1. Rotational Scanning Techniques for Hyperspectral Imaging Timothy Kelman, Stephen Marshall, Jinchang Ren, John R Gilchrist HSI 2012

2. Presentation Outline Pushbroom Acquisition Rotational Linescan Mathematical Representation and Conversion Automatic Offset Determination Interpolation Quantitative Evaluation Conclusion

3. Pushbroom Acquisition Hyperspectral images are 3 dimensional data structures Acquisition usually requires two dimensions remain constant whilst the third is varied λ x y t

4. Perfect Rotational Linescan Axis of rotation coincident with centre of linescan Similar to polar representation

5. Vertically Offset Rotational Linescan Linescan does not pass through axis of rotation Causes a blind spot

6. Horizontally Offset Rotational Linescan Causes a shift in the output scan Does not cause a blind spot

7. Horizontally and Vertically Offset Rotational Linescan Two offsets operate independently Blind spot and shift

8. Mathematical Representation Each line scanned represents a tangent to a circle Radius of the circle equal to the vertical offset Horizontal offset shifts the tangent

9. Cartesian Conversion For each pixel, J, in the output scan, there are two tangents and two points on the circle which intersect these tangents If the vertical offset, r, is known P and Q can be derived

10. Cartesian Conversion The locations of P and Q can be represented by angles on the circle Their Euclidean distances from J are the tangent lengths

11. Cartesian Conversion J is represented by two angles and two tangent lengths The values can be used to extract a pixel from the output scan image

12. Example Scans

14. Automatic Offset Determination Calibration Object scanned Theoretical perfect scan compared with actual scan Difference used to calculate offsets

15. Vertical Offset Determination

16. Horizontal Offset Determination Horizontal offset is equal to the distance between centre of scan and centre of white bar.

17. Interpolation Nearest Neighbour Each Cartesian pixel unlikely to have exact representation in scanned image so some form of interpolation is required Three techniques tested Bilinear offered best tradeoff between performance and complexity Bilinear Bicubic

18. Quantitative Evaluation Three randomly generated synthetic images Synthetic Scan 1Synthetic Scan 2Synthetic Scan 3

19. Quantitative Evaluation Each synthetic image compared with actual scans using image correlation

20. Conclusions Method for converting rotationally scanned images to Cartesian form Automatic offset calculation Bilinear interpolation offers best trade off between performance and complexity Image correlation shows rotational scanning is a viable alternative to pushbroom scanning