CN109377453B - Method, system, storage medium and device for eliminating moire in X-ray image - Google Patents
Method, system, storage medium and device for eliminating moire in X-ray image Download PDFInfo
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Abstract
The invention provides a method, a system, a storage medium and a device for eliminating moire fringes in an X-ray image, which comprise the following steps: adjusting the X-ray image to a target size; judging whether Moire exists in the adjusted X-ray image; when the moire exists, acquiring a frequency band where the moire exists; constructing a filter corresponding to the frequency band based on the frequency band where the moire pattern is located; filtering the X-ray image based on the filter to obtain an X-ray image with moire removed; the X-ray image with the moire removed is cropped to an original size. The method, the system, the storage medium and the device for eliminating the moire in the X-ray image are used for constructing the filter corresponding to the frequency band aiming at the frequency band to achieve the effect of eliminating the moire better.
Description
Technical Field
The invention relates to the field of medical image processing, in particular to a method, a system, a storage medium and a device for eliminating moire fringes in an X-ray image.
Background
The X-ray has strong penetrating power and can penetrate through a plurality of substances which cannot be penetrated by visible light. With this penetration capability, the radiation is used to assist in medical diagnosis and treatment. In the process of obtaining an image by taking a picture by X-ray, particularly when the X-ray is brought into contact with an object to be irradiated, not only primary radiation but also scattered radiation, also called scattered radiation, is generated. These scattered rays are superimposed on the image, thereby reducing the contrast and sharpness of the X-ray image and also reducing the signal-to-noise ratio. In order to effectively eliminate scattered radiation, medical grids are needed, and the use of medical grids causes a new problem in the image, i.e. moire, which is represented as a regular stripe on the image. This can seriously affect the diagnosis of the doctor and reduce the quality of the image.
In the field of medical image processing, in particular X-ray images, many companies and enterprises have invented many methods for eliminating/suppressing moire in images, for example, by physically eliminating moire in images using movable grids instead of using fixed grids. Other companies have used methods for digital image processing, such as removing filters in the frequency domain of the image by means of fourier transforms. However, these digital image processing techniques have many defects, and some techniques need to inform a user whether to load an image for suppressing moire, that is, whether moire exists cannot be judged. Some techniques eliminate moire by improperly selecting filters, resulting in image blurring. Some techniques often only filter one frequency band, and moire frequency bands located in a low frequency region and a medium frequency region cannot be found. Some techniques have a severe drop in MTF after moire removal. And the existing technology carries out error suppression on the part which is not required to be filtered due to the error judgment and positioning of the frequency point.
Therefore, it is desirable to solve the problem of how to identify whether there is moire in an X-ray image and how to determine the frequency band in which moire is located.
Disclosure of Invention
In view of the above-mentioned shortcomings of the prior art, an object of the present invention is to provide a method, a system, a storage medium and a device for eliminating moire in an X-ray image, which are used to solve the problem in the prior art of how to identify whether there is moire in an X-ray image and how to determine the frequency band where moire exists.
To achieve the above and other related objects, the present invention provides a method for eliminating moire in an X-ray image, comprising the steps of: adjusting the X-ray image to a target size; judging whether Moire exists in the adjusted X-ray image; when the moire exists, acquiring a frequency band where the moire exists; constructing a filter corresponding to the frequency band based on the frequency band where the moire pattern is located; filtering the X-ray image based on the filter to obtain an X-ray image with moire removed; the X-ray image with the moire removed is cropped to an original size.
In an embodiment of the present invention, when the X-ray image is adjusted to a target size, the X-ray image is padded to obtain an image of an integral power of 2.
In an embodiment of the present invention, the step of determining whether moire exists in the preprocessed X-ray image includes the following steps: judging whether Moire exists in a high-frequency region of the X-ray image; and when the Moire exists in the high-frequency area, judging whether the Moire exists in the medium-frequency area of the X-ray image.
In an embodiment of the present invention, the determining whether moire exists in the high frequency region of the X-ray image includes: and extracting the one-dimensional line data of the X-ray image in the horizontal and vertical directions, respectively windowing the two one-dimensional line data, and judging that Moire fringes exist in the high-frequency region of the X-ray image if the windowed data is greater than a preset threshold value.
