PRACTICAL TIME BUNDLE ADJUSTMENT FOR 3D RECONSTRUCTION ON THE GPU Siddharth Choudhary ( IIIT...
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Transcript of PRACTICAL TIME BUNDLE ADJUSTMENT FOR 3D RECONSTRUCTION ON THE GPU Siddharth Choudhary ( IIIT...
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PRACTICAL TIME BUNDLE ADJUSTMENT FOR 3D RECONSTRUCTION ON THE GPUSiddharth Choudhary ( IIIT Hyderabad ), Shubham Gupta ( IIIT Hyderabad ), P J Narayanan ( IIIT Hyderabad )
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Abstract
+¿
High Performance Bundle Adjustment
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Outline Motivation Problem Statement What is Bundle Adjustment ? Sparse Bundle Adjustment on the GPU Results and Analysis Summary Future Work
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MotivationImages
Interest Point DetectionInvariant Point
DescriptionImage Matching
Image Geometry Model Fitting
Connected Component Identification and 3D Point Estimation
Refinement using Bundle Adjustment and Model Output
50% of Computation Time
50% of Computation Time
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Problem Statement
The goal is to develop a practical time implementation of Bundle Adjustment by exploiting all computing resources of the CPU and the GPU
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What is Bundle Adjustment ?
min𝑃 ,𝑋
∑𝑖=1
𝑛
∑𝑗=1
𝑚
𝑑 (𝑄 (𝑃 𝑗 , 𝑋 𝑖 ) , 𝑥𝑖𝑗 )2
Objective Function:
is the predicted projection of point i on image j is the Euclidean distance between the image points represented by x and y
Minimizing this function is a sparse non linear least squares problem
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What is Bundle Adjustment ?
The non-linear least squares objective function is solved using LM Algorithm which is an interpolation of Gauss Newton and Gradient descent iteration.
The normal equation to be solved during each linear LM iteration is given as:
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Sparse Bundle Adjustment on the GPU
Compute Hessian Matrix and augment it
Compute the Predicted Projection and Error
Vectors
Compute Jacobian Matrix (J)
Compute L2 Error using Error Vectors
Compute
Compute Schur Complement to form
Reduced Camera System
Compute
Compute Inverse of Reduced Camera System and calculate
GPU CPU
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Results and Analysis
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Results and Analysis
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Summary We introduced a hybrid algorithm using
the GPU and the CPU to perform practical time bundle adjustment.
We achieve a speedup of around 8 – 10 times over the CPU implementation on one quarter of Nvidia Tesla S1070 GPU
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Future Work We are adapting our approach to the
Fermi and expecting significant speedups on it.
A multi GPU implementation is also being explored for faster overall processing