Multi-Scale Spatially Weighted Local Histograms in O(1)

Histograms are commonly used to characterize and analyze the region of interest within an image. Weighting the contributions of the pixels to the histogram is a key feature to handle noise and occlusion and increase object localization accuracy of many histogram-based search problems including object detection, tracking and recognition. The integral histogram method provides an optimum and complete solution to compute the plain histogram of any rectangular region in constant time. However, the matter of how accurately extract the weighted histogram of any arbitrary region within an image using integral histogram has not been addressed. This paper presents a novel fast algorithm to evaluate spatially weighted local histograms at different scale accurately and in constant time using an extension of integral histogram. Utilizing the integral histogram makes it to be fast, multi-scale and flexible to different weighting functions. The pixel-level weighting problem is addressed by decomposing the Manhattan spatial filter and fragmenting the region of interest, subsequently. We evaluated and compared the computational complexity and accuracy of our proposed approach with brute-force implementation and approximation scheme. The proposed method can be integrated into any detection and tracking framework to provide an efficient exhaustive search, improve target localization accuracy and meet the demand of real-time processing.