KR100988431B1 - Method of Image Feature Detection, Recording Medium of performing the same and the Apparatus of performing the same - Google Patents

Abstract

An image feature extraction method, a recording medium recording the same, and an apparatus for performing the same are provided. An image feature extraction method comprising: generating a gradient map representing a pixel in a gradient size and a direction from an input image; Finding a fit straight line for at least one pixel using a gradient map; Generating at least one local likelihood function using the fit line; Combining at least one local likelihood function to generate a global likelihood function; Modifying the global likelihood function by applying an external input for correcting an error of the global likelihood function; And extracting at least one of edge pixel information, blurring degree information, and feature scale information from the global likelihood function. Therefore, the likelihood function can be defined from one image and various features of the image can be extracted at once. This minimizes the amount of computation and minimizes user parameters. In addition, the image can be modified in various ways using an external input.

Likelihood function, fit straight line, edge, gradient map

Description

Method of image feature extraction, recording medium recording the same and apparatus for performing the same {Method of Image Feature Detection, Recording Medium of performing the same and the Apparatus of performing the same}

The present invention relates to an image feature extraction method, a recording medium recording the same, and an apparatus for performing the same, and more particularly, to an image feature extraction method using a likelihood function, a recording medium recording the same, and an apparatus for performing the same.

In general, image analysis techniques have suggested various methods to obtain various features of an image. However, the technologies presented up to now suggest only one specialized method to obtain one feature, and could not analyze various features as a single basis principle. Therefore, in order to obtain and use various features from a single image, it is necessary to apply all the various methods specialized for desired features and to set user parameters for each method separately. There was a problem that the probability between them.

For example, the edge of the image, which is considered as one of the typical features of the image because it contains most of the important information about the image even though the corresponding portion of the image is very small, is Adobe Photoshop, an image editing tool. Photoshop has such a high frequency that the technique of finding edge regions in an image is included as one of the filters. As a result, many good ways to find edges in images have been proposed. However, since most methods are specifically specialized for edge extraction, it is impossible to apply additional tasks such as additional consideration of specific conditions in edge detection or obtaining features other than edges. Therefore, in order to use the blur feature along with the edge feature, an additional method of obtaining a blur feature is additionally required, thereby doubling the amount of calculation and the number of parameters to be input by the user. In addition, since there is no probability between the two feature values thus obtained, there is a problem that it is difficult to guarantee that the values are properly combined when the two values are used together.

An object of the present invention is to provide a method for extracting image features using likelihood function.

Another object of the present invention is to provide a recording medium recording a method for extracting image features using a likelihood function.

Still another object of the present invention is to provide an apparatus for performing an image feature extraction method using likelihood functions.

An image feature extraction method for achieving the above object of the present invention comprises the steps of: generating a gradient map representing a pixel in a gradient size and direction from an input image; Finding a fitting straight line for at least one pixel using the gradient map; Generating at least one local likelihood function using the fit line; Combining the at least one local likelihood function to generate a global likelihood function; Modifying the global likelihood function by applying an external input for correcting an error of the global likelihood function; And extracting at least one of edge pixel information, blurring degree information, and feature scale information from the global likelihood function.

Here, in the step of generating a gradient map representing a pixel in the gradient size and direction from the input image, the gradient size and direction are reflected by reflecting at least one of the RGB value and the transparency value of the pixel. It may be characterized by.

Here, in the step of finding the alignment line for at least one pixel using the gradient map, the alignment line may be characterized in that the sum of the distances from each pixel to the alignment line is the minimum. .

Here, in the step of generating at least one local likelihood function using the alignment line, the local likelihood function may be generated in an ellipse form in which a focal point is positioned on the alignment line.

Here, in the step of generating a global likelihood function by combining the at least one local likelihood function, the global likelihood function may be generated by giving a weight according to the local likelihood function.

The external input may be input through at least one of a keyboard, a mouse, a touch pad, and a storage device in the step of modifying the global likelihood function by applying an external input for correcting an error of the global likelihood function. It can be characterized.

Here, in the step of extracting at least one of edge pixel information, blurring degree information, and feature scale information from the global likelihood function, the edge pixel information is at least one pixel corresponding to a ridge in the global likelihood function. It may be characterized in that the extraction using.

