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Loss-based Visual Learning with Weak Supervision M. Pawan Kumar Joint work with Pierre-Yves Baudin, Danny Goodman, Puneet Kumar, Nikos Paragios, Noura Azzabou, Pierre Carlier

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SPLENDID Nikos Paragios Equipe Galen INRIA Saclay Daphne Koller DAGS Stanford Machine Learning Weak Annotations Noisy Annotations Applications Computer Vision Medical Imaging Self-Paced Learning for Exploiting Noisy, Diverse or Incomplete Data 2 Visits from INRIA to Stanford 1 Visit from Stanford to INRIA 2012ICML 3 Visits Planned2013MICCAI

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Medical Image Segmentation MRI Acquisitions of the thigh

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Medical Image Segmentation MRI Acquisitions of the thigh Segments correspond to muscle groups

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Random Walks Segmentation Probabilistic segmentation algorithm Computationally efficient Interactive segmentation Automated shape prior driven segmentation L. Grady, 2006 L. Grady, 2005; Baudin et al., 2012

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Random Walks Segmentation y(i,s): Probability that voxel ‘i’ belongs to segment ‘s’ x: Medical acquisition min y E(x,y) = y T L(x)y + w shape ||y-y 0 || 2 Positive semi-definite Laplacian matrix Shape prior on the segmentation Parameter of the RW algorithm Convex Hand-tuned

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Random Walks Segmentation Several Laplacians L(x) = Σ α w α L α (x) Several shape and appearance priors Σ β w β ||y-y β || 2 Hand-tuning large number of parameters is onerous

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Parameter Estimation Learn the best parameters from training data Σ α w α y T L α (x)y + Σ β w β ||y-y β || 2

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Parameter Estimation Learn the best parameters from training data w T Ψ(x,y) w is the set of all parameters Ψ(x,y) is the joint feature vector of input and output

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Parameter Estimation –Supervised Learning –Hard vs. Soft Segmentation –Mathematical Formulation Optimization Experiments Related and Future Work in SPLENDID Outline

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Supervised Learning Dataset of segmented fMRIs Sample x k, voxel i z k (i,s) = 1, s is ground-truth 0, otherwise Probabilistic segmentation??

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Supervised Learning w T Ψ(x k,z k ) Energy of Ground-truth w T Ψ(x k,ŷ) Energy of Segmentation - ≥ Δ(ŷ,z k )- ξ k min w Σ k ξ k + λ||w|| 2 Δ(ŷ,z k ) = Fraction of incorrectly labeled voxels Taskar et al., 2003; Tsochantardis et al., 2004 Structured-output Support Vector Machine

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Supervised Learning Convex with several efficient algorithms No parameter provides ‘hard’ segmentation We only need a correct ‘soft’ probabilistic segmentation

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Parameter Estimation –Supervised Learning –Hard vs. Soft Segmentation –Mathematical Formulation Optimization Experiments Related and Future Work in SPLENDID Outline

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Hard vs. Soft Segmentation Hard segmentation z k Don’t require 0-1 probabilities

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Hard vs. Soft Segmentation Soft segmentation y k Compatible with z k Binarizing y k gives z k

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Hard vs. Soft Segmentation y k C(z k ) Soft segmentation y k Compatible with z k Which y k to use?? y k provided by best parameter Unknown

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Parameter Estimation –Supervised Learning –Hard vs. Soft Segmentation –Mathematical Formulation Optimization Experiments Related and Future Work in SPLENDID Outline

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Learning with Hard Segmentation w T Ψ(x k,z k )w T Ψ(x k,ŷ)- ≥ Δ(ŷ,z k )- ξ k min w Σ k ξ k + λ||w|| 2

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Learning with Soft Segmentation w T Ψ(x k,y k )w T Ψ(x k,ŷ)- ≥ Δ(ŷ,z k )- ξ k min w Σ k ξ k + λ||w|| 2

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Learning with Soft Segmentation w T Ψ(x k,y k )w T Ψ(x k,ŷ)- ≥ Δ(ŷ,z k )- ξ k min w Σ k ξ k + λ||w|| 2 Smola et al., 2005; Felzenszwalb et al., 2008; Yu et al., 2009 Latent Support Vector Machine min y k y k C(z k )

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Parameter Estimation Optimization Experiments Related and Future Work in SPLENDID Outline

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Latent SVM Difference-of-convex problem min w Σ k ξ k + λ||w|| 2 w T Ψ(x k,ŷ) – min y k w T Ψ(x k,y k ) ≥ Δ(ŷ,z k ) – ξ k y k C(z k ) Concave-Convex Procedure (CCCP)

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CCCP y k * = min y k w T Ψ(x k,y k ) s.t. y k C(z k ) Repeat until convergence Estimate soft segmentation Update parameters min w Σ k ξ k + λ||w|| 2 w T Ψ(x k,ŷ) – w T Ψ(x k,y k *) ≥ Δ(ŷ,z k ) – ξ k Efficient optimization using dual decomposition Convex optimization

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Parameter Estimation Optimization Experiments Related and Future Work in SPLENDID Outline

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Dataset 30 MRI volumes of thigh Dimensions: 224 x 224 x 100 4 muscle groups + background 80% for training, 20% for testing

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Parameters 4 Laplacians 2 shape priors 1 appearance prior Baudin et al., 2012 Grady, 2005

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Baselines Hand-tuned parameters Structured-output SVM Soft segmentation based on signed distance transform Hard segmentation

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Results Small but statistically significant improvement

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Parameter Estimation Optimization Experiments Related and Future Work in SPLENDID Outline

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Loss-based Learning x: Inputa: Annotation

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Loss-based Learning x: Inputa: Annotationh: Hidden information h a = “jumping”h = “soft-segmentation”

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Loss-based Learning min Σ k Δ(correct a k, predicted a k ) Annotation Mismatch x: Inputa: Annotationh: Hidden information h a = “jumping”h = “soft-segmentation”

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Loss-based Learning min Σ k Δ(correct a k, predicted a k ) Annotation Mismatch Small improvement using small medical dataset

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Loss-based Learning min Σ k Δ(correct a k, predicted a k ) Annotation Mismatch Large improvement using large vision dataset

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Loss-based Learning min Σ k Δ(correct {a k,h k }, predicted {a k,h k }) Modeled using a distributionOutput Mismatch Kumar, Packer and Koller, ICML 2012 Inexpensive annotation No experts required Richer models can be learnt

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