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Quantum image recognition is a technology by using quantum algorithm to process the image information. It can obtain better effect than classical algorithm. In this paper, four different quantum algorithms are used in the three stages of palmprint recognition. First, quantum adaptive median filtering algorithm is presented in palmprint filtering processing. Quantum filtering algorithm can get a better filtering result than classical algorithm through the comparison. Next, quantum Fourier transform (QFT) is used to extract pattern features by only one operation due to quantum parallelism. The proposed algorithm exhibits an exponential speed-up compared with discrete Fourier transform in the feature extraction. Finally, quantum set operations and Grover algorithm are used in palmprint matching. According to the experimental results, quantum algorithm only needs to apply square of

Biological recognition technology is more and more important in this modern society [

Flow chart of palmprint recognition.

Quantum computing and quantum information is a perfect product which combines quantum mechanics theory and classical computing theory. Quantum algorithm can solve some classical nonpolynomial problems in polynomial time and has many advantages of the superposition, coherence, and entanglement of the quantum state. So far, the most representative quantum algorithms are the large prime numbers factorization algorithm proposed by Shor [

Before palmprint filter, an original palmprint is needed to be segmented and normalized. A palmprint is extracted from palmprint database which is shown in Figure

Original palmprint.

Segmented and normalized palmprint.

Traditional gray pretreatment methods include histogram equalization, median filter, mean filter, and Gaussian filter [

For a normalized digital palmprint image

Then

Effect of traditional adaptive median filtering algorithm.

Effect of quantum adaptive median filtering algorithm.

Obviously, by using quantum adaptive median filtering algorithm, not only the image details can be better preserved but also the filtering ability is improved. Next we apply the binarization processing and pixel flip operation to filtered palmprint in order to benefit from the feature extraction.

Figure

Fingerprint subgraph.

Traditional feature extraction method is mainly based on discrete Fourier transform. For a given

The dimension of the filtered palmprint is

A quantum initial state is constructed which expresses the locations of all the white points in palmprint as

Palmprint feature matching algorithm matches between identifying palmprint characteristics and registered palmprint characteristics in signature database; this algorithm makes the final identification decision on the basis of feature extraction. Finally we can determine the identity of a person. The most important part of this process is to select the appropriate feature matching strategy [

We assume that the identifying palmprint after the characteristics extraction has many feature vectors which are

We treat the identifying palmprint feature vector

Quantum circuit of Grover algorithm.

The simulation platform is based on MATLAB; we add QCL (quantum computation language) as a toolbox in MATLAB to simulate quantum algorithms. There are lots of basic operations in quantum algorithms in QCL toolbox. QCL is a high level, architecture-independent programming language for quantum computers, with a syntax derived from classical procedural languages like C. This allows for the complete implementation and simulation of quantum algorithms. The key iterative operation of Grover is shown in Figure

Grove_G(x,n,y)

{

a=Box(x,y,2);

for i=1:n

and

a=G_phase(a,n);

for i=1:n

and

}

The number of identifying palmprints is 1,

Relationship between Grover searching times and the number of quantum bits.

Rossi et al. constructed a link between these initial states and hypergraphs, which provides an illustration of their entanglement properties [

Simulation experiment result is based on the standard library Poly U; Poly U palmprint image library is one of the largest image libraries in palmprint recognition public field. Poly U library has 600 images from 100 people (everyone has 6 images). The experiment is divided into the same palmprint experiment and cross-validation experiment.

In the same palmprint experiment, we extract 64 palmprints and put them in a database; each of the 64 palmprints is from different people. A palmprint in database is selected as an identifying palmprint. We use speed and accuracy to compare our Grover algorithm and quantum set operations with traditional Euclidean distance method. The same palmprint experiment results are shown in Table

The same palmprint experiment results of traditional algorithm and our algorithm.

Algorithm | Euclidean distance calculation method | Quantum set operations and Grover algorithm |
---|---|---|

Matching numbers | 64 | 8 |

Matching time (s) | 0.41 | 0.20 |

Matching accuracy (%) | 94 | 99 |

In the cross-validation experiment, we extract 64 palmprints which are different from above palmprints and put them in a database; each of the 64 palmprints is from different people. In the cross-validation experiment, we first estimate the number of matched palmprints. We can estimate the number of solutions much more quickly than by traditional method by combining the Grover interation with the phase estimation method.

The essence of Grover searching algorithm is to determinate the phase flip angle; if the angle is known, we can get the number of matched palmprints. In this paper we use phase estimation method to identify the phase of target quantum state. Phase estimation method is needed to build two registers. An overall schematic of the algorithm is shown in Figure

Schematic of the overall phase estimation procedure.

The top line (the “/” denotes a bundle of wires) is the first register; the bottom line is the second register. Unitary operator

First we prepare the state

We use phase estimation method to estimate the phase when we search in training palmprints. Then we use Grover to estimate the number of palmprint which is matched with the validation palmprint. The cross-validation experiment results are shown in Table

Cross-validation experiment results of traditional algorithm and our algorithm.

Algorithm | Euclidean distance calculation method | Quantum set operations and Grover algorithm |
---|---|---|

Matching numbers | 64 | 8 |

Matching time (s) | 0.52 | 0.31 |

Matching accuracy (%) | 93 | 99 |

In Table

Quantum algorithms are applied to palmprint recognition in this paper. Palmprint is filtered by using quantum adaptive median filtering algorithm. Compared with the traditional methods, we can see from the filtering effect chart that this method possesses an enhanced ability of filtering and in the meantime conserves palmprint details. Then, the features of palm print are extracted by means of QFT; the features of pattern can be obtained via quantum parallel characteristics. Analysis shows that the pace of our quantum algorithms has increased exponentially compared with the pace of traditional feature extraction algorithm. Eventually, palmprint matching processing is carried out by using Grover algorithm and quantum set operations. As you can see from the analysis of the experimental result, quantum algorithms can increase matching accuracy and shorten the matching time. Therefore, it gets a marvelous matching effect.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by Henan Provincial Department of Education Science and Technology Research Key Project (no. 13A510330) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant no. 11105042).