation 2c, 2c, with with a more a more proment proment primary primary shape shape optimized optimized skelen skelen a smoor a connection smoor connection between skelen between les skelen y les merge, y enhancg merge, enhancg readability readability map. map Optimization skelens Haunert Sester [25]: (a) pologically constraed correctg algorithm, (b) (b) skelen skelen elimation elimation algorithm algorithm (c) connection (c) connection pot reconstruction pot reconstruction algorithm. algorithm Existg Problems Optimization Method The Existg optimized Problems skelen Optimization is aptmethod for le. However, some shortcomgs still exist. The First, optimized structural characteristics skelen apt for branch junctions le. However, not some wellshortcomgs preserved. The still method exist. proposed First, by structural Haunertcharacteristics Sester [25] directly branch aggregates junctions tersections not well preserved. branchthe junctions method aproposed sgle connection by Haunert pot, with Sester a suitable [25] directly fittg aggregates outcome fortersections learly extendg branches junctions with jitter. However, a sgle connection this method pot, is not with applicable a suitable fittg branch outcome junctions for learly that extendg morphologically branches complex with jitter. with disturbance However, this features. method The is not structural applicable description branch se junctions that with this morphologically method is ambiguous complex with cannot disturbance represent features. complexthe structures structural well. description For stance, se solid junctions thick les with this method 4b is skelens ambiguous extracted cannot for represent road tersection complex structures 4a well. withfor stance, skelen solid method, thick les which treats 4b branch skelens extracted junctions for road learly tersection extendg 4a les. with For ce 1, ifskelen talmethod, skelen length which treats type branch II triangles skelens between junctions two branch learly nodes is extendg less than a widthles. threshold, For ce 1, if tal skelen length type II triangles between two branch nodes is less than a width threshold, distance between tersection pots extended branch les is less than width threshold each aggregation region, 4b looks much better than 4c. However, for ce 2, if tal skelen length type II triangles between two branch nodes is larger than a width threshold distance between tersection pots extended branch les is

6 ISPRS Int. J. Geo-Inf. 2018, 7, distance between tersection pots extended branch les is less than width threshold ISPRS each aggregation Int. J. Geo-Inf. 2018, region, 7, x FOR PEER 4b REVIEW looks much better than 4c. However, for ce 2, if 6 tal 17 ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 6 17 skelen length type II triangles between two branch nodes is larger than a width threshold larger larger than than distance width width between threshold, threshold, tersection bis bis pots references references extended [17,25], [17,25], branch local local lesstructural structural is larger than feature feature is is width very very important, threshold, important, on which which bis can t can t be be references ignored, ignored, [17,25], 4c 4c is is local much much structural better better than than feature is4b, very which which important, reflect reflect which accurately accurately can t be ignored, nature nature object. object. 4c is much The The structural better structural thanfeatures 4b, which by by reflect solid solid accurately thick thick les les nature rectangle rectangle object. The structural 4c 4c should should features be be retaed. retaed. by solid thick les rectangle 4c should be retaed Retag structural features branch junctions: (a) branch junctions, (b) skelen les extracted with Haunert Sester (2008) (c) medial axis branch junctions. Moreover, no consideration is given nodes with degree 2 on skelen. The concept degree a node comes from graph ory is defed follows: Defition The out-degree (OutDeg) a node is tal number arcs comg out node. Defition The -degree (InDeg) a node is tal number arcs termatg at node. Defition The degree a node (Deg) is sum its Outdeg Indeg. Haunert Sester [25] defed degree all nodes on skelens a polygon follows: The degree nodes connected boundary is 1, because each node is is related only one one arc arc ma skelen, degree nodes side polygon is is greater than 3, 3, because se se nodes were formed by by edge events segmentation events; y sociated with at at let three three arcs arcs ma skelen. Bed on this analysis, method by Haunert Sester [25] does not not consider nodes nodes with with degree 2 on on polygon skelen. Thus, only simple polygons with no no self-tersection can can be be treated by by method. However, matic l-use data come various shapes shapes self-tersection evitable durg process collapse operations operations for for narrow for narrow narrow long patches long long patches patches with different with with different different semantic semantic semantic attributes. attributes. attributes. Some nodes Some Some nodes thus shd thus thus by boundaries shd shd by by boundaries extendg boundaries extendg different directions, different different directions, directions, Nodes with degree Nodes with degree 2. In 5, Node O, which is on boundary polygon, is tersection pot four In 5, Node O, which is on boundary polygon, is tersection pot four adjacent arc segments: OA, OB, OC, OD. In ory, rational le this polygon should adjacent arc segments: OA, OB, OC, OD. OD. In In ory, rational rational le le this this polygon polygon should should be be same thick le 5. Node is sociated with two arc segments, OE OF, be same same thick thick le le 5. Node 5. Node O iso sociated is sociated with with two two arc arc segments, segments, OE OE OF, OF, skelen. Hence, degree Node O is 2. However, method by Haunert Sester skelen. Hence, degree Node O is 2. However, method by Haunert Sester 25 cannot provide arc segment OF for skelens. 25 cannot provide arc segment OF for skelens.

