Get ready to learn about Gaussian Process's and their application to physical interpolations!

• Students: Nate Schambach, Ben Strober
• Mentor(s): Dr. Kobilarov, Dr. Taylor, Preetham Chalasani

The primary goal of this project is to optimize tissue reconstruction through palpation force measurements. To do this we are employing an online version of gaussian process regression to choose the minimum number of points for an accurate reconstruction. While it has already been employed for AUV optimal trajectories our application could eventually be used for things such as tumor location and identification.

• Minimum: COMPLETED
  1. Geometry reconstruction of a sample image using Gaussian Process

• Expected: COMPLETED
  1. Geometry reconstruction of sample tissue using Gaussian Process
  2. This will utilize the cartesian stage and a phantom

• Maximum: (4/27/15)
  1. Using geometry reconstruction of sample tissue, create model of stiffness within tissue

The ultimate goal of this project is to utilize Gaussian Processes to predict geometry of stiffness within a tissue from a finite number of force sensor palpalpation readings. These force sensor palpation readings will act as the training data for the Gaussian Process. The force sensor palpation readings will provide information on height (z), as well as force (f). Using the height information as training data for the geometry Gaussian Process, we created a Gaussian process to predict height from (x,y) position. Using height and force information as a training data for the stiffness Gaussian Process, we created a separate Gaussian process to predict stiffness from (x,y) position.

Gaussian process makes predictions by utilizing the covariances of the points already trained on and covariances of the points you wish to predict at.

The exact formula is as follows: yhat = Cov(trained, predict)*inv(Cov(trained, trained))*trained.

The beauty of this is that a ground truth is not necessary for comparing against nor is an exact function needed to fit. The gaussian process also predicts the variance in the prediction at each point. We utilize this in the training process to choose the optimal trajectory of the robot. When each point is added to the training set a set of random nearby points is generated as the potential next point and the change in the variance based on the predicted knowledge gain should one of these be added to the model. The point which adds the most information is then chosen.

At this point, almost all of our dependencies have been met.

We currently rely on only:

- Access to more phantoms for testing and validation, particularly for the stiffness reconstruction.

- Access to mentors for advise/guidance

1. Milestone name: Robot Geometry Testing
   • Planned Date: 4/6/15
   • Expected Date: 4/6/15
   • Status: Finalizing for optimal results. Comparison to CAD model after an ICP has been performed.
2. Milestone name: Stiffness Code Development
   • Planned Date: 4/3/15
   • Expected Date: 4/3/15
   • Status: Testing and Revision in Progress
3. Milestone name: Robot Stiffness Testing
   • Planned Date: 4/15/15
   • Expected Date: 4/15/15
   • Status: Testing in Progress

• Project Plan
  • Project plan presentation
  • Project plan proposal
• Project Background Reading
  • See Bibliography below for links.
• Project Checkpoint
  • Project checkpoint presentation
• Paper Seminar Presentations
  • Review of Gaussian Processes and Machine Learning
  • Critical Review of Active Learning
• Project Final Presentation
  • PDF of Poster
• Project Final Report
  • Final Report
  • Working Codes for GP

1. C. E. Rasmussen & C. K. I. Williams, Gaussian Processes for Machine Learning, the MIT Press, 2006, ISBN 026218253X. c 2006 Massachusetts Institute of Technology.

2. Ebden, Mark. Gaussian Process for Regression: A Quick Introduction. N.p., Aug. 2008. Web. Neal, R.M.: Regression and classification using Gaussian process priors (with discussion). In Bernardo, J.M., et al., eds.: Bayesian statistics 6. Oxford University Press (1998) 475–501

3. Williams, C.K.I.: Prediction with Gaussian processes: From linear regression to linear prediction and beyond. In Jordan, M.I., ed.: Learning in Graphical Models. Kluwer Academic (1998) 599–621

4. Kroese, D. “The Cross-Entropy Method.” A Unified Approach to Combinatorial Optimtimization, Monte-Carlo Simulation and Machine Learning. By R. Rubinstein. N.p.: n.p., n.d. N. pag. Print.

All associated codes are in the Reports and Presentations section. Under Project Final Report

This work was supported in part by NRI grant IIS-1327566, in part by NSF NRI 1208540, and in part by Johns Hopkins University internal funds