1. Procrustes Shape Analysis Verification Tool
Steve Lack1, Neil Fox2, George Limpert2, and Brice Lambi1
1NOAA ESRL-Forecast Verification Section
2University of Missouri-Columbia

2. Review
Micheas et al. 2007
Landmark based method (matches points along identified cell boundary)
Identification of cells using minimum threshold of intensity and size
Matches objects based on minimizing centroid location or minimizing error based on fit
Can be run on an ensemble product
Penalty based on sum of squares error of matched cells
MATLAB® code

3. Updates Cell Identification
Added a component to enable the use of identifying cells based on FFT at multiple scales
Size threshold may still be used for binary images
Matching--full attribute matching scheme, tunable
False alarm identification and penalties
Recode into C++, build interactive Java webpage

4. Cell Identification Spectral Analysis
Spectral analysis is performed using the Fourier Transform
Instead of working in a spatial (x,y) domain, some work is done in a frequency (u,v) domain
As u and v increase, structure size decreases
Therefore by selecting appropriate u and v values, some of the work of identifying structures at multiple scales is already done
Use IFFT to get back into the spatial domain

5. RADAR Application
Can easily breakdown image into stratiform (low frequency) and convective (high frequency) components
Breakdown convective image into multiple spatial scales (cells, segments, and clusters)
Larger clusters are used for most of the verification exercises
May be adapted for precip rates or amounts.

6. Classification
Original Image (left) with convective/ stratiform mask (right)

7. Multi-scale Breakdown

8. Matching Get away from centroid matching or minimum shape matching
Combine the two and include other parameters: size, rotation, intensity
Sum of squares penalty function of all attributes becomes a matching tool
Can tune the parameters to put more weight on displacement or intensity, etc

9. Matching – distance vs. Procrustes

10. Fit Comparison

11. Fit Comparison

12. Matching Tags
Once the code finds the correct matches and assesses penalties, cell pairs are tagged
Hits
Misses
False Alarms
Multiple forecast cells can be matched to a single truth (hits and false alarms)
Truth cells can be matched to the same forecast cell (hits and misses)
False alarms penalties can be assessed in a total domain penalty
Allows for higher penalties for false alarms with high displacement
Lower penalties for low displacement (tight cluster of cells in forecast with lower count of truth cells)

13. Interface
Select use cases (geometric test data) through different options available in the Procrustes scheme
Retains a classic version (min. size, min. intensity threshold) and new FFT version
Customize matching criteria
Display SS error results and absolute displacement vector for now