CN112435195B - Image enhancement method and system based on self-adaptive fractional order differentiation - Google Patents
Image enhancement method and system based on self-adaptive fractional order differentiation Download PDFInfo
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Abstract
An image enhancement method and system based on self-adaptive fractional order differentiation, wherein the image enhancement method comprises the following steps: step S1: calculating and improving an image to be processed to obtain an image enhancement template based on R-L fractional differentiation, wherein the image to be processed is marked as F (x, y), and the image enhancement template comprises an image enhancement template with horizontal information removed, an image enhancement template with vertical information removed and an omnibearing image enhancement template; step S2: locally enhancing the image to be processed under the condition of fixed order by using the image enhancement template with the horizontal information removed to obtain a first locally enhanced image P1 (x, y); step S3: and locally enhancing the image to be processed under the condition of fixed order by using the image enhancement template with the vertical information removed, so as to obtain a second image local enhancement P2 (x, y). The invention can effectively enhance texture details, improve image quality, has low algorithm complexity and can well meet the requirement of real-time processing.
Description
Technical Field
The present invention relates to the field of image processing technologies, and in particular, to an image enhancement method and system based on adaptive fractional order differentiation.
Background
Image enhancement is an important component of digital image processing, and is mainly aimed at highlighting the interesting part of the image, weakening or removing unwanted information, and enhancing useful information, so as to obtain a more practical image. In recent years, researchers have attempted to apply fractional calculus theory to image enhancement and achieve satisfactory enhancement effects. The "weak derivative" nature of the fractional differential operator and the fractional Fourier transform theory show that the fractional differential operator can nonlinearly retain the very low frequency component in the image while enhancing the high frequency component of the image. Thus, the fractional differential operator can make the edges of the enhanced image more prominent, while properly preserving the texture information of the smooth region of the image. An extension to integer-order differentiation has been developed.
Many scholars have conducted a great deal of research on fractional differentiation, especially in terms of processing images. Yellow fruit and the like propose an image enhancement algorithm that can dynamically adjust the fractional order according to image characteristics and information. Li Juncheng expands the fractional differential order of the 0-1 order range to 1-2 order for the first time. Jiang Wei et al combine the advantages of both fractional and integer differential to extend the fractional differential to a rational differential. Image enhancement is a problem that needs to be continuously studied, and the method has a certain effect on image enhancement, but has to be improved in aspects of enhancement effect of details and textures, algorithm efficiency and the like.
The foregoing description is provided for general background information and does not necessarily constitute prior art.
Disclosure of Invention
The invention aims to provide an image enhancement method and system based on self-adaptive fractional order differentiation, which can effectively enhance texture details and has low algorithm complexity.
The invention provides an image enhancement method based on self-adaptive fractional order differentiation, which comprises the following steps: step S1: calculating and improving an image to be processed to obtain an image enhancement template based on R-L fractional differentiation, wherein the image to be processed is marked as F (x, y), and the image enhancement template comprises an image enhancement template with horizontal information removed, an image enhancement template with vertical information removed and an omnibearing image enhancement template; step S2: locally enhancing the image to be processed under the condition of fixed order by using the image enhancement template with the horizontal information removed to obtain a first locally enhanced image P1 (x, y); step S3: locally enhancing the image to be processed under the condition of fixed order by using the image enhancement template with the vertical information removed to obtain a second image local enhancement P2 (x, y); step S4: calculating a different first fractional order, denoted V (x, y), for each pixel of said image to be processed using said P1 (x, y) and said P2 (x, y); step S5: and carrying out enhancement processing on the image to be processed by adopting the self-adaptive first fractional order V (x, y) and the omnibearing image enhancement template to obtain final image enhancement.
