Automatic identification of urban street networks using ant colony optimization

1. Automatic identification of urban street networks using ant colony optimization

2. MAP-Aria At MAP-Aria lab, we develop methods and tools for the generative design and assistance in the decision process in architecture, urban planning and landscape, that can assist the designer or decision maker in the development of formal and functional solutions. Today, we present a generative method for identifying qualitative parameters generally affecting a street network organization and automatically calculate optimized solutions. 2

3. Plan Position Related work Our approach Computing a distance map Extracting a plausible periphery Computing a street skeleton Graph computation from skeleton Path determination Adding feedbak to the opimization process Optimization criteria Path classification and typology Constraints to satisfy Ant colony optimization The variant Ant-SSP Multicriteria optimization Test and results Conclusion and future work 3

4. Position Scientific questions rising about the coupling between street networks and buiding locations (that define 2 nested logics). Great interest for urbanists, researchers,... Certainly, for historical reasons, street structures often constraint building plots and building location. But, sometimes the opposite occurs. In this context, we formulate two questions : - is it possible to automatically compute plausible urban street networks from the image I of building footprints ? - in the case of a real city plan, can we more or less retrieve existing street networks, help urban planning ? To answer, we have designed a generative method able to provide optimized solutions to problems based on the physical exploration of complete multivalued graphs. 4

5. Related work Our work is similar to the vectorial approach of X.Decoret, INRIA-GRAVIR, 2002: “Street generation for city modeling”. which computes a non-hierarchical road network from a city map of building outlines by calculating the Voronoï diagram of the ground. BUT : purely geometric approach is insufficient because it lacks a road classification, certainly difficult to obtain, which forbids its use for simulating dynamic problems (traffic, transport, urban planning). 5

6. Our approach In our previous publication : “Can Ants Build Urban Street Networks ?”, Marsault X., CIE'39, Troyes, july 2009, France : we propose a raster approach, where the the Voronoï diagram is replaced by a morphological skeleton computation we use “Mathematical Morphology” tools to compute distance-map, periphery, and obtain a graph we develop ant-based techniques to identify plausible street hierarchies (streets, boulevards, avenues, lanes, water streams) in this graph Why ants ? often related to optimization in graph-based problems. 6

7. building footprints of Saint Genis and Venissieux (France) here, a procedural city 7

8. For each pixel p, we compute the radius of the largest disk centered in p which does not intersect any building. Mathematical Morphology performs the “distance-map” in a whole and elegant process based on neighbourhood-based operators. If we turn the counter variable of each pixel into a grey level, we clearly recognize broad zones: the periphery and some areas within the city, maybe squares. Computing a distance map 8

9. by adding a "virtual building" on the edges of the image, we can compute virtual adaptive frontier all around the city to shape a periphery. the distance-map helps specifying a minimum distance D to the closest buildings. we simply draw filled circles centered on the image borders, respecting the distance D. the first iteration already provides a rather fine periphery. Other iterations provide better results. Extracting a plausible periphery 9

10. Computing a street skeleton We define the open space set as I amputated of its buildings => can be considered as the skeleton of all potential roads at first approximation Morphological skeleton = medial axes of the open space of the city, versus raster gathers all centers of maximal balls, easily obtained by a homotopic process, by iterating the Golay thinning masks for each pixel, up to image stabilization 10

11. the result is sparseness of barbs because of the noise sensitivity of the skeletonization processing barb removal is performed using a Golay morphological filter : 8 masks applied until idempotence result: a clean skeleton made of cells containing each one a unique building (≈ Voronoï diagram) = all the "medial lines” of the open space 11

12. Graph computation from skeleton combine topological information provided by the skeleton with the maximum-balls radii skeleton object = a planar graph structure with junctions and nodes extract a graph from the skeleton with some image analysis procedures Node detection node = intersection pixel of at least 3 junctions detected with at most 33 masks coding 3x3 neighbourhood configurations All types of nodes in a 3x3 square grid neighbourhood 12

13. Path determination Paths are composed with connected graph junctions. In order to obtain the path c(i,j) between 2 nodes i et j, the algorithm used is that of Dijkstra, modified to take lenght, width and rectitude values into account. This gives, for a junction j , the following valuation Vj: Rule: once both extremities are found for a path, we replace all its rj junction values by the minimum value computed along the path. The problem is no longer calculate paths, but select Them among the set C of all eligible paths. The major difficulty is to find their most relevant termination nodes, from a geometric or functional point of view. BUT: we do not have good local criteria to do that ! This justifies the use of an optimization algorithm. Interactive search path simulation in the graph red path = pedestrian / green path = Vj valuation 13

14. Adding feedback to the optimization process Most of the time : Here, we add a feedback in designing relevant criteria to better understand our problem. Define criteria and constraints Find optimized solutions Problem Define criteria and constraints Find optimized solutions Problem 14

15. Morphological analysis of existing urban road structures provides 4 basic optimization criteria related to a set of paths C : We wish to find "in average" the longest possible paths (L), the broadest possible (R), the most straight as possible (Rect) and with the higher possible deviation of path width at junctions (E). Optimization criteria 15

16. Path classification and typology Morphological analysis of many existing urban road structures reveals a road typology based on L, R and Rect criteria , which enables to classify all paths in the set C : 16

17. Constraints to satisfy 3 eligibility constraints, defined as thresholds to reject : streets whose length L is below a certain threshold. streets whose width R is below a certain threshold. those with L / R ratio is below a certain threshold. => significantly reduces the number of eligible paths for the optimization process. 3 construction constraints : any solution forms a connected subgraph of G (ability to move anywhere in the city): - low connectivity : any path added at each iteration has at least one end node shared with Sk, - high connectivity : any path added at each iteration has at least one node shared with Sk (the best option). no solution junction is common to several paths (no path overlapping). minimize the number of isolated path termination. This constrainst becomes a pseudo optimization criteria. 17

