text: 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 @math bytes given a @math input image. By using a recursive technique to avoid integral images, memory usage of intermediate data structures can be reduced significantly to @math bytes, while the time complexity remains @math 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.
  @cite_9: Adaptive binarization is an important first step in many document analysis and OCR processes. This paper describes a fast adaptive binarization algorithm that yields the same quality of binarization as the Sauvola method,1 but runs in time close to that of global thresholding methods (like Otsu's method2), independent of the window size. The algorithm combines the statistical constraints of Sauvola's method with integral images.3 Testing on the UW-1 dataset demonstrates a 20-fold speedup compared to the original Sauvola algorithm.
  @cite_20: Image thresholding is a common task in many computer vision and graphics applications. The goal of thresholding an image is to classify pixels as either "dark" or "light." Adaptive thresholding is a form of thresholding that takes into account spatial variations in illumination. We present a technique for real-time adaptive thresholding using the integral image of the input. Our technique is an extension of a previous method. However, our solution is more robust to illumination changes in the image. Additionally, our method is simple and easy to implement. Our technique is suitable for processing live video streams at a real-time frame-rate, making it a valuable tool for interactive applications such as augmented reality. Source code is available online.
summary: @cite_20 used integral images to speed up the calculation of the mean of gray levels inside a window. @cite_9 extended the trick to calculate the standard deviation. Let @math , then @math as shown in Fig. . The integral image @math can be computed recursively using the following recurrence relation: @math . Therefore, the time complexity of Sauvola's method can be reduced to @math , which is independent of window size. However, consumption of memory increased significantly from @math to @math because the two additional integral images need to be stored.