Comparisons of two approaches of pattern recognition for text detection

Abstract

The paper describes two methods of pattern recognition, one based on soft sets, another based on neural networks. Soft set theory is quite recently developed method of AI. That approach has rather simple mathematical background, but can perform satisfactory. Widespread neural network approach demands much more calculating power to perform at the same level of accuracy. Some hints to make neural network perform better have been written. Authors explain necessary theoretical terms and definitions then describe their idea of two AI systems. At the end some results of first system are presented.

Keywords

• eol>Text detection
• Pattern recognition
• Soft reasoning
• Simple soft classifier
• Weighted soft classifier
• Weighted mean soft classifier

1. Introduction

1.1. Related works

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2. Mathematical part of the algorithm

2.1. Soft sets - introduction

Soft set theory is one of recently developed ideas. That is quite surprising due to its mathematical simplicity and, as we shall see, powerful performance. First re- and denotes cardinality of ( ). That matrix  sults have been published by Russian scholar Dmitri is given by a formula: Molodotsov in his paper [15] in 1999. His idea was to simulate the uncertainty of membership in given set.

Definition 1 (Soft set). Let be the universe and be the set of parameters describing elements of . A soft set is an ordered pair ( , ), where  ⊆ and  ∶  ⟶  ( ). By  ( ) we denote the power set of .

We shall reference to  as membership function.

As we can see from the definition ( 1 ) the name soft originates from parametric description of membership.

It can be clearly seen, that classical set considered in the set theory are special cases of soft sets. Its membership function is its indicator function.

Definition 2 (Soft subset). Let be the universe and  ), (, ) be soft sets specified in . ( , ) is a soft ( , subset of (, ) if •  ⊆  in classical sense, • ∀ ∈  ∶  ( ) = ( ).

We can also define soft set in a relation form. That representation is very useful in further applications.

Definition 3 (Soft set in relation form). be soft set in given universe . Let

Let ( , ) ⎡ 1,1 ⎢ 2,1  = [ , ] × = ⎢⎢ ⋮ 1,2 2,2

⋮ ⎣ , 1 , 2 ⋯ ⋯ ⋱ ⋯ , ⎦ 1, ⎤ 2, ⎥ ⋮ ⎥⎥ ,

( 4 ) where , =  (( , )). More definitions and theoretical introduction can be found in [16]. Our system will depend only on aforementioned terms.

2.2. Soft reasoning

The process of making decisions using soft sets will be called soft reasoning. The classical approach to soft reasoning can be divided into several steps: 1. choose your universe of objects and set  ⊆

, 2. choose parameters which describe your objects

and construct set , 3. construct membership function of every ∈ , 4. choose set which will be called set of demands, 5. for every object ∈  calculate the value of

classifier, 6. choose the best options using results of classi

ifer.

First of all we shall discuss step 4. A demand will  = {(, ) ∶ ∈ , =  ( )}. ( 1 ) be a vector of length the same as the cardinality of . Elements of will be real numbers from interval  is a soft set ( , ) in relation form. [0, 1]. Each of the elements will correspond to priority Now we can consider Cartesian product of  and im- of each of parameters from set . age of  (denote as ( )). It can be seen that: Now, let us consider step 5. A soft classifier is a function which takes vector of parameters of an object and  ⊆  × ( ). ( 2 ) vector of demands and returns a numeric value [17].

We shall discuss several kinds of soft classifiers in next Using relation ( 2 ) we can express the soft set ( , ) section. in language of classical set theory. Especially, we can Lastly, we shall present a few notes about step 6. define an indicator function of that soft set. The determination of number of the best options can depend on the specific problem. For example, someDefinition 4 (Indicator function of a soft set). Let times we can wish to choose the best option, at some  be a soft set in relation form corresponding to soft set other time we wish to find all options better than given ( , ) and (, ) ∈  × ( ). The indicator function threshold value. of the soft set ( , ) is given by following formula:  ((, )) = { 1, when (, ) ∈ , 0, otherwise.

