1. Date of creation
 2025-03-14

2. Title
 Results of centreline extraction based on maximal disks

3. Description of centrepoints with corresponding lane boundaries
 The centrelines of road lanes are extracted based on maximal disks. In the results, the left and right lane boundaries are marked in bule and red respectively. Bule and red dots are sparsely-defined boundary points.

 The resulting centre points are shown as black points, centred at their corresponding maximal disks. Additional centre points to compensate for ligatures are also plotted but without a maximal disk.

 Arrows between two adjacent centre points illustrate the direction of the lane.

4. Author info
 Data creation: Chenhui Yin
 Data manager: Marco Cecotti

5. Data naming and format
 Each file is named after the scenario index and lane index. For example, the results for the third lane in the second scenario is named sce2_lane3. 

 Totally five scenarios are included. The scenario 1~4 are from The Intersection Drone Dataset (https://levelxdata.com/ind-dataset/). 

 The fifth scenario is customized and is named as dummy. An example of results from the dummy scenario is dummy_lane2.

 Each figure is in the format of PNG.

6. Six types of maximal disks
 (a) the circle is constrained by 3 segments. 
 (b) the circle is constrained by 2 segments and 1 extreme point. 
 (c) the circle is constrained by 1 segment and 2 extreme points. 
 (d) the circle is constrained by 3 extreme points. 
 (e) the circle is constrained by 1 segment and 2 extreme points, with one of the two points lying on the segment. 
 (f) the circle is constrained by 2 segments and 1 extreme point, which lies on one of the two segments.

7. Pipeline of centreline extraction based on maximal disks

 -Extract surveyed points of both road lane borders: pts_left, pts_right
 -Build a 2-dimensional tree for the points of each border: KDT_left, KDT_right
 -Perform segment pairing:
   for idx_border = 1:2
     for idx_pt = 1:ptNum_{left/right} 
       Extract a query point queryPt from pts_{left/right}
       Perform range searching based on queryPt and KDT_{left /right} to form point pairs
       Do point-pair filtering
       if point-pair is not found:
         Perform nearest-neighbor search
         Do point-pair filtering
       end
     end

     Build segment pairs segPairs_{left/right} by the point pairs and create a list of them for each segment
   end
-Explore MDs:
   for idx_border = 1:2
     for idx_seg = 1: ptNum_{left/right}-1 
       Select one segment and extract relevant segment pairs from segPairs_{left/right}
       Select constraint elements (points and segments) to calculate MDs of six cases
       Do circle center filtering
     end
     Store the circle centers circleCentres_{idxBorder}
   end
-Connect the circle centers:
   Extract either left or right border pts_{left/right}
   for idx_seg = 1: ptNum_{left/right}-1
     Select one segment from the border
     Extract circles touching the segment
     Sort the circles
   end
-Compensate for ligature:
   Identify ligatures by primary MDs sharing the same constraint point
   for idx_lgt = 1: lgtNum 
     Calculate the projection-to-start range
     Sample new projection points
     Calculate the secondary MDs in the ligature
   end

7. Abbreviations
 MD -> Maximal Disk
 seg -> segment
 pt -> point
 KDT -> k-dimensional tree
 idx -> index
 num -> number
 lgt -> ligature