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Practical Time Bundle Adjustment for 3D Reconstruction on the GPU

Practical Time Bundle Adjustment for 3D Reconstruction on the GPU. Siddharth Choudhary ( IIIT Hyderabad ), Shubham Gupta ( IIIT Hyderabad ), P J Narayanan ( IIIT Hyderabad ). Abstract. High Performance Bundle Adjustment. Outline. Motivation Problem Statement What is Bundle Adjustment ?

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Practical Time Bundle Adjustment for 3D Reconstruction on the GPU

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  1. Practical Time Bundle Adjustment for 3D Reconstruction on the GPU SiddharthChoudhary ( IIIT Hyderabad ), Shubham Gupta ( IIIT Hyderabad ), P J Narayanan ( IIIT Hyderabad )

  2. Abstract High Performance Bundle Adjustment

  3. Outline • Motivation • Problem Statement • What is Bundle Adjustment ? • Sparse Bundle Adjustment on the GPU • Results and Analysis • Summary • Future Work

  4. Motivation Images Interest Point Detection Invariant Point Description 50% of Computation Time Image Matching Image Geometry Model Fitting Connected Component Identification and 3D Point Estimation 50% of Computation Time Refinement using Bundle Adjustment and Model Output

  5. 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

  6. What is Bundle Adjustment ? 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

  7. 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:

  8. Sparse Bundle Adjustment on the GPU • Compute the Predicted Projection and Error Vectors • Compute L2 Error using Error Vectors • Compute Jacobian Matrix (J) • Compute Hessian Matrix and augment it • ComputeSchur Complement to form Reduced Camera System GPU CPU • Compute • Compute • Compute Inverse of Reduced Camera System and calculate

  9. Results and Analysis

  10. Results and Analysis

  11. 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

  12. 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

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