# Automatic Processing of Historical Japanese Mathematics (Wasan) Documents
## 3 Results
### Experiment 1: Blob Detectors for Kanji Segmentation  
This first experiment studies the performances of blob detectors to find Kanji characters. In order to do this, we considered several parameter combinations for the three methods (See [[https://scikit-image.org/docs/dev/auto_examples/features_detection/plot_blob.html](https://scikit-image.org/docs/dev/auto_examples/features_detection/plot_blob.html)]([https://scikit-image.org/docs/dev/auto_examples/features_detection/plot_blob.html](https://scikit-image.org/docs/dev/auto_examples/features_detection/plot_blob.html)) for detailed documentation on the Scikit-learn methods used, accessed on 1 September 2020).  
The main parameters considered were \((min_{\sigma},max_{\sigma},num_{\sigma},threshold,overlap)\). As it was impractical to run all parameter combinations with the full database, five Wasan images were used for the fine-tuning process, several parameter combinations where considered and the results for each of them was visually and automatically checked. \(min_{\sigma}\) and \(max_{\sigma}\) are related to the size of the blobs detected, and we obtained the best results with values \(min_{\sigma}\in(35,45)\), \(max_{\sigma}\in(45,50)\), the \(num_{\sigma}\) parameter related to the step size when exploring the parameter space and was set to 5. The threshold parameter relates to the variation allowed in scale space and was tested in the interval \((0.01,0.05)\). Finally, the overlap parameter relates to the degree of overlap allowed between different blobs. Values between 0 an 0.5 were tested.  
For each blob detector and combination of parameters, we considered the blobs detected as candidates for containing kanji. Then, by comparing these blobs with our manual annotation of the position of the kanji we were able to determine the percentage of kanji that had been correctly detected (\"True Positives\" TP) as well as the regions that did not actually contain kanji (\"False Positives\" FP). By comparing the number of TP with the actual number of kanji regions in the manual annotation we could also determine the percentage of kanji detected/missed. Figure 8 shows the boxplots for the correctly detected kanji percentage (left) and FP detections (right) for the three blob detectors considered.  
The figure shows how the best performance was obtained by the LoG blob detector. The three blob detectors used obtained high success rates with average kanji detection percentages of 79.60, 69.89, 57.27 for the LoG, DoG and DoH detectors and standard deviations of 8.47, 8.10, 13.26. The LoG obtained the best average as well as the most stable performance (smaller standard deviation) with the DoG method obtaining a comparable performance. In terms of false positive detections, the three methods obtained averages of 7.88, 16.86, and 15.07, and standard deviations 6.54, 9.35, and 8.71. Once again, the LoG blob detector performed best and in this criterion the result was clearly superior to that of the DoG method, which proved to be confused more frequently by not properly cleaned up noise regions in the image producing a higher number of false positives.