Woody Plants Model Recognition by Differential Evolution

Transcription

1 Woody Plants Model Recognition by Differential Evolution BIOMA 2010, Ljubljana, May 2010 Woody Plants Model Recognition by Differential Evolution 1 / 22

2 1 Introduction 2 Related Work 3 Woody Plants Recognition by Differential Evolution 4 Experimental Results 5 Conclusion Woody Plants Model Recognition by Differential Evolution 2 / 22

3 Motivation At CEC 2009, an approach for recognition of two-dimensional procedural models was presented, the procedural model used was not as complex to express woody plants, we now extend this approach to the domain of three-dimensional procedural models suitable to model complex woody plants. A new approach: to design three-dimensional geometrical models for woody plants (trees), used in computer graphics and animation. Recognition of trees: evolutionary algorithms (our jde) and procedural modeling of trees (our EcoMod). Woody Plants Model Recognition by Differential Evolution 3 / 22

4 1 Introduction 2 Related Work 3 Woody Plants Recognition by Differential Evolution 4 Experimental Results 5 Conclusion Woody Plants Model Recognition by Differential Evolution 4 / 22

5 Differential Evolution (DE) A floating point encoding EA for global optimization over continuous spaces, trough generations, the evolution process improves population of vectors by combining a parent individual and several other individuals of the same population. We have chosen the strategy jde/rand/1/bin mutation: vi,g+1 = x r1,g { + F (x r2,g x r3,g ), v i,j,g+1 if rand(0, 1) CR or j = j rand crossover: ui,j,g+1 = and x i,j,g otherwise { u i,g+1 if f (u i,g+1 ) < f (x i,g ) selection: x i,g+1 =, x i,g otherwise includes mechanism of F and CR control parameters self-adaptation. Woody Plants Model Recognition by Differential Evolution 5 / 22

6 Problem Domain: Woody Plants Procedural Model 3D tree models are compactly represented using a procedural model our EcoMod framework uses a numerically coded procedural model with fixed dimensionality suitable for parameter estimation using DE. Parameterized procedural model builds a 3D structure of a tree and all its building parts: by recursively executing a fixed procedure, over a given set of numerically coded input parameters, such as branch thickness, relative branch length and branching structure proportions. Woody Plants Model Recognition by Differential Evolution 6 / 22

7 Trees Representable by EcoMod Framework Foliage or coniferous trees with very different branching structures, each branch and each leaf can be animated in real time to show the growth of a tree or its sway in the wind. Woody Plants Model Recognition by Differential Evolution 7 / 22

8 Recognizing Trees: Image-based Approaches to Modeling Image-based approaches have the best potential to produce realistically looking plants they rely on images of real plants. Little work has been done to design trees with the use of a general recognition from images without user interaction use of sketch based guide techniques or the procedural models recognized were only two-dimensional. We now extended this recognition to the domain of 3D procedural models suitable to model woody plants without user interaction. Woody Plants Model Recognition by Differential Evolution 8 / 22

9 1 Introduction 2 Related Work 3 Woody Plants Recognition by Differential Evolution 4 Experimental Results 5 Conclusion Woody Plants Model Recognition by Differential Evolution 9 / 22

10 Woody Plants Recognition by Differential Evolution: Recognition Method Based on an optimization procedure with three main parts: Part I: genotype encoding, Part II: genotype-phenotype mapping, and Part III: fitness evaluation: phenotype and reference image comparison. Woody Plants Model Recognition by Differential Evolution 10 / 22

11 Genotype Encoding An individual genotype vector x of jde population represents a set of procedural model parameters, by computing recursive procedure using a set of parameters, EcoMod renders a woody plant, dimensionality of the genotype x is D = 4509, where g {0, G = 15}, w {0, W = 50}, and each G W = 750 real-coded parameters encode: one matrix of a Gravelius and Weibull ordered parameter for recursive calculations. Woody Plants Model Recognition by Differential Evolution 11 / 22

