Image Approximation with Transparent Introduction Triangles - PowerPoint PPT Presentation

Image Approximation with Transparent Triangles Kevin Stock Image Approximation with Transparent Introduction Triangles Objective Function Search Techniques Kevin Stock Examples Future Work Source Images December 10, 2010

Example (using 1000 triangles) Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Inspiration Image Approximation with Transparent Triangles Kevin Stock Introduction Roger Alsing’s Objective Function Genetic Programming: Evolution of Mona Lisa Search Techniques Not actually genetic programming. Examples Future Work Source Images

Model Image Approximation with Transparent Triangles Kevin Stock The image is drawn from an array of triangles, rendered by Introduction Objective OpenGL in order. Function Each triangle is composed of 10 scalars: Search Techniques r , g , b , a , x 1 , x 2 , x 3 , y 1 , y 2 , y 3 . Examples All 10 scalars are constrained to the range [0 , 1]. Future Work Source Images

Objective Function Image Approximation with Transparent RGB TSS Triangles Kevin Stock Easy to implement. Introduction Good enough results. Objective Function Search HSV TSS Techniques Examples Much slower than comparing RGB. Future Work Optionally weight channels: V is considered more Source Images important than H or S in encoding. Surprisingly, worse results than using RGB.

RGB TSS Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

HSV TSS Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

HSV TSS (Weighted) Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Hill Climber Image Approximation with Transparent Triangles Algorithm Kevin Stock Introduction At each iteration, change one value of one triangle to a Objective new value. Function If the new version is better keep it. Search Techniques Examples Performance Future Work Source Images Very slow convergence.

Simulated Annealing Image Approximation with Transparent Algorithm Triangles Kevin Stock Start with big changes, over time make smaller changes. Introduction Never accepts a worse solution. Objective Function Search Techniques Performance Examples Future Work Converges faster than hill climber. Source Images To help avoid local minimums, the system is ’reheated’ occasionally allowing big changes again.

Incremental Start Image Approximation with Algorithm Transparent Triangles Kevin Stock Start with one triangle, add another triangle every n iterations. Introduction Objective Similar to hill climber, but half of all iterations attempt to Function mutate the most recently added triangle. Search Techniques Examples Performance Future Work Source Images Not actually a complete algorithm. Can be used to seed other algorithms, excellent results with SA.

Genetic Algorithm Image Approximation with Transparent Algorithm Triangles Kevin Stock Uniform random selection of parents. Introduction One point crossover reproduction. Objective Function Random mutations within fix range from starting values. Search Techniques Examples Performance Future Work Not as good convergence as SA, but better than hill Source Images climber. Mutation step could probably be improved.

SA vs SA w/ Inc. Start (100 Tri’s, 90k Iter’s) Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

GA vs SA (100 Tri’s, 600k Iter’s) Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

GA vs SA (50/200 Tri’s, 100k/650k Iter’s) Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

SA w/ Inc. Start (Iter. 1000) Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Iter. 5000 Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Iter. 10k Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Iter. 15k Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Iter. 20k Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Iter. 25k Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Iter. 30k Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Iter. 35k Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Iter. 40k Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Iter. 45k Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Iter. 50k Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Iter. 150k Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Iter. 200k Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Iter. 380k Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Iter. 460k Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Iter. 580k Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Iter. 650k Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

SA w/ Inc. Start (500 Tri’s, 780k Iter’s) Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

SA w/ Inc. Start (500 Tri’s, 1800k Iter’s) Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

GA (500 Tri’s, 600k Iter’s) Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Future Work Image Approximation with Transparent Triangles Kevin Stock Alternative objective functions Introduction Minimum size or angle constraint on triangles Objective Function Eliminate non-contributing triangles Search Techniques Non-uniform choice of channel to mutate Examples Combination of GA/SA for global/local search Future Work More search techniques Source Images

Mona Lisa Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Eva Green Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Tart Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images

Waffles Image Approximation with Transparent Triangles Kevin Stock Introduction Objective Function Search Techniques Examples Future Work Source Images