Memory-efficient and fast implementation of local adaptive binarization methods

Binarization is widely used as an image preprocessing step to separate object especially text from background before recognition. For noisy images with uneven illumination, threshold values should be computed pixel by pixel to obtain a good segmentation. Since local threshold values typically depend on moments-based statistics such as mean and variance of gray levels inside rectangular windows, integral images are commonly used to accelerate the calculation. However, integral images are memory consuming. For Sauvola's method, the two integral images occupy $16HW$ bytes given a $H\times W$ input image. By using a recursive technique to avoid integral images, memory usage of intermediate data structures can be reduced significantly to $6\min\{H,W\}$ bytes, while the time complexity remains $O(HW)$ independent of window size. Therefore, the proposed implementation enable various local adaptive binarization methods to be applied in real-time use cases on devices with limited resources.

Stroke extraction for offline handwritten mathematical expression recognition

Offline handwritten mathematical expression recognition is often considered much harder than its online counterpart due to the absence of temporal information and the presence of background noise. In order to take advantage of the more developed techniques on online recognition and save resources, an oversegmentation approach is proposed to recover strokes from a textual bitmap image automatically. The proposed algorithm first break down the skeleton of a binarized image into junctions and segments, then segments are merged to form strokes, finally the ordering is determined by recursive projection and topological sort. Given a state-of-art online handwritten mathematical expression recognition system, the proposed procedure correctly recognized 58.22%, 65.65% and 65.05% of the offline formulas rendered from CROHME 2014, 2016 and 2019 respectively. Therefore, the effectiveness of stroke extraction to offline recognition is justified.