Further, the image enhancement template further includes a first image enhancement template, and the step S1 includes: step S11: based on the R-L fractional differentiation, a classical 5X 5 first image enhancement basic template of the R-L fractional differentiation is obtained: Wherein/> V is the second fractional order, Γ (2-v) represents the gamma function operation, and then the RL1 is normalized with b1=8× (a1+a2+a3), resulting in the first image enhancement template/>Step S12: the first image enhancement basic template RL1 is improved, information in the horizontal direction is removed, values of the other 4 points except the center point of the 3 rd line of the RL1 are all 0, and then the center point is adjusted to be 6a1 from 8a1, so that a second image enhancement basic template RL2 is obtained: /(I)Then the RL2 is normalized by b2=6× (a1+a2+a3), and finally the graph enhancement template/>, of which the level information is removed, is obtainedStep S13: the first image basic template RL1 is improved, information in the vertical direction is removed, values of the other 4 points except the center point of the 3 rd column of the RL1 are all 0, and then the center point is adjusted to be 6a1 from 8a1, so that a third image enhancement basic template RL3 is obtained: /(I)Then, the RL3 is normalized by b3=6× (a1+a2+a3), and finally the image enhancement template/>, with the vertical information removed, is obtainedStep S14: the first image basic template RL1 is improved, and firstly, a point with a value of 0 in the RL1 is adjusted to be/>Then, the center point is adjusted from 8a1 to 12a1, and a fourth image enhancement basic template RL4 is obtained, wherein the specific formula is as follows: then, the RL4 is normalized by b4=12× (a1+a2+a3), and finally the omnibearing image enhancement template/>
Further, the step S2 specifically includes: using the saidAnd carrying out convolution processing on the F (x, y) to obtain the first local enhanced image P1 (x, y), wherein the specific formula is as follows: /(I)Wherein/>Representing a convolution operation, said/>The second fractional order v used in (c) is a fixed value.
Further, the step S3 specifically includes: using the saidAnd carrying out convolution processing on the F (x, y) to obtain the second local enhanced image P2 (x, y), wherein the specific formula is as follows: /(I)Wherein/>Representing a convolution operation, said/>The second fractional order v used in (c) is a fixed value.
Further, the step S4 includes: step S41: extracting the horizontal gradient information of the P1 (x, y) by using a sobel operator, and marking the horizontal gradient information as G1 (x, y), wherein the specific formula is as follows: wherein/> Representing a convolution operation; step S42: extracting vertical gradient information of the P2 (x, y) by using a sobel operator, and marking the vertical gradient information as G2 (x, y), wherein the specific formula is as follows: /(I)Wherein S' is the transposed matrix of S in step S41,/>Representing a convolution operation; step S43: calculating gradient information of the image F (x, y) to be processed by using the G1 (x, y) and the G2 (x, y), and marking the gradient information as G (x, y), wherein the specific formula is as follows: /(I)Step S44: counting the maximum value of G (x, y), and marking as gmax; step S45: calculating a first fractional order V (x, y) corresponding to each pixel according to gradient information G (x, y) of each pixel of the image to be processed, wherein the specific formula is as follows: /(I)Where ε is the tuning parameter.
Further, the image enhancement template further includes a second image enhancement template, and the step S5 includes: step S51: taking one pixel (x 0, y 0) of the image F (x, y) to be processed, calculating the corresponding values of a1, a2, a3, a4 and b4 by adopting the first fractional order v=V (x 0, y 0), and substituting the values into the omnibearing image enhancement template in the step S14In the specific formula of (2), a corresponding second image enhancement template is calculated and is recorded as/>Then, the pixel (x 0, y 0) is enhanced to obtain a new pixel value P3 (x 0, y 0), and the specific formula is as follows: /(I)Wherein/>Representing convolution operation, wherein F Ω5 (x, y) represents a sub-image formed by a 5X 5 field interval of pixel points (x 0, y 0) on the image F (x, y) to be processed; step S52: and (3) enhancing all pixels of the image to be processed according to the specific formula of the new pixel value P3 (x 0, y 0) in the step S51 to obtain final image enhancement, wherein the image enhancement result is P3 (x, y).
