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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

In this paper a novel feature extraction method for image processing via PCNN and Tsallis entropy is presented. We describe the mathematical model of the PCNN and the basic concept of Tsallis entropy in order to find a recognition method for isolated objects. Experiments show that the novel feature is translation and scale independent, while rotation independence is a bit weak at diagonal angles of 45° and 135°. Parameters of the application on face recognition are acquired by bacterial chemotaxis optimization (BCO), and the highest classification rate is 72.5%, which demonstrates its acceptable performance and potential value.

Face recognition is a hot problem in image processing [

Since face image data are usually high-dimensional and large-scale, it is crucial to design an effective feature extraction method. Researchers have developed many algorithms, such as the Eigenface method [

However, such models are either subject to problems determined by geometric transforms (scaling, translation or rotation) or to high computational complexity [

Neural networks (NN) have been widely employed in face recognition applications. It is feasible for classification and results in similar or higher accuracies from fewer training samples. It has some advantages over traditional classifiers due to two important characteristics: their non-parametric nature and the non-Gaussian distribution assumption.

Pulse coupled neural network (PCNN) is called the 3^{rd} generation NN since it has the following advantages: (i) global optimal approximation characteristic and favorable classification capability; (ii) rapid convergence of learning procedure; (iii) an optimal network to accomplish the mapping function in the feed-forward; (iv) no need to pre-train. Hence, in this article, we present a novel face recognition approach based on PCNN.

The structure of this article is as follows. Section 2 introduces the architecture of our proposed novel model. Section 3 gives a brief overview on PCNN. Section 4 discusses how to obtain TNF by PCNN. Section 5 introduces the Tsallis entropy. Section 6 brings forward the MLP. Section 7 is the experiment which checks the Translation, Scaling, and Rotation Independence of our proposed feature. Section 8 is the face recognition system. This proposed method can achieve as high as 72.5% classification rate on a given database. Finally Section 9 concludes this paper.

The model proposed in this article is based on three modules: the PCNN, the Tsallis entropy, and the MLP classifier (

Pulse coupled neural network (PCNN) is a result of research on artificial neuron model that was capable of emulating the behavior of cortical neurons observed in the visual cortices of animal [

Total number of firing (TNF) is an important parameter obtained in PCNN. It is almost unique and has strong anti-noise ability. How to measure the information obtained in TNF? Communication systems are less well defined in PCNN. Thus traditional Shannon entropy is not fit for measuring. R. Sneddon discussed the Tsallis entropy of neurons and found it is more accurate and useful [

Thus, the novel feature of image is extracted now. We put the Tsallis entropy of the TNF into the multi-layer perceptron (MLP). After training, the MLP will automatically classify the images successfully.

A typical PCNN neuron consists of three parts: the receptive field, the modulation field and the pulse generator. This is shown in

Suppose

_{F}_{L}_{θ}_{F}_{L}_{θ}_{ij}_{ij}

Firstly, the neuron (

There exists a one-to-one correspondence between the image pixels and network neurons, which means, each pixel is associated with a unique neuron and vice versa.

The exponential decay is too time-consuming for fast realization, so an improvement to conventional PCNN is proposed here: the external input _{1}_{0}_{1}_{ij}_{ij}

During the simulation, each iteration updates the internal activity and the output for every neuron in the network, based on the stimulus signal from the image and the previous state of the network. For each iteration the TNF over the entire PCNN is computed and stored in a global array G. The following describes the details:

Initialize the range [_{0}, θ_{1}

Simplify the external input

Determine the expression

Perform the PCNN. Accumulate

Obtain the TNF from

Entropy is usually used to describe the information contained in the system. Shannon defined the concept of information and described the essential components of a communication system as the following: a sender, a receiver, a communication channel, and an encoding of the information set.

However, communication systems are less well defined when they occur in nature, such as the neurons. Neurons appear to both senders and receivers of information. Another question is what are the communication channels for neurons. They might be the synaptic gaps between the axon and dendrites or not. The answer is not acceptable for neurophysiologists. A more question is what is the encoding of the information. There is no clear and obvious answer.

In general, traditional Shannon entropy is not fit for measuring the information contained by PCNN. Thus, Tsallis entropy

_{1}x_{2}_{n}

In R. Sneddon's work, he set

The information contained in TNF is calculated as in the following equation:

The classifier is basically a MLP. The neural architecture consists of one input layer, one hidden layer and one output neuron (

Because of the specific task, the output layer contained only one neuron. An output value of 1 is equivalent to target detection whereas a value of 0 means no target detection. A standard back-propagation algorithm is used for supervised training.

The experiments consist of three stages. Firstly we give an example of obtaining Tsallis entropy of TNF. Secondly we check the property of position, scale and rotation independence.

