Ferns

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Some Methods for Augmented Reality ApplicationsVincent Lepetit, Mustafa Ozuysal, Julien Pilet, Pascal Lagger, Pascal Fua

Vision-Based 3D Tracking

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Recursive TrackingQuickTime and a decompressor are needed to see this picture.QuickTime and a decompressor are needed to see this picture.

t=0

t=1

t=2

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Real-Time 3D Object Detection

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Runs at 15 Hz

Keypoint RecognitionThe general approach [Lowe, Schmid, Mikolajczyk, Matas] is a particular case of classification:Search in the Database Pre-processing Make the actual classification easier Nearest neighbor classification

One class per keypoint: the set of the keypoints possible appearances under various perspective, lighting, noise...

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Training phase

ClassifierUsed at run-time to recognize the keypoints

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A New Classifier: Ferns

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Presentation on an Example

Ferns: TrainingThe tests compare the intensities of two pixels around the keypoint:

Invariant to light change by any raising function. Posterior probabilities:

Ferns: Training0 1 1 1 0 0

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Ferns: Training

Ferns: Training Results

Ferns: Recognition

JustificationWe are looking for proportional to but complete representation of the joint distribution infeasible. Naive Bayesian ignores the correlation:

Compromise:

ie probabilities stored by the leaves.14

It Really Works

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Ferns Implementation1: for(int i = 0; i < H; i++) P[i ] = 0.; 2: for(int k = 0; k < M; k++) { 3: int index = 0, * d = D + k * 2 * S; 4: for(int j = 0; j < S; j++) { 5: index

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