Abstract
Normalized cross-correlation is an important mathematical tool in digital signal processing. This paper presents a new algorithm and its systolic structure for digital normalized cross-correlation, based on the statistical characteristic of inner-product. We first introduce a relationship between the inner-product in cross-correlation and a first-order moment. Then digital normalized cross-correlation is transformed into a new calculation formula that mainly includes a first-order moment. Finally, by using a fast algorithm for first-order moment, we can compute the first-order moment in this new formula rapidly, and thus develop a fast algorithm for normalized cross-correlation, which contributes to that arbitrary-length digital normalized cross-correlation being performed by a simple procedure and less multiplications. Furthermore, as the algorithm for the first-order moment can be implemented by systolic structure, we design a systolic array for normalized cross-correlation with a seldom multiplier, in order for its fast hardware implementation. The proposed algorithm and systolic array are also improved for reducing their addition complexity. The comparisons with some algorithms and structures have shown the performance of the proposed method.
Highlights
Normalized cross-correlation (NCC) is an important mathematical tool in signal and image processing for feature matching, similarity analysis, motion tracking, object recognition, and so on [1,2,3]
For the hardware implementation of NCC, we develop a simple and scalable systolic array derived from the proposed algorithm, due to the fact that the fast algorithm for the first-order moment is performed by systolic structure [27]
NCCs be implemented by efficient algorithms and structures hardware for decreasing high multiplication complexity [35]
Summary
Normalized cross-correlation (NCC) is an important mathematical tool in signal and image processing for feature matching, similarity analysis, motion tracking, object recognition, and so on [1,2,3]. For performing an arbitrary-length digital NCC, our algorithm would first establish the NCC formula based on a first-order moment for correlation sequences, and introduce a fast algorithm without multiplication from [25,26] to compute this first-order moment in the new NCC formula rapidly. For the hardware implementation of NCC, we develop a simple and scalable systolic array derived from the proposed algorithm, due to the fact that the fast algorithm for the first-order moment is performed by systolic structure [27]. The proposed algorithm and systolic array are improved to reduce their addition complexity, according to an even-odd relationship in the computation of the first-order moment.
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