7 ISPRS Int. J. Geo-Inf. 2018, 7, skelen. Hence, degree Node O is 2. However, method by Haunert Sester 25 ISPRS cannot Int. J. Geo-Inf. provide 2018, 7, arc x FOR segment PEER REVIEW OF for skelens Improved Jitter Elimation Topology Correction Method for Split Le In light shortcomgs dimension-reduction (partitiong mergg) long narrow polygons usg aa skelen its its optimization, this this paper paper proposes proposes an improved an improved le extraction le extraction method method with with CDT, CDT, achievg achievg le jitter le removal jitter removal pology pology correction correction bed on bed geometrical on geometrical features features pological pological constrats, constrats, respectively. respectively Delaunay Triangulation Skelen le construction with with CDT CDT is anor is anor method method for le for extraction, le extraction, considerable research considerable h been research carried h out been carried this field. out Triangles this field. a Delaunay Triangles triangular a Delaunay network triangular can benetwork divided can three be divided clses type three I, typeclses type II, III bed I, type II, on number type III bed ir neighborg on number triangles ir polygon neighborg [13]. triangles polygon [13]. Type I triangles have only one adjacent triangle. The two sides type I triangles boundaries polygon. Examples ABG, CDE, EFG 6 6 which vertices A, A, D,, D,, F F end end pots pots skelen skelen les. les. Type Type II triangles II triangles have have two two adjacent adjacent triangles. They They backbone skelen les, les, describg extension direction origal polygon, such BCE The The skelens type type II triangles II unidirectional. Furr, Furr, Type Type III triangles III triangles have have three three adjacent adjacent triangles; triangles; y y located located at tersection skelen branches, which is orig from where les extend three directions. One example is BEG 6, where branches extend three directions at Pot L. The Delaunay triangulation method extracts medial axis for three types triangles followg ways connects medial axis form skelen le. The common edge two adjacent triangles is called adjacent edge. With type I triangles, midpot only adjacent edge is connected its correspondg vertex, such les les AH, AH, DJ, DJ, FK FK 6. With 6. With type IItype triangles, II triangles, midpots midpots two adjacent two edges adjacent edges connected, connected, such le such IJ le IJ 6. With type 6. With III triangles, type III triangles, center center gravity gravity midpots midpots three sides three sides connected, connected, such les such LI, les LK, LI, LK, LH LH Delaunay triangle clsification. Steer nodes some additional nodes which used cree node density between adjacent nodes with larger distances. These nodes need be added around boundary each polygon when constructg triangulation network for narrow long patches. This is because origal nodes ten used describe important morphological characteristics polygons, e.g., flection nodes tersection nodes. nodes. However, However, nodes nodes generally generally smaller, smaller, triangles triangles stretched ward stretched seward pots when se constructg pots when triangulation. constructg As Delaunay triangulation. triangulation As Delaunay consists triangulation more nodes, consists thus more triangles, nodes, thus resultg more skelen triangles, is expected resultg be skelen smoor. is The expected specifics be this smoor. procedure The specifics follows: this First, procedure a densification follows: step, D, First, is defed, a densification where Dstep, is equal D, is defed, 0.4 mm or where a multiple D is equal mm. mm Inor this a multiple study, we use mm. mm In this (4 study, 0.4 mm) we use a 1.6 D value. mm (4 Samplg 0.4 mm) is n a D value. Samplg is n performed between two origal nodes spacg D obta Steer pots, 7.

8 ISPRS Int. J. Geo-Inf. 2018, 7, performed between two origal nodes spacg D obta Steer pots, ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 8 17 ISPRS Int. 7. J. Geo-Inf. 2018, 7, FOR PEER REVIEW Addg Steer nodes: (a) Origal nodes a elements (b) Steer nodes. 7. Addg Steer nodes: (a) Origal nodes a elements (b) Steer nodes Split Le Jitter Removal Bed on Geometric Features 4.2. Split Le Jitter Removal Bed on Geometric Features Spike Jitter Adjustment Algorithm Spike Jitter Adjustment Algorithm The most pressg problem le extraction with Delaunay triangulation is that if The most pressg problem le extraction with Delaunay triangulation is that if polygon boundary is is not considerably smooth, jitter jitter will will be be amplified on on les les even even polygon boundary is not considerably smooth, jitter will be amplified on les even ce ce a slight a slight jitter, jitter, thus thus formg formg spikes spikes that that difficult difficult elimate; elimate; for example, for example, skelen skelen le ce slight jitter, thus formg spikes that difficult elimate; for example, skelen le box Abox A 8a. 8a. le box 8a. The cause for spike jitter (see 8a) lies extraction method for type III triangle skelen The cause for spike jitter (see 8a) lies extraction method for type III triangle skelen les; i.e., center gravity is taken central pot triangle is connected les; i.e., center gravity is taken central pot triangle is connected midpots three edges form skelen le. In this manner, when ty sharp triangles midpots three edges form skelen le. In this manner, when ty sharp triangles appear on polygon boundary, les connectg center gravity midpots appear on polygon boundary, les connectg center gravity midpots two edges will be fset, resultg deviation skelen formed from origal extension two edges will be fset, resultg deviation skelen formed from origal extension direction. Therefore, we propose an algorithm correct for spike jitter by fdg an alternative direction. Therefore, we propose an algorithm correct for spike jitter by fdg an alternative triangle