Here, in the step of extracting at least one of edge pixel information, blurring degree information, and feature scale information from the global likelihood function, the blurring degree information is extracted using the sum of the distances from each pixel to the fitting straight line. It may be characterized by.

Here, in the step of extracting at least one of the edge pixel information, the blurring degree information, and the feature scale information from the global likelihood function, the feature scale information is extracted using a change in the sum of the distances from each pixel to the fitting straight line. It may be characterized by.

In the recording medium recording the image feature extraction method for achieving the above-described other object of the present invention, in the recording medium on which the image feature extraction method is recorded, a gradient map representing a pixel from the input image in the gradient size and direction (Gradient Map) ) Is generated, finding a fit straight line for at least one pixel using the gradient map, generating at least one local likelihood function using the fit straight line, and at least one local A likelihood function is combined to generate a global likelihood function, a step of modifying the global likelihood function by applying an external input for correcting an error of the global likelihood function, and edge pixel information from the global likelihood function, Comprising the step of extracting at least one of the blurring degree information and feature scale information Can be.

An apparatus for performing an image feature extraction method for achieving another object of the present invention described above is a device for performing an image feature extraction method, comprising: a gradient map representing a pixel from an input image in a gradient size and a direction; ) Is generated, finding a fit straight line for at least one pixel using the gradient map, generating at least one local likelihood function using the fit straight line, and at least one local A likelihood function is combined to generate a global likelihood function, a step of modifying the global likelihood function by applying an external input for correcting an error of the global likelihood function, and edge pixel information from the global likelihood function, Comprising the step of extracting at least one of the blurring degree information and feature scale information A controller that performs an image feature extraction method; An input unit for receiving the external input; A display unit for representing the input image, pixel information, alignment line information, local likelihood function, global likelihood function, edge pixel information and rendering; And a storage unit for storing the input image, pixel information, alignment line information, local likelihood function, global likelihood function, edge pixel information, and rendering.

The gradient size and direction may be expressed by the controller to reflect at least one of the RGB value and the transparency value of the pixel.

Here, in the control unit, the alignment line may be characterized in that the sum of the distances from each pixel to the alignment line is the minimum.

Here, the local likelihood function in the controller may be generated in the form of an ellipse in which the focal point is located on the alignment line.

Here, the global likelihood function in the control unit may be generated by giving a weight according to the local likelihood function.

The edge pixel information may be extracted by the controller using at least one pixel corresponding to a ridge in the global likelihood function.

In this case, the blurring degree information may be extracted using the sum of the distances from each pixel to the alignment line.

The feature scale information may be extracted by using the change of the sum of the distances from each pixel to the fitting straight line.

Here, the input unit may be configured to include at least one of a keyboard, a mouse, a touch pad, and a storage device.

According to the image feature extraction method as described above, it is possible to define a likelihood function from a single image and to extract various features of the image at once. This minimizes the amount of computation and minimizes user parameters. In addition, the image can be modified in various ways using an external input.

As the present invention allows for various changes and numerous embodiments, particular embodiments will be illustrated in the drawings and described in detail in the written description.

However, this is not intended to limit the present invention to specific embodiments, it should be understood to include all changes, equivalents, and substitutes included in the spirit and scope of the present invention.

The terms first, second, etc. may be used to describe various components, but the components should not be limited by the terms. The terms are used only for the purpose of distinguishing one component from another. For example, without departing from the scope of the present invention, the first component may be referred to as the second component, and similarly, the second component may also be referred to as the first component. The term and / or includes a combination of a plurality of related items or any item of a plurality of related items.

When a component is referred to as being "connected" or "connected" to another component, it may be directly connected to or connected to that other component, but it may be understood that other components may be present in between. Should be. On the other hand, when a component is said to be "directly connected" or "directly connected" to another component, it should be understood that there is no other component in between.

The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting of the present invention. Singular expressions include plural expressions unless the context clearly indicates otherwise. In this application, the terms "comprise" or "have" are intended to indicate that there is a feature, number, step, operation, component, part, or combination thereof described in the specification, and one or more other features. It is to be understood that the present invention does not exclude the possibility of the presence or the addition of numbers, steps, operations, components, components, or a combination thereof.

Unless defined otherwise, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art. Terms such as those defined in the commonly used dictionaries should be construed as having meanings consistent with the meanings in the context of the related art, and shall not be construed in ideal or excessively formal meanings unless expressly defined in this application. Do not.