In an embodiment of the present invention, when the moire exists, the obtaining the frequency band where the moire exists includes: when only a high-frequency region in the X-ray image has moire fringes, acquiring a high-frequency band where the moire fringes are located; when moire exists in the high frequency region and the medium frequency region of the X-ray image, the high frequency band and the medium frequency band where the moire exists are obtained.
In an embodiment of the present invention, constructing the filter corresponding to the frequency band based on the frequency band where the moire is located includes: constructing a Gaussian rectangular filter for the Moire in the high-frequency band; for moir e at mid-band, a gaussian circular filter is constructed.
In an embodiment of the present invention, the filtering the X-ray image based on the filter to obtain the X-ray image without moire includes: performing two-dimensional Fourier transform on the X-ray image to obtain frequency spectrum data; filtering high-frequency data in the spectrum data based on the Gaussian rectangular filter; filtering intermediate frequency data in the frequency spectrum data based on the Gaussian circular filter; and carrying out inverse Fourier transform on the data after the filtering processing to obtain an image with Moire removed.
To achieve the above object, the present invention further provides a moire resolution system in an X-ray image, comprising: the device comprises an adjusting module, a judging module, an obtaining module, a constructing module, a filtering module and a cutting module; the adjusting module is used for adjusting the X-ray image into a target size; the judging module is used for judging whether Moire exists in the adjusted X-ray image; the acquisition module is used for acquiring the frequency band where the moire fringes are located when the moire fringes exist; the construction module is used for constructing a filter corresponding to the frequency band based on the frequency band where the Moire is located; the filtering module is used for carrying out filtering processing on the X-ray image based on the filter so as to obtain an X-ray image with moire lines eliminated; and the cutting module is used for cutting the X-ray image with the Moire lines eliminated into an original size.
To achieve the above object, the present invention further provides a computer-readable storage medium having a computer program stored thereon, which when executed by a processor, implements any of the above methods for removing moire in an X-ray image.
Finally, the present invention also provides an apparatus for removing moire in an X-ray image, comprising: a processor and a memory; the memory is used for storing a computer program; the processor is connected with the memory and is used for executing the computer program stored in the memory so as to enable the eliminating device of the moire fringes in the X-ray image to execute any one of the eliminating methods of the moire fringes in the X-ray image.
As described above, the method, system, storage medium, and apparatus for eliminating moire in an X-ray image according to the present invention have the following advantages: whether moire exists in an X-ray image can be judged in advance, a filter corresponding to a frequency band is constructed according to the frequency band where the moire exists, so that the moire is eliminated, and the filter is reasonably selected according to the moire of a high frequency band and a medium frequency band, so that the effect of eliminating the moire better is achieved, and the moire is prevented from being eliminated mistakenly.
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FIG. 1 is a flow chart illustrating a method for removing moire in an X-ray image according to one embodiment of the present invention;
FIG. 2 is a schematic diagram of an embodiment of a moire removal system for X-ray images in accordance with the present invention;
FIG. 3 is a schematic structural diagram of an apparatus for removing moire in an X-ray image according to an embodiment of the present invention; .
Description of the element reference numerals
21 regulating module
22 judging module
23 acquisition module
24 building block
25 Filter Module
26 cutting module
31 processor
32 memory
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It is to be noted that the features in the following embodiments and examples may be combined with each other without conflict.
It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention, and the components related to the present invention are only shown in the drawings rather than drawn according to the number, shape and size of the components in actual implementation, and the type, quantity and proportion of the components in actual implementation may be changed freely, and the layout of the components may be more complicated.
According to the method, the system, the storage medium and the device for eliminating the moire fringes in the X-ray image, whether the moire fringes exist in the X-ray image can be judged in advance, and a filter corresponding to the frequency band of the moire fringes is constructed according to the frequency band of the moire fringes, so that the moire fringes are eliminated.
As shown in FIG. 1, in one embodiment, the method for eliminating moire in an X-ray image of the present invention comprises the following steps:
step S11, adjusting the X-ray image to the target size.
