Full-Search-Equivalent Pattern Matching with Incremental Dissimilarity Approximations

This paper proposes a novel method for fast pattern matching based on dissimilarity functions derived from the L_p norm, such as the Sum of Squared Differences (SSD) and the Sum of Absolute Differences (SAD). The proposed method is full-search equivalent, i.e. it yields the same results as the Full Search (FS) algorithm. In order to pursue computational savings the method deploys a succession of increasingly tighter lower bounds of the adopted L_p norm-based dissimilarity function. Such bounding functions allow for establishing a hierarchy of pruning conditions aimed at skipping rapidly those candidates that cannot satisfy the matching criterion. The paper includes an experimental comparison between the proposed method and other full-search equivalent approaches known in literature, which proves the remarkable computational efficiency of our proposal.

1. Introduction

Pattern matching aims at locating the instances of a given template into a reference set. This task occurs in numerous image analysis applications and consists of determining the regions of the reference image that are similar to the template according to a given criterion and discarding those that are dissimilar. The Full Search (FS) pattern-matching algorithm relies on calculating, at each position of the reference image, a function measuring the degree of similarity or dissimilarity between the template and the portion of the image currently under examination, referred to as image subwindow. Once the chosen function is computed for all subwindows, a threshold is usually adopted so as to classify between matching and mismatching patterns. norm-based dissimilarity functions are widely used in pattern-matching applications involving images of the same modality, as thoroughly discussed in [1]. The most popular norm-based dissimilarity functions are the Sum of Squared Differences (SSD) and the Sum of Absolute Differences (SAD). For what concerns the SSD, though the typical alternative to the naive FS algorithm is represented by the FFT-based approach, a novel fast FS-equivalent method [1], referred to here as Projection Kernels (PKs), was recently proposed in the literature. This method was shown to be much more efficient compared to the naive FS-approach, as well as to the FFT. With regard to the SAD, a well-known classical approach is the Sequential Similarity Detection Algorithm (SSDA) [2].