Hereinafter, with reference to the accompanying drawings, it will be described in detail a preferred embodiment of the present invention. In the following description of the present invention, the same reference numerals are used for the same elements in the drawings and redundant descriptions of the same elements will be omitted.

1 is a flowchart illustrating an image feature extraction method according to an embodiment of the present invention. 2 is an exemplary diagram for describing a gradient map in an image feature extraction method according to an embodiment of the present invention. 3 is an exemplary diagram for explaining a fitting straight line in the image feature extraction method according to an embodiment of the present invention. 4 is an exemplary diagram for describing a local likelihood function in an image feature extraction method according to an embodiment of the present invention. 5 is an exemplary diagram for describing a global likelihood function in an image feature extraction method according to an embodiment of the present invention.

Referring to FIG. 1, in the image feature extraction method according to an embodiment of the present invention, in the image feature extraction method, generating a gradient map representing a pixel in a gradient size and a direction from an input image ( S110); Finding a straight line for at least one pixel using the gradient map (S120); Generating at least one local likelihood function using the alignment line (S130); Generating a global likelihood function by combining the at least one local likelihood function (S140); Modifying the global likelihood function by applying an external input for correcting an error of the global likelihood function (S150); And extracting at least one of edge pixel information, blurring degree information, and feature scale information from the global likelihood function (S160).

First, a step of generating a gradient map representing a pixel in a gradient size and a direction from an input image (S110) is performed by using information of each pixel constituting the input image and surrounding pixels of the pixel. The step of generating a gradient map for an image by expressing it in the form of a vector having a size and a gradient direction. In addition, in the step S110 of generating a gradient map representing a pixel in a gradient size and a direction from the input image, the gradient size and direction reflect at least one of an RGB value and a transparency value of the pixel. It may be characterized by being represented. That is, since the pixel may be expressed by including the transparency value in addition to the RGB value, the gradient size and direction may be expressed by including the transparency value in addition to the RGB value of each pixel.

Referring to FIG. 2 in parallel, in the image feature extraction method according to an embodiment of the present invention, a gradient map is applied to represent a gradient map (b) from an input image (a). You can use various gradient maps, or you can use Sobel Operator.

Next, the step (S120) of finding a straight line for at least one pixel using the gradient map is a step required in the method for finally finding the global likelihood function using the input image. In addition, in the step S120 of finding a fitting straight line for at least one pixel using the gradient map, the fitting straight line is characterized in that the sum of the distances from each pixel to the fitting straight line is minimum. Can be. In addition, the fitting straight line may be characterized in that the sum of the weighted distances is minimized by giving a weight to the sum of the distances from each pixel to the fitting straight line.

인 동심원을 이용하여 해당 영역 안에 들어오는 주위 픽셀들을 이용한다. 주위 픽셀들의 그래디언트 크기(gradient magnitude) 및 그래디언트 방향(gradient direction)의 유사도에 가중치(weight)를 적용한다. 이때, 각 픽셀로부터 직선까지의 거리를 에러로 정의할 경우, 에러의 합 또는 에러의 가중 합이 최소화되는 것을 맞춤 직선이라고 할 수 있으므로, 상기와 같은 방법으로 맞춤 직선을 찾을 수 있을 것이다.Referring to FIG. 3, the step (S120) of finding a fitting straight line in the image feature extraction method according to an exemplary embodiment of the present invention will be described in detail. Since we have to calculate the tendency to become the local likelihood function, we use the radius to use together the surrounding pixels within a certain area of each pixel.

Using the concentric circles, the surrounding pixels coming into the area are used. A weight is applied to the similarity of the gradient magnitude and the gradient direction of the surrounding pixels. In this case, when the distance from each pixel to the straight line is defined as an error, since the sum of the error or the weighted sum of the errors is minimized, the fitting straight line may be found as described above.

Next, in the step of generating at least one local likelihood function using the alignment line (S130), the local likelihood function may be generated in the form of an ellipse in which the focal point is located on the alignment line.

Referring to FIG. 4 in parallel, in the image feature extraction method according to an embodiment of the present invention, the local likelihood function is generated in the form of an ellipse having the fitting straight line as the long axis and the focus of the ellipse is positioned on the fitting straight line.

