Automatic Processing of Historical Japanese Mathematics (Wasan) Documents

Abstract

“Wasan” is the collective name given to a set of mathematical texts written in Japan in the Edo period (1603–1867). These documents represent a unique type of mathematics and amalgamate the mathematical knowledge of a time and place where major advances where reached. Due to these facts, Wasan documents are considered to be of great historical and cultural significance. This paper presents a fully automatic algorithmic process to first detect the kanji characters in Wasan documents and subsequently classify them using deep learning networks. We pay special attention to the results concerning one particular kanji character, the “ima” kanji, as it is of special importance for the interpretation of Wasan documents. As our database is made up of manual scans of real historical documents, it presents scanning artifacts in the form of image noise and page misalignment. First, we use two preprocessing steps to ameliorate these artifacts. Then we use three different blob detector algorithms to determine what parts of each image belong to kanji Characters. Finally, we use five deep learning networks to classify the detected kanji. All the steps of the pipeline are thoroughly evaluated, and several options are compared for the kanji detection and classification steps. As ancient kanji database are rare and often include relatively few images, we explore the possibility of using modern kanji databases for kanji classification. Experiments are run on a dataset containing 100 Wasan book pages. We compare the performance of three blob detector algorithms for kanji detection obtaining 79.60% success rate with 7.88% false positive detections. Furthermore, we study the performance of five well-known deep learning networks and obtain 99.75% classification accuracy for modern kanji and 90.4% for classical kanji. Finally, our full pipeline obtains 95% correct detection and classification of the “ima” kanji with 3% False positives.