The invention also provides an image enhancement system based on the self-adaptive fractional order differential, which comprises a calculation module and an enhancement module, wherein the calculation module is used for calculating and improving an image to be processed to obtain an image enhancement template based on the R-L fractional order differential, the image to be processed is marked as F (x, y), and the image enhancement template comprises an image enhancement template for removing horizontal information, an image enhancement template for removing vertical information and an omnibearing image enhancement template; the enhancement module is used for locally enhancing the image to be processed under the condition of fixed order by using the image enhancement template with the horizontal information removed to obtain a first locally enhanced image P1 (x, y), and locally enhancing the image to be processed under the condition of fixed order by using the image enhancement template with the vertical information removed to obtain a second locally enhanced image P2 (x, y); the calculation module is further configured to calculate a different first fractional order, denoted as V (x, y), for each pixel of the image to be processed using the P1 (x, y) and the P2 (x, y); the enhancement module is further used for enhancing the image to be processed by adopting the adaptive first fractional order V (x, y) and the omnibearing image enhancement template to obtain final image enhancement.
Further, the image enhancement template further includes a first image enhancement template, where the first image enhancement template, the image enhancement template with horizontal information removed, the image enhancement template with vertical information removed, and the omnidirectional image enhancement template are specifically obtained in the following manner: based on the R-L fractional differentiation, a classical 5X 5 first image enhancement basic template of the R-L fractional differentiation is obtained: Wherein, V is the second fractional order, Γ (2-v) represents the gamma function operation, and then the RL1 is normalized with b1=8× (a1+a2+a3), resulting in the first image enhancement template/>The first image enhancement basic template RL1 is improved, information in the horizontal direction is removed, values of the other 4 points except the center point of the 3 rd line of the RL1 are all 0, and then the center point is adjusted to be 6a1 from 8a1, so that a second image enhancement basic template RL2 is obtained: /(I)Then the RL2 is normalized by b2=6× (a1+a2+a3), and finally the graph enhancement template/>, of which the level information is removed, is obtainedThe first image basic template RL1 is improved, information in the vertical direction is removed, values of the other 4 points except the center point of the 3 rd column of the RL1 are all 0, and then the center point is adjusted to be 6a1 from 8a1, so that a third image enhancement basic template RL3 is obtained: then, the RL3 is normalized by b3=6× (a1+a2+a3), and finally the image enhancement template/>, with the vertical information removed, is obtained The first image basic template RL1 is improved, and firstly, a point with a value of 0 in the RL1 is adjusted to be/>Then, the center point is adjusted from 8a1 to 12a1, and a fourth image enhancement basic template RL4 is obtained, wherein the specific formula is as follows: /(I)Then, the RL4 is normalized by b4=12× (a1+a2+a3), and finally the omnibearing image enhancement template/>The first locally enhanced image P1 (x, y) is obtained by: using the/>And carrying out convolution processing on the F (x, y) to obtain the first local enhanced image P1 (x, y), wherein the specific formula is as follows: /(I)Wherein/>Representing a convolution operation, said/>The second fractional order v used in (a) is a fixed value; the second locally enhanced image P2 (x, y) is obtained by: using the/>And carrying out convolution processing on the F (x, y) to obtain the second local enhanced image P2 (x, y), wherein the specific formula is as follows: /(I)Wherein/>Representing a convolution operation, said/>The second fractional order v used in (a) is a fixed value; the first fractional order is obtained by the following steps: extracting the horizontal gradient information of the P1 (x, y) by using a sobel operator, and marking the horizontal gradient information as G1 (x, y), wherein the specific formula is as follows: /(I)Wherein/> Representing a convolution operation; extracting vertical gradient information of the P2 (x, y) by using a sobel operator, and marking the vertical gradient information as G2 (x, y), wherein the specific formula is as follows: wherein S' is the transposed matrix of S,/> Representing a convolution operation; calculating gradient information of the image F (x, y) to be processed by using the G1 (x, y) and the G2 (x, y), and marking the gradient information as G (x, y), wherein the specific formula is as follows: /(I)Counting the maximum value of G (x, y), and marking as gmax; calculating a first fractional order V (x, y) corresponding to each pixel according to gradient information G (x, y) of each pixel of the image to be processed, wherein the specific formula is as follows: /(I)Wherein ε is the tuning parameter; the image enhancement template further comprises a second image enhancement template, and the final image enhancement acquisition mode is as follows: taking one pixel (x 0, y 0) of the image F (x, y) to be processed, calculating the corresponding values of a1, a2, a3, a4 and b4 by adopting the first fractional order v=V (x 0, y 0), and substituting the values into the omnibearing image enhancement templateIn the specific formula of (2), a corresponding second image enhancement template is calculated and is recorded as/>Then, the pixel (x 0, y 0) is enhanced to obtain a new pixel value P3 (x 0, y 0), and the specific formula is as follows: /(I)Wherein/>Representing convolution operation, wherein F Ω5 (x, y) represents a sub-image formed by a 5X 5 field interval of pixel points (x 0, y 0) on the image F (x, y) to be processed; and after all pixels of the image to be processed are enhanced according to a specific formula of the new pixel value P3 (x 0, y 0), obtaining final image enhancement, wherein the image enhancement result is P3 (x, y).