center. triangle center. The bic idea fdg an an alternative triangle triangle center center is firstly is firstly arrange arrange length length three The bic idea fdg an alternative triangle center is firstly arrange length three edges three edges a type a III type triangle III triangle with with jitter. jitter. The order The order cendg cendg length length consists consists three three edges: edges: The edges type III triangle with jitter. The order cendg length consists three edges: The shortest The shortest side side (SS), (SS), middle middle side side (MS), (MS), longest longest side side (LS). (LS). If If SS SS MS shortest side (SS), middle side (MS), longest side (LS). If SS MS approximately equal length (SS MS), LS is marked. If If MS LS approximately approximately equal length (SS MS), LS is marked. If MS LS approximately equal length (MS LS), SS SSis ismarked. If Ifnone above conditions is ismet, no action is istaken. equal length (MS LS), SS is marked. If none above conditions is met, no action is taken. The length difference between two sides must be less than mimum visually distct distance The length difference between two sides must be less than mimum visually distct distance 0.4 mm if it is be called approximately equal. Connect midpot marked edge its 0.4 mm if it is be called approximately equal. Connect midpot marked edge its correspondg vertex. Then, midpot connectg le is taken alternative center correspondg vertex. Then, midpot connectg le is taken alternative center type III triangle, which is joed midpots two unmarked edges form skelen type III triangle, which is joed midpots two unmarked edges form skelen le, 8b. le, 8b. 8. Spike jitter adjustment algorithm: (a) spike jitter (b) adjustment result spike jitter. 8. Spike jitter adjustment algorithm: (a) spike jitter (b) adjustment result spike jitter Jitter Adjustment Algorithm for Branch Junctions Jitter Adjustment Algorithm for Branch Junctions The key skelen le extraction at at branch junction region is mata local structural The key skelen le extraction at branch junction region is mata local structural features, which volves preservg lear extension each skelen le branch ensurg features, which volves preservg lear extension each skelen le branch ensurg shape consistencybetween between skelen le le this this region region actual actual object. object. The shape consistency between skelen le this region actual object. The followg The followg algorithm algorithm is thus is thus proposed proposed correct correct jitter jitter at at branch convergence region any followg algorithm is thus proposed correct jitter at branch convergence region any arbitrary shape. arbitrary shape. Step 1: Identifyg branch junctions. The pological relation between nodes arcs is Step 1: Identifyg branch junctions. The pological relation between nodes arcs is established for polygon skelen le a be generalized, branch junctions established for polygon skelen le a be generalized, branch junctions identified accordg degree nodes. Danglg nodes first removed from pology identified accordg degree nodes. Danglg nodes first removed from pology for more accurate efficient identification. The retaed nodes arcs used cidate for more accurate efficient identification. The retaed nodes arcs used cidate set; if re exist any nodes whose Degnode 3, n node s location is identified branch set; if re exist any nodes whose Degnode 3, n node s location is identified branch

9 ISPRS Int. J. Geo-Inf. 2018, 7, Step 1: Identifyg branch junctions. The pological relation between nodes arcs is established for polygon skelen le a be generalized, branch junctions identified accordg degree nodes. Danglg nodes first removed from pology for more accurate efficient identification. The retaed nodes arcs used cidate set; if re exist any nodes whose Deg node 3, n node s location is identified branch junction. Type III triangles contag se nodes also noted. Step 2: Determg aggregation zone. In an actual cargraphic databe, several type III triangles can be adjacent, givg rise dense branch nodes; or y can be far apart, leadg dispersed branch nodes. Therefore, adjustment scope for each branch node (i.e., node aggregation zone) needs be determed before skelen is adjusted a branch junction for objects at any location. This scope can be determed by skelen length between two branch nodes. In this study, two branch nodes form itial boundary an aggregation region when tal skelen length type II triangles between m is less than a width threshold ( 0.4 mm). All or nearby branch nodes fulfillg this aggregation criterion placed at boundary pot set, y ger form aggregation zone. All nodes, cludg branch nodes, marked fittg nodes. If tal skelen length type II triangles between two branch nodes is more than or equal 0.4 mm, skelen le segment describes a structure that cannot be directly corporated, skelen needs be retaed. As 9a, only one type II triangle is present between branch nodes N1 N2, its skelen length is below width threshold 0.4 mm. The two nodes refore constitute an aggregation region (oval a), whose terior nodes all fittg nodes. Multiple type II triangles exist between branch nodes N1 N3, with tal skelen length above 0.4 mm. These skelen les n kept. Step 3: Node fittg aggregation region. Direction consistency is an important condition for conformance skelen extracted visual perception rules; however, less attention is paid this existg literature. Haunert Sester [25] stipulated that if three or more skelen les extended one pot, n that pot is fittg node. However, such a strong constrat is unsuitable situations with complicated branch junctions. Thus, accordg our proposal, nodes fittg region aggregated considerg direction nearby skelen les, such that if difference between azimuth angles two skelen les at a branch node is less than angle threshold (δ angle ), two les said be same direction. Accordg a large number experiments, this