Next, in the step of generating a global likelihood function by combining the at least one local likelihood function (S140), the global likelihood function may be generated by giving a weight according to the local likelihood function. That is, in combining at least one local likelihood function, the global likelihood function is not generated by a simple combination, but by assigning various weight values to each of the local likelihood functions and combining them by reflecting them. Can be generated.

Referring to FIG. 5, in the image feature extraction method according to an embodiment of the present invention, the global likelihood function is a gradient size of the importance of each local likelihood function to generate a likelihood function for the entire image input from the local likelihood function. We will define by using and weight it and calculate the global likelihood function for the whole image. This likelihood function will indicate the tendency for each pixel to be an edge.

In particular, the size of concentric circles plays an important role when calculating the global likelihood function. Small concentric circles express details well, but lines are broken or lines are entangled in blurred images. Large concentric circles express long lines even in blurred images, but have a weakness in that they cannot express a small range of detailed lines. To take advantage of both, one could use a combination of concentric circles of different sizes.

Next, the external likelihood is modified by applying an external input for correcting an error of the global likelihood function (S150). It may be input. That is, the external input device may be used if it is obvious to those skilled in the art. Various external inputs may be received through the external input device as described above.

Next, in operation S160, at least one of edge pixel information, blurring degree information, and feature scale information is extracted from the global likelihood function, the edge pixel information is at least corresponding to a ridge in the global likelihood function. The blurring degree information may be extracted using the sum of the distances from each pixel to the fitting straight line, and the feature scale information is the fitting straight line from each pixel. It may be extracted using a change in the sum of distances to.

Ridges with high function values in the global likelihood function best represent the original edge lines. The purpose of grouping is to gather all the pixels that belong to the same line into a group. Therefore, we start from the ridge pixel larger than the highest function value and follow the ridge direction up to the pixel larger than the smallest value. In tracking this, each group is connected to each other by dots. In the same manner as described above, the edge pixel information may be extracted from the global likelihood function.

The blurring degree information may be extracted using the sum of the distances from each pixel to the alignment line. If the sum of the distances to the alignment line is large, it is difficult to define the exact alignment line at the corresponding pixel, so the blurring degree is large. If the sum of the distances to the alignment line is small, the accuracy of the alignment line is correct at the pixel. The definition is easy, so the blur is small.

In the general case, important areas are clearly represented and non-essential areas are blurred. It can also be created by deliberately defocusing the picture. Therefore, it can be judged that the degree of blurring indicates the importance of the region. Using large concentric circles and small concentric circles, the blurring degree can be extracted by combining the linear alignment error for the large concentric circles and the linear alignment error for the small concentric circles found in the process of generating the likelihood function. In this case, each linear alignment error can be calculated by weighting it.

The feature scale information can be extracted using a change in the sum of the distances from each pixel to the fit straight line. The feature scale is a measure of whether the features of each part of the image correspond to an important structural part of the image or a relatively less important part of the image. Extract through how to change accordingly. That is, when the sum of the distances from each pixel to the alignment line decreases as the concentric radius increases, it means that there is a small probability that there are similar edges around. If the sum of the distances from each pixel to the alignment line increases as the radius of the concentric circle increases, it means that there is a high probability that there are other similar edges around. Therefore, the feature scale of the corresponding pixel is small.

In addition, the extracted edge pixel information, blurry scale information, and feature scale information may be used independently or collectively, and in particular, may be used for rendering the input image. By using the feature scale value, a small feature scale can be deleted to control the degree of detail in the line drawing. Two thresholds can be defined to control detail and line thickness. In the case of a feature scale smaller than the small threshold value, the minimum line thickness may be drawn or deleted, while in the case of a feature scale larger than the large threshold value, the maximum line thickness may be drawn. Similar to the feature scale, the cloudiness can also be calculated as the average of the cloudiness of the feature points along the line. Depending on the importance or focus of the image, the blurring of the surrounding area is expressed. The degree of blurring can be used to adjust the degree of focus of the line. You can also delete unimportant lines, depending on how blurry they are.

FIG. 6 is an exemplary diagram for explaining a difference between rendering an image feature extraction method according to an embodiment and an image feature extraction method according to another embodiment.