According to the image enhancement method and system based on the self-adaptive fractional order differentiation, the self-adaptive first fractional order V (x, y) and the omnibearing image enhancement template are adopted to enhance the image to be processed, so that the final image enhancement is obtained, the texture detail can be effectively enhanced, the image quality is improved, the algorithm complexity is low, and the real-time processing requirement can be well met.
Drawings
Fig. 1 is a flowchart of an image enhancement method based on adaptive fractional order differentiation according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of a specific flow for obtaining an image enhancement template in the image enhancement method based on adaptive fractional order differentiation shown in fig. 1.
Fig. 3 is a schematic diagram of a specific flow chart for calculating the first fractional order in the image enhancement method based on the adaptive fractional order differentiation shown in fig. 1.
Fig. 4 is a schematic flow chart of obtaining a final enhanced image in the image enhancement method based on adaptive fractional order differentiation shown in fig. 1.
Fig. 5 is a schematic structural diagram of an image enhancement system based on adaptive fractional order differentiation according to an embodiment of the present invention.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are illustrative of the invention and are not intended to limit the scope of the invention.
As shown in fig. 1 to 4, in the present embodiment, an image enhancement method based on adaptive fractional differentiation is provided. The image enhancement templates include a first image enhancement template, an image enhancement template from which horizontal information is removed, an image enhancement template from which vertical information is removed, an omnidirectional image enhancement template, and a second image enhancement template. The image enhancement method comprises the following steps:
step S1: and (3) calculating improvement on the image to be processed, and obtaining an image enhancement template based on R-L fractional differentiation, wherein the image to be processed is marked as F (x, y).
The specific flow diagram of the image enhancement template is obtained in the image enhancement method based on adaptive fractional order differentiation as shown in fig. 2. In a specific application example, the detailed flow of the step S1 of the present invention includes:
step S11: based on the R-L fractional differentiation, a classical 5X 5 first image enhancement basic template of the R-L fractional differentiation is obtained: Wherein/> V is the second fractional order, Γ (2-v) represents the gamma function operation, and then the normalization of RL1 is performed with b1=8× (a1+a2+a3), finally obtaining the first image enhancement template/>
Step S12: the first image enhancement basic template RL1 is improved, information in the horizontal direction is removed, values of the other 4 points of the center point are all 0 except for the 3 rd line of the RL1, then the center point is adjusted to be 6a1 from 8a1, and a second image enhancement basic template RL2 is obtained: Then, normalization processing is carried out on RL2 by b2=6× (a1+a2+a3), and finally, the graph enhancement template/>, with the horizontal information removed, is obtained
Step S13: the first image basic template RL1 is improved, information in the vertical direction is removed, values of the other 4 points of the 3 rd column of the RL1 except the center point are all 0, and then the center point is adjusted from 8a1 to 6a1, so that a third image enhancement basic template RL3 is obtained: Then, the RL3 is normalized by b3=6× (a1+a2+a3), and finally the image enhancement template/>, with the vertical information removed, is obtained
Step S14: the first image basic template RL1 is improved, and firstly, the point with the value of 0 in RL1 is adjusted to beThen, the center point is adjusted from 8a1 to 12a1, and a fourth image enhancement basic template RL4 is obtained, wherein the specific formula is as follows: /(I)Then, the RL4 is normalized by b4=12× (a1+a2+a3), and finally the omnibearing image enhancement template/>
Step S2: the image enhancement template from which the horizontal information is removed is used to locally enhance the image to be processed under the condition of fixed order, and a first locally enhanced image P1 (x, y) is obtained.