value δ angle is set 5 degrees this article. The followg algorithm is suggested for nodes fittg aggregation region, accordg skelen le direction features: (1) Branch skelen les with same direction connected preferentially a le. The or branch skelen les extended this le along ir respective directions. (2) If two skelen les which same direction did not exist, Euclidean distance between nodes is taken a similarity meurement. The fittg node is aggregated geometric center aggregation zone. The branch skelen les n connected fittg nodes along ir respective directions. Two key problems encountered here: The calculation skelen le direction re-aggregation extension les. The skelen le direction refers its ma extension direction, which, triangular network, is steady direction formed by nodes type II triangles next type III ones. However, type III triangle usually found branch junctions, direction formed by neighborg type II triangles at a bend cannot represent direction branch skelen le well. The large number nodes at boundary result dense type II triangles, length ir skelen les is usually less than distance node encryption distance (D). If skelen le length type II triangles is less than distance threshold (δ TD ), it w recognized filtered skelens at bends. The value δ TD is set 1/4D this article. For any type III triangle, type II triangles connected it recognized by adjacency. The azimuth length each type II triangle calculated order. If skelen le a

10 ISPRS Int. J. Geo-Inf. 2018, 7, type II triangle Li < TD, triangle is filtered until four consecutive triangles found with a uniform skelen le direction, where L i TD. The direction is taken skelen le direction. If, after a ISPRS certa Int. number J. Geo-Inf. 2018, type 7, x II FOR triangles PEER REVIEW computed, four triangles determg direction 10 still 17 not found, overall curvature branch skelen is said be large. At this time, direction four four triangles closest closest type type III III triangle triangle is taken is taken skelen le le direction. As 9b, pots P1 P2 on skelen L3 around a bend. The type II triangles y belong filtered because because y y cannot cannot form form a uniform a uniform skelen skelen le direction, le direction, direction direction arc segments arc formed segments by formed P3, P4, P5, by P6, P3, P4, P7 P5, meets P6, P7 aforementioned meets aforementioned requirements; requirements; refore, it is refore, used it skelen is used direction, skelen with direction, P3 with startg P3 node startg direction. node direction. 9. Two key steps jitter adjustment algorithm for branch aggregation region: (a) defg aggregation region (b) computg skelen le direction. When aggregation region is sufficiently wide, extendg along respective directions merge branch skelens will not guarantee tersection extended branch les at same pot. Therefore, nodes extension les closer each or need be re-aggregated if distance between two m is is lower than mimum width threshold. Because pots pots on on same same le, le, this this re-aggregation is is performed by by fittg each node bed on ir average on horizontal axis. As seen 10, skelen les L1 L2 have an identical direction preferentially connected form a a le, with or branches extendg it. it. In In 10a, 10a, distance between tersection pots skelen les L3 L4 is greater than 0.4 mm, so structure rem unchanged. In 10b, distance between tersection pots skelen les L3 L4 is less than 0.4 mm, so it is fitted middle node, 10c. 10. Re-aggregation extended les: (a) (a) ter-node distance > TD, > TD, (b) (b) ter-node distance distance < TD < TD (c) re-aggregated (c) skelen skelen le. le Split Le Topology Correction 4.3. Split Le Topology Correction To seamlessly partition long narrow patches, followg pological constrats at To seamlessly partition long narrow patches, followg pological constrats at polygon boundary must be imposed: (1) every le needs termate at a boundary node polygon boundary must be imposed: (1) every le needs termate at boundary node adjacent polygon (2) boundary nodes every neighborg polygon must cocide with a le end pot. The terior les a polygon extracted with Delaunay triangulation should not stretch patch boundary. Orwise, external skelen les will fail lk terior les, resultg a pological difference between extracted skelen les origal map,

11 ISPRS Int. J. Geo-Inf. 2018, 7, adjacent polygon (2) boundary nodes every neighborg polygon must cocide with a le end pot. The terior les a polygon extracted with Delaunay triangulation should not stretch patch boundary. Orwise, external skelen les will fail lk terior les, ISPRS resultg Int. J. Geo-Inf. a pological 2018, 7, x FOR difference PEER REVIEW between extracted skelen les origal map, which11 n 17 requires le pology correction Topology Correction for Nodes with Degree Topology Correction for Nodes with Degree 1 The boundary nodes which sociated with adjacent polygon only lk one skelen arc side The boundary polygon. nodes As such, which this is sociated called a sgle withnode adjacent polygon polygon, onlyhavg lk one a degree skelen arc 1 on side polygon. le. As As such, this is called 11a, anode sgle A node is a sgle node polygon, polygonal havg a degree P1. In 1 on11b, nodes le. A As B sgle nodes 11a, node polygon A is a sgle P2. node Because polygonal Delaunay P1. triangulation In 11b, is nodes constructed A B bed sgle on boundary nodes polygon constrats, P2. Because tersection Delaunay pots triangulation adjacent is polygons constructed bed boundary on boundary constrats, polygons be tersection divided (see pots A, B adjacent polygons 11b) must be vertices boundary Delaunay polygons triangles. behowever, divided (see se A, tersection B 11b) pots must do not be vertices connect with Delaunay triangles. les because However, y se not tersection ma pots skelen dole. not It connect is obvious withthat les les because at y sgle nodes not on se ma figures skelen do not le. satisfy It obvious aforementioned that constrat les at imposed sgle nodes by connectg se figures nodes do not adjacent satisfy polygon aforementioned boundaries, constrat thus imposed les byneed pology connectg correction. nodes adjacent polygon boundaries, thus les need pology correction. 