Fast Line-Based Imaging of Small Sample Features

1. M.A. Iwen1, G.S. Mandair2, M.D. Morris2, M. Strauss1,3University of Michigan 1 - Department of Mathematics, 2 - Department of Chemistry, 3 - Electrical Engineering and Computer Science Fast Line-Based Imaging of Small Sample Features Problem Setup Proposed Solutions Experiments • Given a low resolution First-Pass Raman spectroscopic image, I, and a small set of interesting image features, P, how can we obtain higher resolution images of P using the smallest number of scans possible? • Image I is an n x m rectangle of pixels • P is an interesting set of pixels in I • Each scan images an entire row/column • Minimizing Scans minimizes both acquisition time and sample damage • Optimal Columns: • Scan only the columns containing at least one P pixel. • Skips uninteresting columns in between the first and last interesting columns with P pixels • Easy to implement, but not the best solution • Optimal Rows + Columns: • Find a smallest possible set of rows and columns that covers every interesting pixel in P. Scan the found optimal rows + columns. • Finding an optimal rows + columns covering of P is a special case of the Set cover problem • The Set cover problem is generally NP hard • However, rows + columns is solvable in polynomial time using Ford-Fulkerson method Number of Lightest “HELLO” Pixels to Scan Vs. Number Rows/Columns to Cover Them 4 x 3 Image I with Interesting P = Black Pixels Optimal Rows + Columns Standard Solution Form Scan Graph. • Push Broom: • Scan from the first column containing a P pixel to the last column containing a P pixel (and all columns in between). • Limitations: • Manual and Non-adaptive Scan Time (sec) to Image Lightest Bone Pixels, Scan Time = 60 + 8(scanned rows/columns)‏ Conclusions Find min-cut and get Residual Network (RN). Label RN nodes not reachable from source white and RN nodes reachable from source gray. • Both Optimal Columns and Optimal Rows + Columns can decrease integration time and sample damage • Optimal Columns is guaranteed to use <= the scans Push Broom uses • Optimal Rows + Columns is guaranteed to use <= the scans Optimal Columns uses Push Broom Scan white rows and gray columns. = scanned = scanned This work was supported in part by NSF grant DMS-0510203