The step S2 is specifically implemented byPerforming convolution processing on F (x, y) to obtain a first local enhancement image P1 (x, y), wherein the specific formula is as follows: /(I)Wherein/>Representing convolution operations,/>The second fractional order v used in (c) is a fixed value.
In this embodiment, the second fractional order v takes a fixed value of 0.6. In other embodiments, there may be fixed values of other values.
Step S3: and locally enhancing the image to be processed under the condition of fixed order by using the image enhancement template with the vertical information removed, so as to obtain a second image local enhancement P2 (x, y).
The step S3 is specifically implemented byAnd (3) carrying out convolution processing on the F (x, y) to obtain a second local enhancement image P2 (x, y), wherein the specific formula is as follows: /(I)Wherein/>Representing convolution operations,/>The second fractional order v used in (c) is a fixed value.
In this embodiment, the second fractional order v takes a fixed value of 0.6. In other embodiments, there may be fixed values of other values.
Step S4: a different first fractional order is calculated for each pixel of the image to be processed using P1 (x, y) and P2 (x, y), denoted V (x, y).
Specifically, the optimal fractional order of each pixel is adaptively determined using gradient information of the first locally enhanced image and the second locally enhanced image.
The specific flow chart of calculating the first fractional order in the adaptive fractional order derivative-based image enhancement method is shown in fig. 3. In a specific application example, the detailed flow of step S4 of the present invention includes:
step S41: extracting horizontal gradient information of P1 (x, y) by using sobel operator, and marking as G1 (x, y), wherein the specific formula is as follows: wherein/> Representing a convolution operation.
Step S42: the sobel operator is used to extract the vertical gradient information of P2 (x, y), which is marked as G2 (x, y), and the specific formula is as follows: wherein S' is the transposed matrix of S in step S41,/> Representing a convolution operation.
Step S43: gradient information of the image F (x, y) to be processed is calculated by using G1 (x, y) and G2 (x, y), and is marked as G (x, y), and the specific formula is as follows:
step S44: the maximum value of G (x, y) is counted and noted as gmax.
Step S45: the first fractional order V (x, y) corresponding to the pixel is calculated according to the gradient information G (x, y) of each pixel of the image to be processed, and the specific formula is as follows: Where ε is the tuning parameter.
In this embodiment, the epsilon has a value of 0.1. In other embodiments, ε may also be another value.
Step S5: and carrying out enhancement processing on the image to be processed by adopting the adaptive first fractional order V (x, y) and the omnibearing image enhancement template to obtain final image enhancement.
In this embodiment, specifically, the adaptive first fractional order V (x, y) is substituted into the omnibearing image enhancement template to perform convolution processing on the image to be processed, so as to obtain a final enhanced image.
The specific flow diagram of the final enhanced image is obtained in the image enhancement method based on adaptive fractional order differentiation as shown in fig. 4. In a specific application example, the detailed flow of step S5 of the present invention includes:
Step S51: taking one pixel (x 0, y 0) of the image F (x, y) to be processed, calculating the corresponding values of a1, a2, a3, a4 and b4 by adopting the first fractional order v=V (x 0, y 0), and substituting the values into the omnibearing image enhancement template in the step S14 In the specific formula of (2), a corresponding second image enhancement template is calculated and is recorded as/>Then, the pixel (x 0, y 0) is enhanced to obtain a new pixel value P3 (x 0, y 0), which has the following specific formula: Wherein/> Representing convolution operation, F Ω5 (x, y) represents a sub-image consisting of a 5 x 5 region segment of pixel points (x 0, y 0) on the image to be processed F (x, y).
Step S52: after all the pixels of the image to be processed are enhanced according to the specific formula of the new pixel value P3 (x 0, y 0) in step S51, the final image enhancement is obtained, and the image enhancement result is P3 (x, y).
As shown in fig. 5, the present invention further provides an image enhancement system based on adaptive fractional order differentiation, which comprises a calculation module 60 and an enhancement module 61. The image enhancement templates include a first image enhancement template, an image enhancement template from which horizontal information is removed, an image enhancement template from which vertical information is removed, an omnidirectional image enhancement template, and a second image enhancement template.