11. Topological relation constrats: (a) (a) perpendicular boundary boundary adjacent adjacent polygon polygon (b) at (b) anat angle angle boundary boundary adjacent adjacent polygon. polygon. The The most common method le pology correction is closest pot method [26] triangulation supplement method [27]. However, se two methods have less consideration for extension nature boundary les. les. When When le le boundary boundary le le perpendicular perpendicular each each or, or, effect effect new new le le is is better better (see (see arc arc segment segment AB AB 12a), when two les have anor angle relationship, new le is explicitly blunt (see arc segment BD 12b). Thus, we propose a reverse extension method a complement closest pot method. method. The The bic bic idea idea is is determe determe extension extension direction direction adjacent polygon adjacent boundary polygon boundary accordg accordg positional relationship positional relationship between between two adjacent two boundary adjacent pots boundary near pots patches. near Then, patches. polygon Then, boundary polygon is boundary extended along is extended opposite along direction opposite direction tersect tersect le patches, le patches, boundary nodes boundary connected nodes connected tersection pots tersection get pots les. get As les. As 12a, adjacent 12a, polygon adjacent boundary polygon is reversely boundary extended is reversely from node extended A node from B, node obta A node new B, obta le AB new le AB 12a. In 12b, 12a. adjacent In polygon 12b, boundary adjacent composed polygon boundary nodes A, composed B extends back nodes A, nodes B extends C 1, D 1 back reverse, nodes resultg C1, D1 reverse, newresultg les ACnew 1, BD 1 les AC1, 12b. BD1 12b. Redundant skelenle lebranches, such such C1E C 1 E D1F D 1 F 12b, 12b, need need be deleted. be deleted. The The ma ma operation operation for achievg for achievg this this is iterative iterative deletion deletion danglg danglgarcs arcs skelen pology, while retag new le, until no more danglg arcs found, fal le is obtaed 12c.

12 ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW ISPRS Int. J. Geo-Inf. 2018, 7, ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW Split le pology correction method for nodes with degree 1: (a) closest pot method, (b) reverse 12. extension Split le method pology correction (c) danglg method skelen for for le nodes removal. with with degree degree 1: (a) 1: (a) closest closest pot pot method, method, (b) (b) reverse reverse extension extension method method (c) danglg (c) danglg skelen skelen le le removal. removal Topology Correction for Nodes with Degree Topology Correction for Nodes with Degree The Topology pology Correction origal for Nodes map with is now Degree established. By means pology relationship between The The <nodes, pology pology arcs> origal origal <arcs, arcs>, map map a is is node now now with established. established. degree 2 By By on means means le can pology pology be identified. relationship relationship That is, between between when <nodes, a <nodes, is arcs> arcs> sociated <arcs, <arcs, with arcs>, arcs>, four connected a node with node with arcs degree degree 2 on 2 same on polygon, le le can can node be identified. be identified. h a degree That That is, when 4 is, on when a node a origal is sociated node is polygon with sociated four with a degree connected four connected 2 arcs arcs same le polygon, same side polygon, polygon. node h node When a degree h a usg 4 degree on traditional origal 4 origal method polygon polygon extract a degree a degree 2 onle at 2 on a node le side with le a degree polygon. side 2, When polygon. extracted usg When traditional usg le is consistent method extract traditional method with pology le extract at a origal node with le at polygon, a degree a node with illustrated 2, extracted a degree 2, 13a. extracted Hence, le is consistent we propose le is with a consistent pology pology correction with pology algorithm origal for polygon, a origal le illustrated polygon, a node with illustrated degree 13a. 2, Hence, specific we propose 13a. Hence, process a we for pology propose which is correction a pology follows: algorithm for a le a node with degree 2, specific process for which is follows: correction algorithm for a le a node with degree 2, specific process for which Step 1: With pot O orig, arrange arc segments sociated with O a counterclockwise is follows: Step 1: (or With clockwise) pot O direction, orig, obta arrange adjacent arc segments arc segments sociated before with O after a each counterclockwise arc. For example, Step 1: (or With clockwise) adjacent pot O direction, arcs OB orig, obta OA arrange OD. adjacent arc segments arc segments sociated before with O after a each counterclockwise example, arc. For Step 2: (or Select clockwise) adjacent an arc segment direction, arcs OB romly obta OA itial OD. adjacent arcs arc judge segments spatial before relationship after each between arc. For a example, Step formed 2: Select by adjacent an this arc arc segment arcs itsob romly adjacent OA arcs itial AdjArc OD. arcs (Area judge spatial <Arc, AdjArc> ) relationship origal polygon. between a Step formed 2: Select by an this arc arc segment its romly adjacent arcs itial AdjArc (Area<Arc, arcs judge AdjArc>) spatial relationship origal polygon. between (1) a If formed a isby side this arc polygon its adjacent h arcs a AdjArc le(area<arc, sociated AdjArc>) with pot O, origal no action polygon. is taken. (1) If a is side polygon h a le sociated with pot O, no action is taken. (2) (2) If a is side polygon does not have a