1 Tree Crown Extraction Using Marked Point Processes Guillaume Perrin Xavier Descombes – Josiane Zerubia ARIANA, joint research group CNRS/INRIA/UNSA INRIA Sophia Antipolis, FRANCE MAS, Applied Mathematics Laboratory Ecole Centrale Paris, FRANCE EUSIPCO 2004 – 10 th, September 2004

2 Contents  Motivations  Notations and Definitions  Our Model for Tree Crown Extraction  Results  Conclusion 1

3 EUSIPCO 2004 – 10 th, September 2004 Motivations Remote sensing in forestry management - Near infrared images - Could avoid human investigations : economic considerations - More control on forest stands evolution 900nm 520nm Forestry statistics to estimate - Stem number - Diameter distribution - Forestry cover area Automatic Extraction - [Gougeon 95] ; valley following - [Larsen 97] : template based model 2 French Inventory (IFN) - Aerial images - 50 cm/pixel

4 Contents  Motivations  Notations and Definitions  Our Model for Tree Crown Extraction  Results  Conclusion 3

5 EUSIPCO 2004 – 10 th, September 2004 Notations and Definitions Object Space U An Object (position/marks) A Configuration A Marked Point Process X with - Probability Distribution P X - Unnormalized Density h(.) - Reference Poisson measure (uniform point process) Example : Strauss Process X Y k pypy pxpx u r s=5 with t 1 P P s=1 with t 2 <t 1

6 Contents  Motivations  Notations and Definitions  Our Model for Tree Crown Extraction  Results  Conclusion 5

7 EUSIPCO 2004 – 10 th, September 2004 Objects of the process - Disk process : position of the center and radius Density of the marked point process (1) - Prior density (knowledge) 1.Penalizes intersections of disks 2.Favours alignments 3.Hard Core (stability reasons) >0 repulsive <0 attractive Proposed model for Tree Crown Extraction 6

8 EUSIPCO 2004 – 10 th, September 2004 Proposed model for Tree Crown Extraction Density of the marked point process (2) - Likelihood = Gaussian Mixture - Each pixel belongs to one of these 2 classes : -Tree Class, with normal distribution -Background Class, with normal distribution Stability condition of the density 7

9 EUSIPCO 2004 – 10 th, September 2004 Proposed model for Tree Crown Extraction MCMC Simulation of point processes [Geyer 98] - Markov Chain (X) with equilibrium distribution P X (ergodic convergence) - Algorithm : Metropolis Hastings with Reversible Jumps [Green 95] - Application to feature extraction : Maximum A Posteriori Estimator 1.Simulate a point process defined by a density h(.) 2.Explore the whole state space 3.Find one of the global maxima of h(.) Simulated Annealing 8

10 EUSIPCO 2004 – 10 th, September 2004 Proposed model for Tree Crown Extraction Reversible Jump MCMC Algorithm Configuration of objects X i = x Simulate y ~ Q(x,.) (proposal kernel) Evaluate Green ratio R=F[Q(.,.),h(.),x,y] Accept y with probability min(1,R) XiXi Y Proposal Kernel : - Birth / Death - Translation - Dilation - Split / Merge - BD alignment, … Goal : find the MAP as fast as possible and avoid local maxima of h(.) 9

11 Contents  Motivations  Notations and Definitions  Our Model for Tree Crown Extraction  Results  Conclusion 10

12 EUSIPCO 2004 – 10 th, September 2004 Results Results depend on - Simulated annealing scheme -In theory : logarithmic decrease to get the MAP estimator -In practice : geometric decrease. every N iterations - Parameters of density h(.) -Which parameters for the priori ? -Experimental / Parameter Estimation -Which parameters for the likelihood ? -KMeans / Parameter Estimation 11

13 EUSIPCO 2004 – 10 th, September 2004 Results SLOW : 50M iterations ~ 17 minutes 304 objects - U= FAST : 1,5M iterations ~ 30 seconds 299 objects - U= Original image 12

14 EUSIPCO 2004 – 10 th, September 2004 Results Extraction evolution / Green ratio - High Temperature : Green ratio dominated by Poisson measure ratio - Low Temperature : Green ratio dominated by density ratio Critical Temperature 13 Density ratio Poisson measure ratio Kernel ratio Diaporama

15 Contents  Motivations  Notations and Definitions  Our Model for Tree Crown Extraction  Results  Conclusion 14

16 EUSIPCO 2004 – 10 th, September 2004 Conclusion Advantages of the modeling - Geometrical information of stands taken into account - Can be adapted to multi-species extraction Drawbacks - Computational time - Trees have to be separable (pb on too dense areas) Future work - Parameter estimation on the global model (in progress) - Texture information in the density (distinguish btw different species) 15

17 EUSIPCO 2004 – 10 th, September 2004 References [Gougeon 95] A crown-following approach to the automatic delineation of individual tree crowns in high spatial resolution aerial images – Canadian Journal of Remote Sensing – 21(3), , [Larsen 97] Using ray-traced templates to find individual trees in aerial photographs – Proc. 10 th Scandinavian Conference on Image Analysis, vol.2, , [Green 95] Reversible Jump Markov Chain Monte Carlo computation and Bayesian model determination – Biometrika 82, , [Geyer 98] Stochastic geometry, likelihood and computation : “Likelihood inference for spatial point processes”, Chapman et Hall, London,

18 EUSIPCO 2004 – 10 th, September 2004 Results Extraction evolution / Green ratio - High Temperature : Green ratio dominated by Poisson measure ratio - Low Temperature : Green ratio dominated by density ratio Critical Temperature 13 Back to presentation Density ratio Poisson measure ratio Kernel ratio