Using function  ((, )) a special matrix called binary relation table can be constructed. Its dimensions are × , where denotes cardinality of the set  ( 3 )

2.3. Soft classifiers

We shall discuss three kinds of soft classifiers: • simple soft classifier (SSC), • weighted soft classifier (WSC), • weighted mean soft classifier (WMSC). (, ) = ∑ . (, ) = ∑ . (, ) =

For SSC we simply need binary vector of demands its values are only 0 or 1. For readability purposes we SSC - results eters which have value 1. Let be the length of vector of demands . This classifier and object is given WSC does not demand binarity of vector of demand.

We will use weighted sum in our calculations:

be the set of goods in grocery store and  ⊆

2.4. SSC - example

Let such that:  = {, , , ℎ, ,

= { ℎ, , ℎ, ,

, , , , ,

• = { ℎ, ℎ, • = { , , ,

• = { ℎ, , , , } Now we can choose set of interesting parameters: ( 3 ).

Now we can construct a binary relation table using standard function. That table is presented in table

Now consider three binary vectors of demands: We calculate the values of the SSC which are presented in table ( 1 ). Now we can choose goods with highest in that model: value of SSC for every demand: • input signals, • activation function, • output signal. • A - pepper, • B - spinach, • C - apple. , } }.

2.5. WSC - example

Let ,  be defined as in previous example. Now, we shall construct non-binary vectors of demands (we shall also omit zero-valued elements): • { • {ℎ 0.4, 0.3,

− 0.6} − 0.7} − 0.7, − 0.3, − 1, − 0.6, − 0.4, − 0.5, − − Values of WSC are presented in table ( 2 ). As we can see the best option for each of demands is spinach. It can be clearly seen that SSC is special case of WSC, but WSC gives much more precise results.

2.6. Neural networks - model of neuron

To analyze neural network architecture we have to start with the definition of a McCulloch-Pitts’s neuron model.

It is an attempt to simulation of real neurons known from neurobiology. Three main parts can be separated

Input signals come to neuron through synapses which Dimension of input layer has to be equal to number are connections with other neurons. Let us suppose, of parameters describing given category of objects. It values of input signals is calculated: that we have synapses in given neuron. Signal of th synapse shall be referenced to as Each of synapses has special number called weight. We shall denote as weight assigned to -th synapse. A weighted sum of  = ∑ .

=1 ̂ =  + .

Every neuron can also have a special number called bias. That means a fixed treshold value of each neuron.

It is added to weighted sum : ( 9 ) ( 10 ) ( 11 ) ( 12 ) ( 13 ) is first layer in the network, so neurons are only connected to the next layer. For example if we want to classify pictures of dimension 28 × 28 pixels we have to use 28 × 28 = 784 input neurons. There are no set rules about optimal number and dimension of hidden layer, but generally more hidden layers cause better performance of neural network.

Those numbers have to be tailored for each task separately. There will be neurons on output layer where corresponds to number of classes in our system. For binary classification 1 neuron will be suficient, but for 10 classes we will need 10 neurons on output layer.

2.8. Neural reasoning

layer is as follows: To make a decision using neural network we have to feed forward input signal. We calculate output of each of layer and the output of the last layer is decision of the network. Formula for output of -th neuron on -th

( =1

( , ) = ∑( , , −1) + , ) ,

( 14 ) layer, • is number of neurons on − 1-st layer. • , is weight of connection between -th neu

ron on ( − 1)-th layer and -th neuron on -th • , is bias of -th neuron on -th layer, • is activation function.

Formula ( 14 ) has to be applied on every layer startNow, special function (̂ ) called activation function is calculated. Result of that calculation is assigned to output signal of the neuron. There exist plenty of possible activation functions. One of the simplest is threshold function: 1(̂ ) = { 1 when ̂ > , 0 otherwise is demanded. Very popular activation function is called In further applications diferentiability of function (̂ ) where: sigmoid function: 2(̂ ) = + 1 3(̂ ) = tanh ( ̂ )= − − + − .

We can observe analogies and similarities between sin- ing with first hidden layer. After several steps we get gle neuron and soft classifiers. The neuron can be considered as a little more sophisticated soft classifier.

2.7. Neural networks - architecture

the output of the network. That process, however, requires well suited weights. Due to complexity of architecture there can be thousands of weights to adjust which task is unbearable to do manually.