le sociated with pot O, closest (1) If a a is is side side polygon polygon h does a not le have sociated a le with sociated pot O, no with action pot is O, taken. closest pot method is applied correct it with le. (2) If pot a method is side is applied polygon correct does it with not have a le. le sociated with pot O, (3) (3) If a is outside polygon, no action is taken. closest If pot a method is outside is applied polygon, correct no action it with is taken. le. In In (3) If 13a, a 13a, Area is Area<OC, outside OD> OD> is is side polygon, no polygon action is taken. h h no no le. It It is n corrected with le OE. Area<OA, In Area <OA, OB> 13a, OB> is side is side Area<OC, OD> is side polygon polygon h h a a h le. le. no As As such, such, le. no It no action is action n is corrected taken, is taken, with le OE. 13b. 13b. Area<OA, OB> is side polygon h a le. As such, no action is taken, 13b. 13. Split le pology correction method for nodes with degree 2: (a) origal polygon (b) correction 13. result. Split le pology correction method for nodes with degree 2: (a) origal polygon (b) 5. Experiments correction result. Results 5. Experiments Results 5. Experiments Our improved Results jitter elimation pology correction method for le narrow Our improved jitter elimation pology correction method for le narrow long long Our patches patches improved w w embedded embedded jitter elimation with with pology WJ-III WJ-III mappg mappg correction workstation workstation method for developed developed le by by Chese narrow Chese Academy Academy long patches Surveyg Surveyg w embedded Mappg. Mappg. with To To WJ-III verify verify mappg reliability reliability workstation our our method, method, developed we we by compd compd Chese Academy Surveyg Mappg. To verify reliability our method, we compd

13 ISPRS Int. J. Geo-Inf. 2018, 7, ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW processg result skelen method with method proposed this paper on onsample data; meanwhile, experiments conducted usg actual data from Cha s al conditions census Guizhou provce verified superiority our method Reliability Test Analysis In order verify reliability our method, les road data Haunert Sester [25] [25] ( 14a) 14a) extracted usg usg our our method method were were compd compd with with les les extracted extracted usg usg skelen skelen method method ( ( 14b). A14b). A boundary-cdt w constructed w constructed for for narrow narrow long patches, long patches, 1.6 mm1.6 w mm set w encrypt set encrypt boundary boundary node. node. The threshold The threshold fittg fittg length length node node junction junction w setw 0.4 set mm, 0.4 mm, extraction extraction results results were obtaed were obtaed ( ( 14c). 14c) Reliability Reliability test test analysis: analysis: (a) (a) origal origal data, data, (b) (b) le le obtaed obtaed with with proposal proposal by by Haunert Haunert Sester Sester [25] [25] (c) (c) le le obtaed obtaed usg usg our our method. method. By observg results 14b,c, le extracted from origal data accordg By observg results 14b,c, le extracted from origal data accordg our method is bically same le extracted by method proposed by Haunert our method is bically same le extracted by method proposed by Haunert Sester [25]. Both les suitably reflect extension direction spatial structure road Sester [25]. Both les suitably reflect extension direction spatial structure network. road network. The transition The transition T - T - + -type + -type its its les les rectangular rectangular box box smooth smooth re re no redundant no redundant hangg nodes. hangg Thus, nodes. it correctly Thus, it summarizes correctly summarizes ma road ma network s road structure, network s confirmg structure, confirmg reliability reliability our method our when method extractg when extractg les. les. It It is is noteworthy noteworthy that that road road data data given Haunert Sester [25] [25] perta perta roads roads a a similar similar width width with a parallel extensionon onboth bothsides. sides. These These regular regular polygons polygons can can be regarded be regarded simple, simple, ir ir les les relativelyey ey extract. However, usg usg connectionpot reconstruction algorithm proposed by by Haunert Sester [25] will result le le extractionerrors errors when data data processed road or or river data with several bends irregular complex junctions. Thus, we evaluated our method usg polygons with irregular features, bedon Cha s al conditions census Guizhou provce. The results described next subsection Superiority Superiority Test Test Analysis Analysis Actual Actual data data from from Cha s al conditions census Guizhou provcew wused used verify superiority our our method preservg spatial structure pological relations irregular complex geomorphic objects. The spatial range data is is 560 squ kilometers, origal scale scale is is 1:10,000, target scale for generalization is 1:100,000. The number jitter elimation pology correction completed experiment is Table 1. Table Statistics jitter elimation pology correction experimental region. Jitter Elimation Topology Correction Total Nodes with Nodes with Total Spike Jitters Jitters Jitters Branch Branch Junctions Nodes with Nodes with Spike Jitters Junctions Degree Degree 1 1 Degree 2 Number Number Proportion (%) Proportion (%) Three ces with actual data bed on conditions were selected verify collapse