Referring to FIG. 6, an input image (a) may be compared with a rendering (b) not reflecting blurring degree information and feature scale information. In addition, it is possible to compare the rendering (b) that does not reflect the blurring degree information and the feature scale information with the rendering (c) which additionally reflects the feature scale information and the rendering (d) which reflects both the blurring degree information and the feature scale information. will be.

7 is a block diagram illustrating an apparatus for performing an image feature extraction method according to another embodiment of the present invention.

Referring to FIG. 7, an apparatus for performing an image feature extraction method according to another embodiment of the present invention is a device for performing an image feature extraction method, comprising: a gradient map representing a pixel from a input image in a gradient size and a direction; Generating a gradient map; finding a fit straight line for at least one pixel using the gradient map; generating at least one local likelihood function using the fit straight line; Generating a global likelihood function by combining one local likelihood function, modifying the global likelihood function by applying an external input for correcting an error of the global likelihood function, and an edge from the global likelihood function Extracting pixel information, and rendering the input image using the edge pixel information A controller 710 for performing an image feature extraction method including the step of generating (Rendering); An input unit 720 for receiving the external input; A display unit 730 for representing the input image, pixel information, alignment line information, local likelihood function, global likelihood function, edge pixel information and rendering; And a storage unit 740 for storing the input image, pixel information, alignment line information, local likelihood function, global likelihood function, edge pixel information, and rendering.

First, since the features of the controller 710 have been described above, they will be omitted.

Next, the input unit 720 may be configured to include at least one of a keyboard, a mouse, a touch pad, and a storage device. That is, various types of input / output devices may be used in the input unit, and in particular, may be stored in a file form and input through the storage device. All input devices that will be apparent to those skilled in the art will be included.

Next, the display unit 730 may include any device that displays all data generated in the process of being input or processed by the device for performing the image feature extraction method through an output device such as a monitor and a printer. That is, it may be an apparatus including an output from the input image to the rendering screen reflecting the final image characteristics.

Next, the storage device 740 may also be a device for storing all data generated in the process of being input or processed in the device for performing the image feature extraction method, and may include a storage device such as a memory and a disk. .

Although described with reference to the above embodiments, those skilled in the art will understand that various modifications and changes can be made without departing from the spirit and scope of the invention as set forth in the claims below. Could be.

1 is a flowchart illustrating an image feature extraction method according to an embodiment of the present invention.

2 is an exemplary diagram for describing a gradient map in an image feature extraction method according to an embodiment of the present invention.

3 is an exemplary diagram for explaining a fitting straight line in the image feature extraction method according to an embodiment of the present invention.

4 is an exemplary diagram for describing a local likelihood function in an image feature extraction method according to an embodiment of the present invention.

5 is an exemplary diagram for describing a global likelihood function in an image feature extraction method according to an embodiment of the present invention.

FIG. 6 is an exemplary diagram for explaining a difference between rendering an image feature extraction method according to an embodiment and an image feature extraction method according to another embodiment.

7 is a block diagram illustrating an apparatus for performing an image feature extraction method according to another embodiment of the present invention.

Description of the Related Art

710: control unit 720: input unit

730: display unit 740: storage unit

Claims (19)