A special algorithm called back-propagation of erA neural network is set of interconnected neurons. Neu- ror was developed to improve performance of neural rons are organized into layers, every neuron of next network. Process of adjusting the weights is called layer is connected to every neuron in previous layer. training or learning of the network. We define three categories of layers: • input layer, • hidden layers, • output layer. Diferentiability of activation function shall be used in that algorithm. We shall start with randomly chosen weights and biases. We shall compare desired output apple 0 0 0 1 0 0 2 0 0 1 0 0 0 (, ) = ∑

( − )

1 =1 2 Let us consider how much (,

) is being influenced by each of weights and biases. That influence can be expressed as partial derivative with respect to given parameter : We have to apply chain rule to calculate the derivative ( 16 ). That is the reason of demanding diferentiability of activation function. Now we have to define the learning rate ∈ ( 0, 1 ). That coeficient will tell us how fast we want to correct parameters in the network. We can formulate correction equations: (, ) (, ) (, ) , , (, ) = ∑ , ) 1 =−1 ( =−1 1 ∑ ( 15 ) (, ) =

(, ) + where

(, RGB value of pixel with coordinates (, , ) (, ) correspond to (, ). Let: (, ) + 3 (, )

(19) ( + , + ) , (20) ) (21) (22) (23)

and are given weights and biases respectively. After several steps we can significantly minimize error of the network. Neural classifier can be As we can see, large networks demand a lot of calculations to be trained, because gradients ( 16 ) has to be calculated for each of multiple parameters.

3. Description of proposed system

3.1. Soft classifier

applied only after training to give acceptable results. treat dark points as having higher values. We have to define an mean square error function: scale with value: of the network with actual output of the network. erenced as pattern. Then page is converted to grayOur system takes two pictures - one large which will Simple soft classifier or weighted soft classifier do be referenced as page and one small, which will be ref- not work well in our case. That happens because they (, ) = (, ) −

(, ).

After converting to grayscale image is binarized using the formula: (, ) = { 1 when 0 otherwise.

(, ) < (, ) 8

, (18) ( 17 ) Then the pattern is converted to gray-scale using the following formula: same function and normalized into interval [0, 1] using (, ) = 255 − 255 (, )

Gray-scale is reversed, that operation enables us to

Now binarized page is divided into segments of size of pattern. Then both, pattern and segment of page are converted into one dimensional vectors. After repeating whole process for every possible segment of page we have our universe

consisting of segments . For every we have our membership function and we can build binary relation table for them. Then we take vector built from pattern and check which of the segments meets the demands expressed by number from interval [0, 1]. demand knowledge about number of patterns existing in our page or calculating threshold values for every pattern. After taking these objectives into account we decided to use WMSC. After several trials we have determined suficient values for aforementioned threshold. Results are presented in table ( 4 ).

After calculation every segment with WMSC value greater than specified treshold value is highlighted and ifnal result is saved.

3.2. Neural classifier

We propose also a neural classifier for that task. We wanted to train our classifier on MNIST dataset of handwritten digits to recognize similar patterns and then apply that to our binarized page and pattern. Our idea was to build a neural network with 2×28×28 = 1568 inputs and one binary output telling us whether images are similar or not. After training it had to go through whole segment of page and find similarities with pattern.

4. Experiments

4.1. Soft classifier

After some trials and errors we determined satisfying threshold values for WMSC. We prepared test set for our classifier. It consisted of pairs (page, pattern). We manually included type of documents and run the program. Then we also manually checked the behavior the classifier. Results are presented on following figures: • searching for printed sign - fig. 2, • searching for handwritten word or letter - fig. 1. Threshold values determined experimentally are shown in table 4.

4.2. Neural classifier

As it was mentioned earlier we constructed few architectures of neural network and tried to train them on MNIST dataset. All of the attempts unfortunately failed - network learned to return the same answers rather than recognize patterns. After some research we found main disadvantages of our system: • too shallow architecture, • too low computing power accessible, • too large training batches.

Keeping that in mind we can construct classifiers with better performance in the future.

5. Conclusions

As we can see, soft classifiers are quite well performing in given task. We plan to develop method of determination of threshold values of soft classifier and use them to more demanding tasks. We want also to improve training of neural classifier. To achieve that goal we will have to optimize code for training algorithm to perform calculations faster. That will allow us to explore deeper architectures of neural networks and then find suficient number of layers to our task.

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