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Estimating Natural Activity by Fitting 3D Models via Learned Objective Functions

1 Faculty of Science and Engineering, Waseda University, Tokyo 169-8555, Japan 2 Institut für Informatik, Technische Universität München, 85748 Garching, German y 3 Kognitive Neuroinformatik, Universität Bremen, 28359 Bremen, Germany.

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Estimating Natural Activity by Fitting 3D Models via Learned Objective Functions

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  1. 1Faculty of Science and Engineering, Waseda University, Tokyo 169-8555, Japan 2Institut für Informatik, Technische Universität München, 85748 Garching, Germany 3Kognitive Neuroinformatik, Universität Bremen, 28359 Bremen, Germany Estimating Natural Activity by Fitting 3D Models via Learned Objective Functions Matthias Wimmer1, Christoph Mayer2, Freek Stulp3 and Bernd Radig2

  2. Natural Activity visual channel visual channel auditory channel auditory channel tactile channel tactile channel olfactory channel olfactory channel

  3. Model-based Image Interpretation ModelDescribes the image content with the help of a parameter vector p. Objective FunctionCalculates how well a parameterized model p fits to an image I. Fitting AlgorithmOptimizes the objective function and therefore estimates the model that fits the image best.

  4. Objective Functions f(I,p) 0.6 0.0 0.3 • Splitting the Objective Function to Local Objective Functions • Evaluate one objective function per model point. • Approximate the model parameters. • Evaluation of the Objective Function • Along characteristic direction. • Often perpendicular to the model.

  5. Traditional Approach Manually evaluate on test images Shortcomings: • Requires domain knowledge. • Based on designer’s intuition. • Time-consuming. Manually design the objective function designed objective function good not good

  6. Ideal Objective Functions P1: Correctness Property:The global minimum corresponds to the best model fit. P2: Uni-modality Property:The objective function has no local extrema. ¬ P1 P1 ¬P2 P2

  7. Learning the Objective Function (1)

  8. Learning theObjective Function (2) Generate further Annotations Annotations in three-dimensional space along characteristic direction One characteristic direction is not sufficient.

  9. Learning theObjective Function (3)

  10. Learning theObjective Function (4) Three characteristic directions in three-dimensional space. Model point is moved along the most important characteristic direction. Characteristic direction with largest angle to the image normal is considered most important.

  11. Learning theObjective Function (5)

  12. Learning theObjective Function (6) Advantages • The loop is removed. • The objective function approximates the ideal objective function. • No domain-dependent knowledge is needed.

  13. Evaluation General approach • Uniformly distributed error is applied to models and fitting is performed afterwards. • Distances are measured in centimeters. • Fraction of models located at a certain distance or better is evaluated. • Two objective functions fA and fB with learning radii • ∆A= 3 × ∆B.

  14. Evaluation (2) • fB handles small displacements better. • fA handles large displacements better. • Subsequent execution shows both advantages.

  15. Evaluation (3) • Results are improved with every iteration. • Lower bound of quality is reached after several iterations.

  16. Thank you !

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