In an embodiment of the present invention, when the X-ray image is adjusted to the target size, the X-ray image is padded to obtain an image with a power of 2. Specifically, first, the raw data of the raw X-ray image is converted into data of double precision. Then the data after the conversion precision is based on a formula
And calculating to obtain the size of the filled X-ray image. Where b is the original X-ray image size and a is 2, rounding the calculated value to the nearest integer value as an integer power of 2 to obtain the new X-ray image size. The redundant portion of the image without data is filled with 0. The processed X-ray image is square.
And step S12, judging whether the adjusted X-ray image has Moire lines.
In an embodiment of the present invention, the step of determining whether moire exists in the preprocessed X-ray image includes the following steps: judging whether Moire exists in a high-frequency region of the X-ray image; and when the Moire exists in the high-frequency area, judging whether the Moire exists in the medium-frequency area of the X-ray image. Specifically, one-dimensional line data of the X-ray image in the transverse and vertical directions of the central axis are extracted, and the two one-dimensional line data are respectively windowed, wherein the windowing is a Hanning window, and the purpose of windowing is to eliminate interference of other factors on a frequency spectrum, so that the frequency spectrum is clearer. And carrying out one-dimensional spectrum analysis on the windowed image, and judging that Moire exists in the high-frequency region of the X-ray image if the windowed data is larger than a preset threshold value. And if the windowed data is smaller than a preset threshold value, judging that no Moire exists in the high-frequency region of the X-ray image. It is indicated that the X-ray image is not moire-free and no further action is taken.
And step S13, when the moire exists, acquiring the frequency band where the moire exists.
In an embodiment of the present invention, when the moire exists, the obtaining the frequency band where the moire exists includes: specifically, if the windowed data is larger than a preset threshold, it is determined that moire exists in the high-frequency region of the X-ray image. It is further determined whether moire exists in the mid-frequency region of the X-ray image. When only a high-frequency region in the X-ray image has moire fringes, acquiring a high-frequency band where the moire fringes are located; when moire exists in the high frequency region and the medium frequency region of the X-ray image, the high frequency band and the medium frequency band where the moire exists are obtained.
And S14, constructing a filter corresponding to the frequency band based on the frequency band of the Moire pattern.
In an embodiment of the present invention, constructing the filter corresponding to the frequency band based on the frequency band where the moire is located includes: constructing a Gaussian rectangular filter for the Moire in the high-frequency band; for moir e at mid-band, a gaussian circular filter is constructed. Specifically, a gaussian rectangular filter is constructed when moire exists only in a high frequency region in an X-ray image. A Gaussian rectangular filter and a Gaussian circular filter are constructed when moire exists in both high-frequency regions and medium-frequency regions of an X-ray image.
Step S15, filtering the X-ray image based on the filter to obtain the X-ray image with Moire lines eliminated
In an embodiment of the present invention, the filtering the X-ray image based on the filter to obtain the X-ray image without moire includes: performing two-dimensional Fourier transform on the X-ray image to obtain frequency spectrum data; filtering high-frequency data in the spectrum data based on the Gaussian rectangular filter; filtering intermediate frequency data in the frequency spectrum data based on the Gaussian circular filter; and carrying out inverse Fourier transform on the data after the filtering processing to obtain an image with Moire removed. Specifically, the two-dimensional discrete fourier transform formula is as follows:
in the formula, F (x, y) represents a matrix with the size of M x N, wherein x is 0,1,2, …, M-1 and y are 0,1,2, …, N-1, and F (u, v) represents the fourier transform of F (x, y). The two-dimensional discrete fourier transform is used for transforming an image from a spatial domain to a frequency domain, and plays an extremely important role in image enhancement, image denoising, image edge detection, image feature extraction, image compression and other applications. The coordinate system in which F (u, v) is located is called the frequency domain, and the coordinate system in which F (x, y) is located is called the spatial domain. Then, the filtering processing is carried out, namely, the frequency spectrum data obtained by the two-dimensional Fourier transform of the image is multiplied by a filter, wherein, when the fact that the Moire exists only in the high-frequency area in the X-ray image is judged, the high-frequency data is multiplied by the Gaussian rectangular filter, and when the fact that the Moire exists only in the high-frequency area in the X-ray image is judged, the high-frequency data is multiplied by the Gaussian rectangular filterAnd judging that the high-frequency data is multiplied by the Gaussian rectangular filter and the intermediate-frequency data is multiplied by the Gaussian circular filter when Moire exists in the high-frequency region and the intermediate-frequency region of the X-ray image. And then carrying out inverse Fourier transform on the frequency spectrum data subjected to filtering processing to obtain an X-ray image with moire fringes eliminated.
