Chaining Convolution and Correlation in Practice: A Case Study in Visual Tracking

Two dimensional convolution and cross-correlation operations are used in many image processing and computer vision applications, with algorithms commonly using a number of these operations. It is well known that these operations can be performed quickly by using a FFT to reduce computational complexity. In this paper we investigate the extent that the structure of algorithms with multiple convolution and cross-correlation operations can be exploited to further reduce computational complexity. Using the CACTuS visual tracking algorithm as a case study, we demonstrate how successive convolution and correlation operations may be chained together in the Fourier domain by taking into account the growth and shift of the output. We experimentally demonstrate that our chaining technique can result in run-time reductions of up to 55% when compared to the individual FFT approach.