12 Genotype Encoding (x i,j [0, 1], i 1..NP in j 1..D) Number of strands of a tree S = 400x i, (S [10, 410]), height of base trunk l 0,0 0 = x i,1 10 m (l 0,0 0 [0 m, 10 m]), coefficient of branch thickness k d = 0.05x i,2 (k d [0, 0.05]), phyllotaxis angle α p = 360 x i,3 (α p [0, 360 ]), branching ratio of subbranch strands distribution ks g,w = 0.5x i,j + 0.5, j {4, 753} (ks g,w [0.5, 1]), branching angle between dividing subbranches α g,w = 180 x i,j, j {754, 1503} (α g,w [0, 180 ]), maximum relative subbranch to base branch length M g,w = 20x i,j, j {1504, 2253} (M g,w [0, 20]), minimum relative subbranch to base branch length m g,w = 20x i,j, j {2254, 3003} (m g,w [0, 20]), branch length scaling factor k g,w l = 20x i,j, j {3004, 3753} (k g,w l [0, 20]), gravicentralism impact k c = x i,3754 (k c [0, 1]), gravimorphism impact (i.e. gravitational bending of branches) αm g,w = 360 x i,j 180, j {3755, 4504} (α g,w m [ 180, 180 ]), enabling leaves display on a tree B l = x i, (B l {0, 1}), density of leaves ρ l = 30x i,4507 (ρ l {0, 30}), size of leaves l l = 0.3x i,4506 (l l [0, 0.3]), and leaf distribution type l type = 5x i,4508 (l type {Spiral, Stacked, Staggered, Bunched, Coniferous}). Woody Plants Model Recognition by Differential Evolution 12 / 22

13 Genotype-phenotype Mapping Recognition method is based on recognition of two-dimensional images of woody plants z (digital camera), to compare the three-dimensional tree evolved with the use of genotype x to the reference image z, genotype x must be transformed to its phenotype first, phenotype is a rendered two-dimensional image z, images z and z are all of dimensionality X Y pixels, both images are converted to black and white, where white (0) pixels mark background and black (1) pixels mark material, e.g. wood, the reference image is scaled to the given resolution, if necessary. An evolved procedural model is compared to reference images twice, to favor three-dimensional procedural models generation, projections differ by β = 90 camera view angle along the trunk base. Woody Plants Model Recognition by Differential Evolution 13 / 22

14 Phenotype and Reference Image Comparison The recognition success is measured by similarity of the reference original images and the generated rendered images of evolved parametrized procedural models. Images are compared pixel-wise: in the evolved image, for each pixel rendered as material: the Manhattan distance to the nearest material pixel in the reference image is computed, and vice-versa. Fitness evaluation of each phenotype is the sum of this distances: f (x) = f (g(x, 0 ), g(x, 90 )) = h(z 1 ) + h(z 2 ), h(z) = x,y m 1 (z x,y, z x,y ) + x,y m 1 (z x,y, z x,y ), where m 1 denotes a function computing Manhattan distance to the nearest material pixel in the image z. Woody Plants Model Recognition by Differential Evolution 14 / 22

15 1 Introduction 2 Related Work 3 Woody Plants Recognition by Differential Evolution 4 Experimental Results 5 Conclusion Woody Plants Model Recognition by Differential Evolution 15 / 22

16 Experiment Design Sampling rate dimension of the rendered parametrized procedural model was set to 250x250, the maximal number of strands in the tree was S = 410, the maximal number of fitness evaluations (FEs) for jde algorithm was FEs = 10, 000, the tests were run for different settings of population size NP in the evolutionary algorithm, each over 30 runs, the remaining parameters were kept default as in original algorithms from their literature. Reference model to recognize: (rendered in EcoMod) Woody Plants Model Recognition by Differential Evolution 16 / 22

17 Final Fitness (varied on the NP) Best Worst Average Std 2000 Fitness Population size Worst possible fitness is = 31, 250, 000 =3.125e7. Tests run for population sizes NP 50 to 500, step 50, best obtained results at NP=100, Woody Plants Model Recognition by Differential Evolution 17 / 22

18 Evolution of a sample procedural model For population size of NP = 100, the algorithm in 30 runs obtained the best fitness value of 1806 (i.e. 5,7792e-05 of quality), the worst being 1870, and the average of (with standard deviation of 84.4). NP=100, run 1 (seed RN 0 = 1): < 0.01% different Woody Plants Model Recognition by Differential Evolution 18 / 22

19 1 Introduction 2 Related Work 3 Woody Plants Recognition by Differential Evolution 4 Experimental Results 5 Conclusion Woody Plants Model Recognition by Differential Evolution 19 / 22

20 Summary We presented an approach to design woody plant geometrical models, parameters of the procedural model were evolved using jde differential evolution algorithm to recognize geometrical models, sampled procedural models were rendered using EcoMod framework, rendered images were then compared to the reference source images, for recognition, to guide the optimization process. Recognition of a sample woody plant model and statistical analysis of the obtained results demonstrate usability of the proposed approach. Woody Plants Model Recognition by Differential Evolution 20 / 22

21 Future research Improve metrics for comparison of rendered and reference images, add segmentation methods to separate tree imagery from background, use multiple metrics recognition combined with the use of multi-objective optimization, implement the application for mobile phones, and add interactive methods for optimization. Woody Plants Model Recognition by Differential Evolution 21 / 22

22 Thank you for listening. Questions? Woody Plants Model Recognition by Differential Evolution 22 / 22