14 ISPRS Int. J. Geo-Inf. 2018, 7, ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW ISPRS Three Int. J. ces Geo-Inf. with 2018, 7, actual x FOR PEER data REVIEW bed on conditions were selected verify 14 collapse 17 operation, one ce w selected verify operation. operation, one ce w selected verify operation. operation, The characteristics one ce w region selected verify Ce 1operation. follows: Two branch junctions consistg The characteristics region Ce follows: Two branch junctions consistg six branch The roads a, characteristics b, c, d, e, region f adjacent Ce each 1 or, follows: wheretwo a branch b junctions same consistg direction, six branch roads a, b, c, d, e, f adjacent each or, where same six direction branch roads a, c b, dc, isd, also e, f same, adjacent but length each or, typewhere II triangular a b ternal skelen same direction, direction is also same, but length type II triangular ternal le direction, diagram is direction greater than c 0.4d mm is also between same, but branch length nodes, type II triangular rectangular ternal skelen le diagram is greater than 0.4 mm between branch nodes, box skelen le 15a. In this diagram study, is greater structural than 0.4 features mm between reserved, branch rectangular box 15a. In this study, structural features reserved, nodes, two branch two junctions branch rectangular box 15a. In this study, structural features reserved, two branch junctions processed separately. processed separately. Accordg Accordg direction property, direction property, le is adjusted, le is adjusted, junctions processed separately. Accordg direction property, le is adjusted, 15b. However, 15b. However, distance between distance adjacent between nodes adjacent nodes rectangular rectangular frame frame 15b is 15b. However, distance between adjacent nodes rectangular frame less than 15b 0.4 mm, is less sothan 0.4 mm, leso is furr optimized, le is furr optimized, 15c. The dhed 15c. le The 15b is less than 0.4 mm, so le is furr optimized, 15c. The dhed 15cle shows 15c le shows extracted accordg le extracted accordg method Haunert method Haunert Sester [25]. ASester visual dhed le 15c shows le extracted accordg method Haunert Sester comparison [25]. visual clearly comparison shows clearly that shows proposed that method proposed this method paper this better paper preserves better preserves structural [25]. A visual comparison clearly shows that proposed method this paper better preserves characteristics structural characteristics a. a. structural characteristics a Ce 1: 1: Branch junctions with a consistent direction skelen: (a) origal (a) origal skelen skelen les, (b) les, 15. Ce 1: Branch junctions with a consistent direction skelen: (a) origal skelen les, (b) (b) le extracted from skelen les considerg direction features (c) (c) re-aggregation le extracted from skelen les considerg direction features (c) re-aggregation les les branch junction. les branch junction. The The characteristics region Ce follows: The directions a, b, c, d, e The characteristics region Ce 2 follows: The directions a, b, c, d, branch branch roads not same at road 16a. It is e branch roads roads not not same same at at road road junction junction rectangular rectangular box box 16a. 16a. It is It is thus thus difficult le when fittg thus difficult difficult reconstruct reconstruct connection connection pot pot bed on onbranch branchskelen skelenle leextension extension when when fittg fittg each each branch branch same same we we connect fittg each branch same aggregation node, 16b. Therefore, we connect fittg fittg node node branch le by all all nodes this this a a node branch skelen le derive le by fittg all a geometric center, 16c. It can be that our method appropriately adjusted geometric center, 16c. It can be seen that our method appropriately adjusted skelen le this ce, although it also caused some jitters skelen le region; this is skelen le le this this ce, although it it also caused some jitters skelen le le region; this this is an issue which we shall address future research. an an issue issue which we we shall address future research. 16. Ce 2: Branch aggregation region with no consistent direction skelen: (a) origal Ce Ce 2: Branch 2: Branch aggregation aggregation region region with with no consistent no consistent direction direction skelen: skelen: (a) origal (a) origal skelen skelen les, (b) le extracted bed on branch skelen le extension (c) le les, skelen (b) les, le(b) extracted le bed extracted on branch bed skelen branch le skelen extension le extension (c) le (c) extracted le by extracted by fittg all nodes geometric center. fittg extracted all by nodes fittg all geometric nodes center. geometric center.

15 ISPRS Int. J. Geo-Inf. 2018, 7, 402 x FOR PEER REVIEW ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW The characteristics region Ce 3 follows: The ditches with The characteristics region Ce 3 follows: The ditches with rectangular The characteristics box 17a region have self-tersectg Ce 3 pological follows: structure, The ditches with if skeletal rectangular le is rectangular box 17a have a self-tersectg pological structure, if skeletal le is box extracted directly, 17a have re awill self-tersectg be no skeletal pological le at node structure, degree 2. ifhowever, skeletal after lecorrection is extracted for extracted directly, re will be no skeletal le at node degree 2. However, after correction for directly, skelen rele willat be noboundary, skeletal le at node le w degree obtaed, 2. However, after correction 17b. for It is clear skelen that skelen le at boundary, le w obtaed, 17b. It is clear that le at adjusted boundary, skelen le realized le w obtaed, pology correction at this 17b. site It is clear effectively that adjusted avoided adjusted skelen le realized pology correction at this site effectively avoided skelen pological leerrors. realized pology correction at this site effectively avoided pological errors. pological errors. 17. Ce 3: Self-tersection narrow long patches: (a) skelen le extracted directly (b) le pology correction. Ce 4 is an an example for for operation. operation. A narrow A narrow road road is surrounded is surrounded by by farml, by farml, garden garden l, l, forest forest l l grsl, grsl, 18a. 18a. Then Then le le this thisroad roadw wextracted accordg method method proposed proposed this this paper, paper, 18b. It18b. can It be It can seen be be that seen that tg le tg at le boundary at boundary extends naturally. extends naturally. 