Image Approximation with Transparent Introduction Triangles - - PowerPoint PPT Presentation

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image approximation with transparent

Image Approximation with Transparent Introduction Triangles - - PowerPoint PPT Presentation

Jul 27, 2023 257 likes •678 views

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

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

Image Approximation with Transparent Triangles

Kevin Stock December 10, 2010

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

Example (using 1000 triangles)

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

Inspiration

Roger Alsing’s Genetic Programming: Evolution of Mona Lisa Not actually genetic programming.

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

Model

The image is drawn from an array of triangles, rendered by OpenGL in order. Each triangle is composed of 10 scalars: r, g, b, a, x1, x2, x3, y1, y2, y3. All 10 scalars are constrained to the range [0, 1].

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

Objective Function

RGB TSS Easy to implement. Good enough results. HSV TSS Much slower than comparing RGB. Optionally weight channels: V is considered more important than H or S in encoding. Surprisingly, worse results than using RGB.

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

RGB TSS

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

HSV TSS

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

HSV TSS (Weighted)

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

Hill Climber

Algorithm At each iteration, change one value of one triangle to a new value. If the new version is better keep it. Performance Very slow convergence.

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

Simulated Annealing

Algorithm Start with big changes, over time make smaller changes. Never accepts a worse solution. Performance Converges faster than hill climber. To help avoid local minimums, the system is ’reheated’

ccasionally allowing big changes again.

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

Incremental Start

Algorithm Start with one triangle, add another triangle every n iterations. Similar to hill climber, but half of all iterations attempt to mutate the most recently added triangle. Performance Not actually a complete algorithm. Can be used to seed other algorithms, excellent results with SA.

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

Genetic Algorithm

Algorithm Uniform random selection of parents. One point crossover reproduction. Random mutations within fix range from starting values. Performance Not as good convergence as SA, but better than hill climber. Mutation step could probably be improved.

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

SA vs SA w/ Inc. Start (100 Tri’s, 90k Iter’s)

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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)

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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)

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

SA w/ Inc. Start (Iter. 1000)

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

Iter. 5000

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

Iter. 10k

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

Iter. 15k

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

Iter. 20k

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

Iter. 25k

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

Iter. 30k

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

Iter. 35k

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

Iter. 40k

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

Iter. 45k

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

Iter. 50k

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

Iter. 150k

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

Iter. 200k

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

Iter. 380k

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

Iter. 460k

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

Iter. 580k

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

Iter. 650k

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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)

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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)

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

GA (500 Tri’s, 600k Iter’s)

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

Future Work

Alternative objective functions Minimum size or angle constraint on triangles Eliminate non-contributing triangles Non-uniform choice of channel to mutate Combination of GA/SA for global/local search More search techniques

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Mona Lisa

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

Eva Green

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Tart

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Waffles