In the image feature extraction method, Generating a gradient map representing a pixel in a gradient size and a direction from an input image; Finding a fitting straight line for at least one pixel using the gradient map; Generating at least one local likelihood function using the fit line; Generating a global likelihood function by weighting the at least one local likelihood function; Modifying the global likelihood function by applying an external input for correcting an error of the global likelihood function; And And extracting, from the global likelihood function, at least one of edge pixel information, blurring degree information indicating whether a region is in focus, and quantifying feature scale information indicating whether a pixel included in an image corresponds to a structural part of the image. Video feature extraction method. The method of claim 1, In the step of generating a gradient map representing a pixel in a gradient size and a direction from the input image, the gradient size and direction are represented by reflecting at least one of an RGB value and a transparency value of the pixel. Image feature extraction method. The method of claim 1, And in the step of finding a fitting straight line for at least one pixel by using the gradient map, the fitting straight line is a sum of the distances from each pixel to the fitting straight line. The method of claim 1, And generating the at least one local likelihood function using the fitting straight line, wherein the regional likelihood function is generated in the shape of an ellipse in which the focal point is positioned on the fitting straight line. The method of claim 1, And in the step of generating a global likelihood function by combining the at least one local likelihood function, the global likelihood function is generated by giving a weight according to the local likelihood function. The method of claim 1, The external input may be input through at least one of a keyboard, a mouse, a touch pad, and a storage device in the step of modifying the global likelihood function by applying an external input for correcting an error of the global likelihood function. Image feature extraction method. The method of claim 1, In the step of extracting at least one of edge pixel information, blurring degree information, and feature scale information from the global likelihood function, the edge pixel information may be obtained by using at least one pixel corresponding to a ridge in the global likelihood function. Image feature extraction method characterized in that the extraction. The method of claim 1, In the step of extracting at least one of the edge pixel information, the blurring degree information, and the feature scale information from the global likelihood function, the blurring degree information is defined as the magnitude of the sum of the distances from each pixel to the fitting straight line. If the size is large, the blur has a large value, and if the size is small, the blur has a small value. The method of claim 1, In the step of extracting at least one of edge pixel information, blurring degree information, and feature scale information from the global likelihood function, the feature scale information is from each pixel to the fitting straight line according to a concentric circle size change including at least one pixel. Is defined as a change in the sum of the distances, and the sum of the distances to the fitting straight line becomes smaller when the concentric circle size becomes larger, and the sum of the distances to the fitting straight line becomes larger when the concentric circle size becomes larger when the feature scale is larger. The method of claim 1, wherein the feature scale has a small value when it becomes large. In the recording medium in which a program of instructions executable by a digital processing apparatus for performing the image feature extraction method is tangibly implemented, and records a program that can be read by the digital processing apparatus, Generating a gradient map representing a pixel in a gradient size and a direction from an input image; Finding a fitting straight line for at least one pixel using the gradient map; Generating at least one local likelihood function using the fit line; Generating a global likelihood function by weighting the at least one local likelihood function; Modifying the global likelihood function by applying an external input for correcting an error of the global likelihood function; And extracting, from the global likelihood function, at least one of edge pixel information, blurring degree information indicating whether a region is in focus, and quantifying feature scale information indicating whether a pixel included in an image corresponds to a structural part of the image. Recording medium that records the program. An apparatus for performing an image feature extraction method, Generating a gradient map representing a pixel in a gradient size and a direction from an input image; Finding a fitting straight line for at least one pixel using the gradient map; Generating at least one local likelihood function using the fit line; Generating a global likelihood function by weighting the at least one local likelihood function; Modifying the global likelihood function by applying an external input for correcting an error of the global likelihood function; And extracting, from the global likelihood function, at least one of edge pixel information, blurring degree information indicating whether an area is in focus, and quantifying feature scale information indicating whether a pixel included in an image corresponds to a structural part of the image. A controller for performing a method of extracting an image feature; An input unit for receiving the external input; A display unit for representing the input image, pixel information, alignment line information, local likelihood function, global likelihood function, edge pixel information and rendering; And And a storage unit for storing the input image, pixel information, alignment line information, local likelihood function, global likelihood function, edge pixel information, and rendering. The method of claim 11, And the gradient size and direction are reflected by the controller to reflect at least one of an RGB value and a transparency value of the pixel. The method of claim 11, And the fitting line is the sum of the distances from each pixel to the alignment line in the control unit. The method of claim 11, And the local likelihood function in the control unit is generated in the form of an ellipse in which the focal point is located on the alignment line. The method of claim 11, And the global likelihood function in the controller is generated by assigning a weight to the local likelihood function. The method of claim 11, And the edge pixel information is extracted by the controller using at least one pixel corresponding to a ridge in the global likelihood function. The method of claim 11, In the control unit, the blurring degree information is defined as a sum of the sum of distances from each pixel to the alignment line. When the size is large, the blurring degree has a large value, and when the size is small, the blurring degree is a small value. Apparatus for performing an image feature extraction method characterized in that it has a. The method of claim 11, In the control unit, the feature scale information is defined as a change in the sum of the distances from each pixel to the fitting straight line according to the change in the concentric circle size including at least one pixel, and when the size of the concentric circles is increased, Apparatus for performing an image feature extraction method characterized in that the feature scale has a large value when the sum is small and the feature scale has a small value when the sum of the distances to the fitting straight line increases when the concentric circle size is increased . The method of claim 11, And the input unit comprises at least one of a keyboard, a mouse, a touch pad, and a storage device.

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