Fast Template Matching by Subsampled Circulant Matrix

TL;DR

This paper introduces a probabilistic, fast template matching method that reduces computational complexity by downsampling signals, making it suitable for real-time image and signal processing applications.

Contribution

It proposes a novel matching scheme based on subsampled circulant matrices that significantly lowers computation costs compared to traditional methods.

Findings

Achieves O(N) additions and O(K log K) multiplications in matching process.

High probability of successful match for binary signals under certain conditions.

Experimental results confirm the efficiency and theoretical analysis of the method.

Abstract

Template matching is widely used for many applications in image and signal processing and usually is time-critical. Traditional methods usually focus on how to reduce the search locations by coarse-to-fine strategy or full search combined with pruning strategy. However, the computation cost of those methods is easily dominated by the size of signal N instead of that of template K. This paper proposes a probabilistic and fast matching scheme, which computation costs requires O(N) additions and O(K \log K) multiplications, based on cross-correlation. The nuclear idea is to first downsample signal, which size becomes O(K), and then subsequent operations only involves downsampled signals. The probability of successful match depends on cross-correlation between signal and the template. We show the sufficient condition for successful match and prove that the probability is high for binary signals with K^2/log K >= O(N). The experiments shows this proposed scheme is fast and efficient and supports the theoretical results.