Integral histogram: a fast way to extract histograms in Cartesian spaces

We present a novel method, which we refer as an integral histogram, to compute the histograms of all possible target regions in a Cartesian data space. Our method has three distinct advantages: 1) It is computationally superior to the conventional approach. The integral histogram method makes it possible to employ even an exhaustive search process in real-time, which was impractical before. 2) It can be extended to higher data dimensions, uniform and nonuniform bin formations, and multiple target scales without sacrificing its computational advantages. 3) It enables the description of higher level histogram features. We exploit the spatial arrangement of data points, and recursively propagate an aggregated histogram by starting from the origin and traversing through the remaining points along either a scan-line or a wave-front. At each step, we update a single bin using the values of integral histogram at the previously visited neighboring data points. After the integral histogram is propagated, histogram of any target region can be computed easily by using simple arithmetic operations.