Take Lena as an example. First, we normalize the pixel values into the range [0, 1]. Then we perform PCNN with

Hence, from

The

We use the Tsallis entropy

As expected, the system showed total translation independence. Then seven different scales of the rectangle were selected for testing scaling independence (

As for the rotation independent, the triangle had been rotated at different angles and the MSE had been computed for each rotation. Results shown in

From Section 7 it is obvious that the features extracted via our model is effective. Hence, we apply this method to face recognition. The datasets come from the University of Essex School of Computer Science and Electronic Engineering website (

Each individual is averagely split into training and testing sets, namely, 10 images are used for training while the other 10 images are used for testing. The optimal parameters (

The highest correct classification rate (CR) of our proposed algorithm has of 72.5%. Although it is not as ideal as some other mature face recognition algorithms, we consider it more potential since research on pattern recognition via PCNN is currently progressing.

Firstly we adjust one parameter while fix others to check the robustness of our method. Firstly, the parameter

From

Secondly, the parameter

Finally we changed the value of

The three important parameters are analyzed above. It can conclude that the parameters are essential to the performance of this model. Hence, it is important for researchers to tune these parameters before the network works.

In this study, a novel feature extraction method was described and applied for face recognition. This paper is just the first attempt to explore the potential of Tsallis entropy of TNF obtained by PCNN to handle the face recognition problems.

Experiments demonstrate that this new feature is unique, translation and scale independent. The future work shall focus on combining this proposed feature with others to improve the classification rate. Another possible research topic is to simplify the procedures in this model. Actually, PCNN does not need pre-training, so the calculation time is expected to decline faster.

Furthermore, this proposed approach is new and potential. It can be applied on all sorts of recognition fields.

This research was supported under following projects: 1) National Technical Innovation Project Essential Project Cultivate Project (706928); 2) Nature Science Fund in Jiangsu Province (BK2007103). Also thanks to referees for their suggested improvements to the contents of this article.

The architecture of the recognition system.

PCNN neuromime.

Feature extraction.

Shapes used for testing.

Seven different scales of the rectangle.

MSE for different rotation angles.

Several typical faces in the database.

The curve of CR with

The curve of CR with

The curve of CR with

The impact of scaling (Size of the origin image is 200 pixels).

Size | MSE | |
---|---|---|

50 | 0.0016, 0.0361, 0.1247, 0.2414, 0.3714, 0.4608, 0.4969, 0.4920, 0.4548, 0.3875, 0.3233, 0.2516, 0.1813, 0.1100, 0.0612, 0.0423, 0.0245, 0.0135, 0.0096, 0.0000 | 3.9524e-3 |

100 | 0.0006, 0.0280, 0.1163, 0.2376, 0.3657, 0.4581, 0.4967, 0.4930, 0.4539, 0.3887, 0.3148, 0.2509, 0.1818, 0.1119, 0.0612, 0.0380, 0.0243, 0.0139, 0.0086, 0.0000 | 1.1543e-3 |

150 | 0.0004, 0.0287, 0.1143, 0.2368, 0.3629, 0.4577, 0.4967, 0.4926, 0.4536, 0.3908, 0.3169, 0.2482, 0.1809, 0.1098, 0.0603, 0.0379, 0.0239, 0.0142, 0.0085, 0.0000 | 7.59e-4 |

200 | 0.0006, 0.0288, 0.1167, 0.2371, 0.3634, 0.4579, 0.4968, 0.4925, 0.4533, 0.3913, 0.3162, 0.2480, 0.1818, 0.1106, 0.0618, 0.0377, 0.0238, 0.0141, 0.0090, 0.0000 | 0 |

250 | 0.0004, 0.0285, 0.1165, 0.2381, 0.3635, 0.4583, 0.4967, 0.4926, 0.4539, 0.3921, 0.3167, 0.2484, 0.1815, 0.1110, 0.0629, 0.0378, 0.0242, 0.0142, 0.0088, 0.0000 | 4.6218e-4 |

300 | 0.0007, 0.0290, 0.1168, 0.2384, 0.3638, 0.4582, 0.4967, 0.4926, 0.4538, 0.3923, 0.3165, 0.2487, 0.1817, 0.1116, 0.0627, 0.0377, 0.0240, 0.0143, 0.0090, 0.0000 | 5.2731e-4 |

350 | 0.0006, 0.0294, 0.1168, 0.2389, 0.3639, 0.4584, 0.4967, 0.4925, 0.4537, 0.3923, 0.3163, 0.2482, 0.1819, 0.1120, 0.0631, 0.0379, 0.0242, 0.0145, 0.0090, 0.0000 | 6.6282e-4 |

The optimal parameters used in face recognition.

Parameters | |||||
---|---|---|---|---|---|

1.86 | 20 | 4 | 50000 | 72.5% |