Integral Images: Efficient Algorithms for Their Computation and Storage in Resource-Constrained Embedded Vision Systems

The integral image, an intermediate image representation, has found extensive use in multi-scale local feature detection algorithms, such as Speeded-Up Robust Features (SURF), allowing fast computation of rectangular features at constant speed, independent of filter size. For resource-constrained real-time embedded vision systems, computation and storage of integral image presents several design challenges due to strict timing and hardware limitations. Although calculation of the integral image only consists of simple addition operations, the total number of operations is large owing to the generally large size of image data. Recursive equations allow substantial decrease in the number of operations but require calculation in a serial fashion. This paper presents two new hardware algorithms that are based on the decomposition of these recursive equations, allowing calculation of up to four integral image values in a row-parallel way without significantly increasing the number of operations. An efficient design strategy is also proposed for a parallel integral image computation unit to reduce the size of the required internal memory (nearly 35% for common HD video). Addressing the storage problem of integral image in embedded vision systems, the paper presents two algorithms which allow substantial decrease (at least 44.44%) in the memory requirements. Finally, the paper provides a case study that highlights the utility of the proposed architectures in embedded vision systems.