And step S16, cutting the X-ray image without the moire fringes into an original size.
In one embodiment of the present invention, the X-ray image without moire is cropped to the original size, and then the data type of the processed X-ray image is switched back to the same data type as the original data of the original X-ray image.
As shown in FIG. 2, in one embodiment, the system for eliminating moire in an X-ray image of the present invention comprises: an adjusting module 21, a judging module 22, an obtaining module 23, a constructing module 24, a filtering module 25 and a clipping module 26.
The adjusting module 21 is used for adjusting the X-ray image to a target size.
In an embodiment of the present invention, when the X-ray image is adjusted to the target size, the X-ray image is padded to obtain an image with a power of 2. Specifically, first, the raw data of the raw X-ray image is converted into data of double precision. Then the data after the conversion precision is based on a formula
And calculating to obtain the size of the filled X-ray image. Where b is the original X-ray image size and a is 2, rounding the calculated value to the nearest integer value as an integer power of 2 to obtain the new X-ray image size. The redundant portion of the image without data is filled with 0. The processed X-ray image is square. .
The judging module 22 is configured to judge whether moire exists in the adjusted X-ray image.
In an embodiment of the present invention, the step of determining whether moire exists in the preprocessed X-ray image includes the following steps: judging whether Moire exists in a high-frequency region of the X-ray image; and when the Moire exists in the high-frequency area, judging whether the Moire exists in the medium-frequency area of the X-ray image. Specifically, one-dimensional line data of the X-ray image in the transverse and vertical directions of the central axis are extracted, and the two one-dimensional line data are respectively windowed, wherein the windowing is a Hanning window, and the purpose of windowing is to eliminate interference of other factors on a frequency spectrum, so that the frequency spectrum is clearer. And carrying out one-dimensional spectrum analysis on the windowed image, and judging that Moire exists in the high-frequency region of the X-ray image if the windowed data is larger than a preset threshold value. And if the windowed data is smaller than a preset threshold value, judging that no Moire exists in the high-frequency region of the X-ray image. It is indicated that the X-ray image is not moire-free and no further action is taken.
The obtaining module 23 is configured to obtain, when the moire exists, a frequency band where the moire exists.
In an embodiment of the present invention, when the moire exists, the obtaining the frequency band where the moire exists includes: specifically, if the windowed data is larger than a preset threshold, it is determined that moire exists in the high-frequency region of the X-ray image. It is further determined whether moire exists in the mid-frequency region of the X-ray image. When only a high-frequency region in the X-ray image has moire fringes, acquiring a high-frequency band where the moire fringes are located; when moire exists in the high frequency region and the medium frequency region of the X-ray image, the high frequency band and the medium frequency band where the moire exists are obtained.
The building module 24 is configured to build a filter corresponding to the frequency band based on the frequency band where the moire is located.
In an embodiment of the present invention, constructing the filter corresponding to the frequency band based on the frequency band where the moire is located includes: constructing a Gaussian rectangular filter for the Moire in the high-frequency band; for moir e at mid-band, a gaussian circular filter is constructed. Specifically, a gaussian rectangular filter is constructed when moire exists only in a high frequency region in an X-ray image. A Gaussian rectangular filter and a Gaussian circular filter are constructed when moire exists in both high-frequency regions and medium-frequency regions of an X-ray image.
The filtering module 25 is configured to perform filtering processing on the X-ray image based on the filter to obtain an X-ray image with moire fringes eliminated.
