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Latent SVMs for Human Detection with a Locally Affine Deformation Field Ľubor Ladický 1 Phil Torr 2 Andrew Zisserman 1 1 University of Oxford 2 Oxford Brookes University

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Object Detection Find all objects of interest Enclose them tightly in a bounding box

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HOG Detector Dalal & Triggs CVPR05 Sliding window using learnt HOG template Post-processing using non-maxima suppression

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Dalal & Triggs CVPR05 HOG Detector Sliding window using learnt HOG template Post-processing using non-maxima suppression

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Dalal & Triggs CVPR05 HOG Detector Sliding window using learnt HOG template Post-processing using non-maxima suppression

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Dalal & Triggs CVPR05 HOG Detector Sliding window using learnt HOG template Post-processing using non-maxima suppression

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Dalal & Triggs CVPR05 HOG Detector Sliding window using learnt HOG template Post-processing using non-maxima suppression

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Dalal & Triggs CVPR05 HOG Detector Sliding window using learnt HOG template Post-processing using non-maxima suppression

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Classifier response : HOG Detector Dalal & Triggs CVPR05 The weights w * and the bias b * learnt using the Linear SVM as:

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Dalal & Triggs CVPR05 Does not fit well ! Sliding window using learnt HOG template Post-processing using non-maxima suppression HOG Detector

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Deformable Part-based Model Felzenszwalb et al. CVPR08 Allows parts to move relative to the centre Effectively allows the template to deform Multiple models based on an aspect ratio

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Felzenszwalb et al. CVPR08 Deformable Part-based Model Allows parts to move relative to the centre Effectively allows the template to deform Multiple models based on an aspect ratio

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Cells c displaced by the deformation field d: Our approach

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Cells c displaced by the deformation field d: Our approach Regularisation takes the form of a pairwise MRF: Classifier response :

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Cells c displaced by the deformation field d: Our approach The weights w * and the bias b * learnt using the Latent Linear SVM as: Classifier response :

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Comparison with our approach HOG template (no deformation) Part-based model (rigid movable parts) Our model (deformation field)

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Our approach Why hasnt anyone tried it before?

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Our approach Why hasnt anyone tried it before? Latent models with many latent variables tend to overfit Inference not feasible for a sliding window

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Our approach Why hasnt anyone tried it before? Latent models with many latent variables tend to overfit Inference not feasible for a sliding window Deformation field used before only for Classification task (Duchenne et al ICCV11) Rescoring of detections (Ladický, PhD thesis)

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Our approach We restrict the deformation field to be locally affine ( ):

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Our approach We restrict the deformation field to be locally affine ( ):

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Our approach We restrict the deformation field to be locally affine ( ):

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Optimisation Weights / bias (w *, b * ) and the deformation fields d k estimated iteratively

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Optimisation Weights / bias (w *, b * ) and the deformation fields d k estimated iteratively Given the deformation fields the problem is a standard linear SVM:

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Optimisation Weights / bias (w *, b * ) and the deformation fields d k estimated iteratively Given (w *, b * ) the problem is a constrained MRF optimisation: The last can be decomposed as : By definingthe optimisation becomes:

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Optimisation The location of the cells in the first row and in the first column fully determine the location of each cell Any locally affine deformation field can be reached by two moves : each column i moves by (Δ c d i x,Δ c d i y ) each row j moves by (Δ r d j x,Δ r d j y )

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Optimisation The location of the cells in the first row and in the first column fully determine the location of each cell Any locally affine deformation field can be reached by two moves : each column i moves by (Δ c d i x,Δ c d i y ) each row j moves by (Δ r d j x,Δ r d j y )

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Optimisation The location of the cells in the first row and in the first column fully determine the location of each cell Any locally affine deformation field can be reached by two moves : each column i moves by (Δ c d i x,Δ c d i y ) each row j moves by (Δ r d j x,Δ r d j y ) Such moves do not alter the local affinity

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Optimisation The location of the cells in the first row and in the first column fully determine the location of each cell Any locally affine deformation field can be reached by two moves : each column i moves by (Δ c d i x,Δ c d i y ) each row j moves by (Δ r d j x,Δ r d j y ) Such moves do not alter the local affinity Both moves can be solved quickly using dynamic programming

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Learning multiple poses / viewpoints

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We define a similarity measure between two training samples as : where

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Learning multiple poses / viewpoints We define a similarity measure between two training samples as : where K-medoid clustering of S matrix clusters the data into multi model

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Experiments Buffy dataset (typically used for pose estimation) Contains large variety of poses, viewpoints and aspect ratios Consists of 748 images Episode s5e3 used for training Episode s5e4 used for validation Episodes s5e2, s5e5 and s5e6 used for testing Ferrari et al. CVPR08

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Clustering of training samples Each row corresponds to one model (out of 10 models)

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Qualitative results

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Quantitative results

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Conclusion We propose Novel inference for locally affine deformation field (LADF) Object detector using LADF Clustering using LADF

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Questions? Thank you

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