18c describes 18c describes result result operation. operation. The result fers The result an appropriate fers an appropriate representation representation for operation for operation l-use matic l-use data matic withdata respect with pological respect pological geometrical geometrical feature. feature. (a) (b) (c) (c) 18. Ce 4: Split operation for narrow long patches: (a) origal data, (b) le narrow long patches (c) result operation Discussion Conclusions Extractg Extractg le le le narrow narrow narrow long long long patches patches patches is is an is an important important important difficult difficult difficult problem problem problem for for for generalization generalization generalization l-use l-use l-use matic matic matic data. data. Extracted data. Extracted Extracted les les need need les take need take account take account natural account natural natural smooth smooth geometric geometric smooth features features geometric features structural structural features structural features that features that accord accord with that with visual accord visual perception with visual perception perception ir ir actual actual ir pological actual pological features. By features. overcomg By overcomg shortcomgs shortcomgs skelen method, skelen an improved method, pological features. By overcomg shortcomgs skelen method, an improved an method improved w method proposed w proposed this paper this extract paper extract les bed les on bed constraed constraed Delaunay method w proposed this paper extract les bed on constraed Delaunay Delaunay triangulation. triangulation. Our method Ourremoves methodjitters removes jitters pology correction pology correction for les for accordgly les accordgly order triangulation. Our method removes jitters pology correction for les accordgly order order solve solve problems problems shape jitters shape jitters pological pological consistency consistency along along skelen skelen le. Test le. solve problems shape jitters pological consistency along skelen le. Test Test results results on sample on sample data data actual actual data data show showthat that our our methodnot not only appropriately results on sample data actual data show that our method not only appropriately extracts les long narrow patches with regular shapes, but also well mat extracts les long narrow patches with regular shapes, but also well mat

16 ISPRS Int. J. Geo-Inf. 2018, 7, extracts les long narrow patches with regular shapes, but also well mat consistency structural features pological relations when dealg with irregular complex polygons. As for our method, densification step (D) plays an important role avoidg fset skelen le at boundary polygon, when calculatg direction each branch le branch convergence zone. If threshold is o large, skeletal le at boundary polygon will appear partial. If threshold value is o small, however, filter type II triangle at corner will be complete, leadg misjudgments direction each branch skelen le. Therefore, a method for selectg threshold densification step must be sought for polygons with different geometrical characteristics different geometries. We shall pursue this method future research. In addition, re have been some effective methods solvg problem pologically correct connection a le boundaries adjacent polygons, we need analyze characteristics se methods our method future work. Author Contributions: C.L. proposed origal concept for study. All co-authors conceived designed methodology. Y.Y. P.G. were responsible for processg analysis data. C.L., P.W. X.L. drafted manuscript. All authors read approved fal manuscript. Fundg: This research w funded by National Natural Science Foundation Cha under grant number Bic Surveyg Mappg Project under grant number A1705. Acknowledgments: The authors would like thank National Geomatics Center Cha for providg geospatial data used this study thank anonymous reviewers from journal IJGI for ir help improvg this paper. Conflicts Interest: The authors decl no conflict terest. References 1. Van Oosterom, P. The GAP-tree, an approach on--fly map generalization an a partitiong. In GIS Generalization, Methodology Practice; CRC Press: Boca Ran, FL, USA, 1995; pp Beard, K.; Mackaness, W. Generalization operations supportg structures. In Au-Car 10: Technical Papers 1991 ACSM-ASPRS Annual Convention; ACSM-ASPRS: Baltimore, ML, USA, 1991; Volume 6, pp McMter, R.B.; Shea, K.S. Generalization Digital Cargraphy; Association American Geographers: Whgn, DC, USA, Mitropoulos, V.; Xydia, A.; Nakos, B.; Vescoukis, V. The use epsilon convex a for attributg bends along a cargraphic le. In Proceedgs 22nd International Cargraphic Conference, La Corona, Spa, 9 16 July Muller, J.C. Fractal Aumated Le Generalization. Cargr. J. 1987, 24, [CrossRef] 6. Lee, D.T. Medial axis transformation a planar shape. IEEE Trans. Pattern Anal. Mach. Intell. 1982, 4, [CrossRef] [PubMed] 7. Montanari, U. A method for obtag skelens usg a qui-euclidean distance. J. ACM 1968, 15, [CrossRef] 8. Ru, A. Multiple paradigms for aumatg map generalization: Geometry, pology, hierarchical partitiong local triangulation. ACSM/ASPRS Annu. Conv. Expos. 1995, 4, W, J.M.; Jones, C.B.; Bundy, G.L. A Triangulated Spatial Model for Cargraphic Generalization Areal Objects. In Advance GIS Research II, Proceedgs 7th International Symposium on Spatial Data Hlg, Delft, The Nerls, August 1996; Kraak, M.J., Molenaar, M., Eds.; Taylor & Francis: London, UK, 1997; pp Cao, T.; Edelsbrunner, H.; Tan, T. Pro correctness digital Delaunay triangulation algorithm. Comput. Geom. Theory Appl. 2015, 48, [CrossRef] 11. Stunata, V.; Aoki, T. Skelen extraction cluttered image bed on delaunay triangulation. In Proceedgs 2016 IEEE International Symposium on Multimedia (ISM), San Jose, CA, USA, December 2016; pp

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