18. Ant Colony Concept of « distributed intelligence »: - when ants choose their path, they tend to select - in a probabilistic way - the one which has the highest pheromone concentration. - gradual evaporation of pheromones => probabilistic path selection constantly changing. Advantages: - robustness (continue functioning in case of component failure), - flexibility (adaptation, efficiency on dynamical problems). This strategy has inspired researchers and given birth to metaheuristic ACO : - to solve problems known to be difficult (NP-complete), ranging from graph exploration to task planning or object selection in a set, - to approach optimal solutions by exploring a small fraction of possible combinations. 18

19. Ant Colony Optimization Generic ACO algorithm : choose a number of runs R and N ants (N depends on the problem ; R = 10..12) For each run { initialize the pheromone trails Loop cycle { let ants build N competing solutions, store the best cycle solutions, update the pheromone trails for the best cycle solutions } until some stop criterion is reached } Analyze the best solutions over all cycles 19

20. Ant Colony Optimization How each ant builds a solution : Starting with an empty solution, at each iteration, an ant adds a new component i (among eligible set Cand), with probability p(i), until the solution is complete : t(i) = pheromone factor associated with component i, • clamped between tmin and tmax (ensures diversification) h(i) = heuristic factor associated with component i, • reflects the local interest to choose i knowing all solution components yet added to the partial solution Sk, in order to improve its construction and quality, • a good mean to force the algorithm to solve an internal objective during the building stage, • eg. h(L) = L ; h(R) = R ; h(E) = L / R ; h(LR) = LR ; h(LR, Rect) = LR / Rect Pheromone update : - performed at the end of each cycle, - light evaporation (rau parameter), - best component reward (pheromone deposit). 20

21. The variant Ant-SSP Algorithm well suited to incrementally build a set of paths whose introduction order into the solution has non importance. Solution construction is performed with « vertex pheromonal structure » (resp. clique) associated with each single component (resp. pair) Here, the goal is to find a subset C of the graph components satisfying some constraints and optimizing one or several criteria (objectives). This variant is called SSP (Subset Selection Problems), the best known being the backpack problem. 21

22. Multicriteria optimization It is very rare to have only one objective to optimize. Calculate an overall objective by weighting the partial targets (of different nature) is often clumsy, and yet very common. Instead, find a set of non-dominated solutions (the Pareto front), none systematically lower on all other objectives => no global optimum, but a set of optimum forming the best "compromise area" of the problem. These solutions are not comparable, and the user ultimately choose, involving non-quantifiable criteria. 22

23. Other simple and combined criteria have been designed and tested within the optimization process. Combined optimization criteria 23

24. Tests and results SSP parameter settings : Experimentally, the number of ants can be set between 80 and 120. a=3, b=4, tmin=0,01, tmax=5, rau=0,01, nb_cycles ranging from 1000 to 30000. We tested 36 morphological parameters, and retain 8 as able to provide good solutions : R (7), Σrαl (12), Σ(rαl) / Rect(18), L.Rα / Rect(20), L.Rα.E / Rect(26), L+R-Rect+E(30), Σ(rαl).E/Rect(35) and LRα / Rect+E(36). A simple urban pattern, with 208 nodes and 6978 eligible paths (reasonable computation time: 18 minutes for 10000 cycles). Optimisation of criteria : a) 2 – b) 5 – c) 7 – d) 9. Green = avenue, red = ring or boulevard, grey = streets 24

25. Tests and results Optimisation of criteria : a) 12 – b) 18 – c) 20 – d) 26 Optimisation of criteria : e) 28 – f) 30 – g) 35 – h) 36 25

26. Tests and results Part of Decines city (in the neighbourhood of Lyon), with 2580 nodes and 194584 eligible paths (high computing times : 15 h for 1000 cycles, despite the high degree of code optimization). Optimization of: a) Σ(rαl)/Rect – b) Σ(rαl).E/Rect – c) Pareto L+R-Rect+E – d) Pareto LRRect+E 26

27. Conclusions We have put forward the steps of a modular and robust protocol for extracting a hierarchical network of urban roads, drawing on Mathematical Morphology tools, graph exploration and Ant Colony Optimization. Our research shows that we can reduce to a selecting paths problem. Only using building footprint data, we obtain emerging street hierarchies, with quantitative and qualitative aspects (typology: ring roads / boulevards, avenues, streets and lanes). Our contribution includes : - automatic and parametrizable periphery calculation, - skeleton extraction that represents a set of potential routes that can be used to connect a city to its neighbours, - a shortest path algorithm variant suited to search for wider and regular streets, - a generative method to help identify qualitative parameters affecting a street network organization and automatically compute optimized solutions. 27

28. Future works Consolidate the present approach : more work has to be done on the nature of relevant criteria. Improve the skeletonization process to allow some roads to be closer to buildings, as it often happens in a real city. Analyze the influence of parameter  on the solutions quality (a value close to 0.8 seems better for the samples showed). Is there a link with fractal dimension ? Develop a visualization tool for our street network 3D models, gathering all extracted objects (roads, rivers, intersections) and their fittings. Extend our work to the detection and automatic placement of urban squares. Extend our algorithm to deal with other decision-making problems, including urban planning. Our generic approach is rather open, and can be used on any existing urban graph with any type of eligible junction valuation. Potential links with “flow” works (trafic, analysis and prediction), economical optimizations. 28

29. Thank you very much ! please read our paper and visit our new site www.aria.archi.fr for details and regular updates, demos and free available codes (soon) 29