In an embodiment of the present invention, the filtering the X-ray image based on the filter to obtain the X-ray image without moire includes: performing two-dimensional Fourier transform on the X-ray image to obtain frequency spectrum data; filtering high-frequency data in the spectrum data based on the Gaussian rectangular filter; filtering intermediate frequency data in the frequency spectrum data based on the Gaussian circular filter; and carrying out inverse Fourier transform on the data after the filtering processing to obtain an image with Moire removed. Specifically, the two-dimensional discrete fourier transform formula is as follows:
in the formula, F (x, y) represents a matrix with the size of M x N, wherein x is 0,1,2, …, M-1 and y are 0,1,2, …, N-1, and F (u, v) represents the fourier transform of F (x, y). The two-dimensional discrete fourier transform is used for transforming an image from a spatial domain to a frequency domain, and plays an extremely important role in image enhancement, image denoising, image edge detection, image feature extraction, image compression and other applications. The coordinate system in which F (u, v) is located is called the frequency domain, and the coordinate system in which F (x, y) is located is called the spatial domain. And then, performing filtering processing, namely multiplying the frequency spectrum data obtained by two-dimensional Fourier transform of the image by a filter, wherein the high-frequency data is multiplied by the Gaussian rectangular filter when the fact that only a high-frequency region in the X-ray image has moire is judged, and the high-frequency data is multiplied by the Gaussian rectangular filter and the medium-frequency data is multiplied by the Gaussian circular filter when the fact that both the high-frequency region and the medium-frequency region of the X-ray image have moire is judged. And then carrying out inverse Fourier transform on the frequency spectrum data subjected to filtering processing to obtain an X-ray image with moire fringes eliminated.
The cropping module 26 is used to crop the X-ray image with moire fringes removed to the original size.
In one embodiment of the present invention, the X-ray image without moire is cropped to the original size, and then the data type of the processed X-ray image is switched back to the same data type as the original data of the original X-ray image.
It should be noted that the division of the modules of the above system is only a logical division, and the actual implementation may be wholly or partially integrated into one physical entity, or may be physically separated. And these modules can be realized in the form of software called by processing element; or may be implemented entirely in hardware; and part of the modules can be realized in the form of calling software by the processing element, and part of the modules can be realized in the form of hardware. For example, the x module may be a processing element that is set up separately, or may be implemented by being integrated in a chip of the apparatus, or may be stored in a memory of the apparatus in the form of program code, and the function of the x module may be called and executed by a processing element of the apparatus. Other modules are implemented similarly. In addition, all or part of the modules can be integrated together or can be independently realized. The processing element described herein may be an integrated circuit having signal processing capabilities. In implementation, each step of the above method or each module above may be implemented by an integrated logic circuit of hardware in a processor element or an instruction in the form of software.
For example, the above modules may be one or more integrated circuits configured to implement the above methods, such as: one or more Application Specific Integrated Circuits (ASICs), one or more microprocessors (DSPs), one or more Field Programmable Gate arrays (receivers), etc. For another example, when one of the above modules is implemented in the form of a Processing element scheduler code, the Processing element may be a general-purpose processor, such as a Central Processing Unit (CPU) or other processor capable of calling program code. For another example, these modules may be integrated together and implemented in the form of a system-on-a-chip (SOC).
In an embodiment of the present invention, the present invention further includes a computer readable storage medium, on which a computer program is stored, which when executed by a processor implements any of the above methods for removing moire in an X-ray image.
Those of ordinary skill in the art will understand that: all or part of the steps for implementing the above method embodiments may be performed by hardware associated with a computer program. The aforementioned computer program may be stored in a computer readable storage medium. When executed, the program performs steps comprising the method embodiments described above; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
As shown in FIG. 3, in one embodiment, the apparatus for eliminating moire in an X-ray image of the present invention comprises: a processor 31 and a memory 32; the memory 32 is for storing a computer program; the processor 31 is connected to the memory 32 and is configured to execute a computer program stored in the memory 32, so that the removing device for removing moire in the X-ray image performs any one of the methods for removing moire in the X-ray image.
Specifically, the memory 32 includes: various media that can store program codes, such as ROM, RAM, magnetic disk, U-disk, memory card, or optical disk.
Preferably, the Processor 31 may be a general-purpose Processor, including a Central Processing Unit (CPU), a Network Processor (NP), and the like; the device may also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (Field Programmable Gate Array, or other Programmable logic device, discrete Gate or transistor logic device, or discrete hardware components.
