# Stephen Marshall

```Rotational Scanning Techniques
for Hyperspectral Imaging
Timothy Kelman, Stephen Marshall, Jinchang Ren, John R Gilchrist
HSI 2012
Presentation Outline
• Pushbroom Acquisition
• Rotational Linescan
• Mathematical Representation and Conversion
• Automatic Offset Determination
• Interpolation
• Quantitative Evaluation
• Conclusion
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
Perfect Rotational Linescan
• Axis of rotation coincident with centre of linescan
• Similar to polar representation
Vertically Offset Rotational Linescan
• Linescan does not pass through axis of rotation
• Causes a blind spot
Horizontally Offset Rotational Linescan
• Causes a shift in the output scan
• Does not cause a blind spot
Horizontally and Vertically Offset
Rotational Linescan
• Two offsets operate independently
• Blind spot and shift
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
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
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
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
Example Scans
Example Scans
Automatic Offset Determination
• Calibration Object scanned
• Theoretical perfect scan compared with actual scan
• Difference used to calculate offsets
Vertical Offset Determination
Horizontal Offset Determination
• Horizontal offset is equal to the distance between centre of scan
and centre of white bar.
Interpolation
• Each Cartesian pixel unlikely
Nearest Neighbour
to have exact representation
in scanned image so some
form of interpolation is
Bilinear
required
• Three techniques tested
between performance and
complexity
Bicubic
Quantitative Evaluation
• Three randomly generated synthetic images
Synthetic Scan 1
Synthetic Scan 2
Synthetic Scan 3
Quantitative Evaluation
• Each synthetic image compared with actual scans using image
correlation
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
```