scholarly journals The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment

Sensors ◽  
2020 ◽  
Vol 20 (5) ◽  
pp. 1353 ◽  
Author(s):  
Chao Pan ◽  
Zhicheng Lv ◽  
Xia Hua ◽  
Hongyan Li
Keyword(s):  
Systolic Array ◽  
Fast Algorithm ◽  
Cross Correlation ◽  
Inner Product ◽  
Order Moment ◽  
Mathematical Tool ◽  
Arbitrary Length ◽  
First Order ◽  
Normalized Cross Correlation ◽  
Systolic Structure

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.

scholarly journals NCC Based Correspondence Problem for First- and Second-Order Graph Matching

Sensors ◽  
2020 ◽  
Vol 20 (18) ◽  
pp. 5117
Author(s):  
Beibei Cui ◽  
Jean-Charles Créput
Keyword(s):  
Input Data ◽  
Cross Correlation ◽  
Graph Matching ◽  
Second Order ◽  
Consensus Algorithm ◽  
Interaction Method ◽  
Matching Algorithm ◽  
Scale Interaction ◽  
First Order ◽  
Normalized Cross Correlation

Automatically finding correspondences between object features in images is of main interest for several applications, as object detection and tracking, identification, registration, and many derived tasks. In this paper, we address feature correspondence within the general framework of graph matching optimization and with the principal aim to contribute. We proposed two optimized algorithms: first-order and second-order for graph matching. On the one hand, a first-order normalized cross-correlation (NCC) based graph matching algorithm using entropy and response through Marr wavelets within the scale-interaction method is proposed. First, we proposed a new automatic feature detection processing by using Marr wavelets within the scale-interaction method. Second, feature extraction is executed under the mesh division strategy and entropy algorithm, accompanied by the assessment of the distribution criterion. Image matching is achieved by the nearest neighbor search with normalized cross-correlation similarity measurement to perform coarse matching on feature points set. As to the matching points filtering part, the Random Sample Consensus Algorithm (RANSAC) removes outliers correspondences. One the other hand, a second-order NCC based graph matching algorithm is presented. This algorithm is an integer quadratic programming (IQP) graph matching problem, which is implemented in Matlab. It allows developing and comparing many algorithms based on a common evaluation platform, sharing input data, and a customizable affinity matrix and matching list of candidate solution pairs as input data. Experimental results demonstrate the improvements of these algorithms concerning matching recall and accuracy compared with other algorithms.

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