In summary, the method, the system, the storage medium and the device for eliminating moire in an X-ray image of the present invention can determine in advance whether moire exists in the X-ray image, construct a filter corresponding to a frequency band in which moire exists so as to eliminate moire, and reasonably select a filter for moire of a high frequency band and a medium frequency band so as to achieve an effect of better eliminating moire and prevent false elimination of moire. Therefore, the invention effectively overcomes various defects in the prior art and has high industrial utilization value.
The foregoing embodiments are merely illustrative of the principles and utilities of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or change the above-mentioned embodiments without departing from the spirit and scope of the present invention. Accordingly, it is intended that all equivalent modifications or changes which can be made by those skilled in the art without departing from the spirit and technical spirit of the present invention be covered by the claims of the present invention.
Claims (8)
1. A method for eliminating moire in an X-ray image, comprising the steps of:
adjusting the X-ray image to a target size;
extracting one-dimensional line data of the X-ray image in the transverse and vertical directions, respectively windowing the two one-dimensional line data, and judging that Moore lines exist in a high-frequency region of the X-ray image if the windowed data is greater than a preset threshold; judging whether Moire exists in the medium-frequency region of the X-ray image;
when the moire exists in any one of the high-frequency region and the medium-frequency region, acquiring a frequency band where the moire is located;
constructing a filter corresponding to the frequency band based on the frequency band where the moire pattern is located;
filtering the X-ray image based on the filter to obtain an X-ray image with moire removed; the X-ray image with the moire removed is cropped to an original size.
2. The method according to claim 1, wherein the filling of the X-ray image when the X-ray image is adjusted to a target size results in an image of an integral power of 2.
3. The method for eliminating moire in an X-ray image according to claim 1, wherein when the moire exists, the obtaining of the frequency band in which the moire exists comprises: when only a high-frequency region in the X-ray image has moire fringes, acquiring a high-frequency band where the moire fringes are located; when moire exists in the high frequency region and the medium frequency region of the X-ray image, the high frequency band and the medium frequency band where the moire exists are obtained.
4. The method according to claim 3, wherein constructing a filter corresponding to the frequency band based on the frequency band in which the moire is located comprises: constructing a Gaussian rectangular filter for the Moire in the high-frequency band; for moir e at mid-band, a gaussian circular filter is constructed.
5. The method according to claim 4, wherein the filtering the X-ray image based on the filter to obtain the X-ray image with moire fringes eliminated comprises: performing two-dimensional Fourier transform on the X-ray image to obtain frequency spectrum data; filtering high-frequency data in the spectrum data based on the Gaussian rectangular filter; filtering intermediate frequency data in the frequency spectrum data based on the Gaussian circular filter; and carrying out inverse Fourier transform on the data after the filtering processing to obtain an image with Moire removed.
6. A moire resolution system for X-ray images, comprising: the device comprises an adjusting module, a judging and calculating module, an obtaining module, a constructing module, a filtering module and a cutting module;
the adjusting module is used for adjusting the X-ray image into a target size;
the judging module is used for extracting the one-dimensional line data of the X-ray image in the horizontal and vertical directions, respectively windowing the two one-dimensional line data, and judging that Moire exists in the high-frequency region of the X-ray image if the windowed data is larger than a preset threshold; judging whether Moire exists in the medium-frequency region of the X-ray image;
the acquisition module is used for acquiring a frequency band where the moire fringes are located when the moire fringes exist in any one of the high-frequency region and the medium-frequency region;
the construction calculation module is used for constructing a filter corresponding to the frequency band based on the frequency band of the Moire;
the filtering module is used for carrying out filtering processing on the X-ray image based on the filter so as to obtain an X-ray image with moire lines eliminated;
and the cutting module is used for cutting the X-ray image with the Moire lines eliminated into an original size.
7. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out a method of removing moir e in an X-ray image according to any one of claims 1 to 5.
8. An apparatus for removing moire in an X-ray image, comprising: a processor and a memory;
the memory is used for storing a computer program;
the processor is connected with the memory and is used for executing the computer program stored in the memory so as to enable the eliminating device of the moire fringes in the X-ray image to execute the eliminating method of the moire fringes in the X-ray image according to any one of claims 1 to 5.
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