The calculation module 60 is used for calculating improvement on the image to be processed, and obtaining an image enhancement template based on R-L fractional differentiation, wherein the image to be processed is marked as F (x, y).
In this embodiment, specifically, the acquiring modes of the first image enhancement template, the image enhancement template from which the horizontal information is removed, the image enhancement template from which the vertical information is removed, and the omnibearing image enhancement template are specifically as follows: based on the R-L fractional differentiation, a classical 5X 5 first image enhancement basic template of the R-L fractional differentiation is obtained: Wherein/> V is the second fractional order, Γ (2-v) represents the gamma function operation, and then the normalization of RL1 is performed with b1=8× (a1+a2+a3), finally obtaining the first image enhancement template/>The first image enhancement basic template RL1 is improved, information in the horizontal direction is removed, values of the other 4 points of the center point are all 0 except for the 3 rd line of the RL1, then the center point is adjusted to be 6a1 from 8a1, and a second image enhancement basic template RL2 is obtained: /(I)Then, normalization processing is carried out on RL2 by b2=6× (a1+a2+a3), and finally, the graph enhancement template/>, with the horizontal information removed, is obtainedThe first image basic template RL1 is improved, information in the vertical direction is removed, values of the other 4 points of the 3 rd column of the RL1 except the center point are all 0, and then the center point is adjusted from 8a1 to 6a1, so that a third image enhancement basic template RL3 is obtained: /(I)Then, the RL3 is normalized by b3=6× (a1+a2+a3), and finally the image enhancement template with the vertical information removed is obtainedThe first image basic template RL1 is improved, and firstly, the point with the value of 0 in the RL1 is adjusted to be/>Then, the center point is adjusted from 8a1 to 12a1, and a fourth image enhancement basic template RL4 is obtained, wherein the specific formula is as follows: Then, the RL4 is normalized by b4=12× (a1+a2+a3), and finally the omnibearing image enhancement template/>
The enhancement module 61 is configured to locally enhance the image to be processed with a fixed order using the image enhancement template from which the horizontal information is removed, to obtain a first locally enhanced image P1 (x, y), and locally enhance the image to be processed with a fixed order using the image enhancement template from which the vertical information is removed, to obtain a second locally enhanced image P2 (x, y).
The first locally enhanced image P1 (x, y) is acquired in the following manner:
Using Performing convolution processing on F (x, y) to obtain a first local enhancement image P1 (x, y), wherein the specific formula is as follows: /(I)Wherein/>Representing convolution operations,/>The second fractional order v used in (c) is a fixed value.
The second locally enhanced image P2 (x, y) is acquired in the following manner:
Using And (3) carrying out convolution processing on the F (x, y) to obtain a second local enhancement image P2 (x, y), wherein the specific formula is as follows: /(I)Wherein/>Representing convolution operations,/>The second fractional order v used in (c) is a fixed value.
In this embodiment, the second fractional order v is a fixed value of 0.6. In other embodiments, other fixed values are also possible.
The calculation module 60 is further configured to calculate a different first fractional order, denoted V (x, y), for each pixel of the image to be processed using P1 (x, y) and P2 (x, y).
Specifically, the first fractional order is obtained by:
Extracting horizontal gradient information of P1 (x, y) by using a sobel operator, and marking the information as G1 (x, y), wherein the specific formula is as follows: wherein/> Representing a convolution operation; the sobel operator is used to extract the vertical gradient information of P2 (x, y), which is marked as G2 (x, y), and the specific formula is as follows: /(I)Wherein S' is the transposed matrix of S,/>Representing a convolution operation; gradient information of the image F (x, y) to be processed is calculated by using G1 (x, y) and G2 (x, y), and is marked as G (x, y), and the specific formula is as follows: /(I)Counting the maximum value of G (x, y), and marking as gmax; the first fractional order V (x, y) corresponding to the pixel is calculated according to the gradient information G (x, y) of each pixel of the image to be processed, and the specific formula is as follows: /(I)Where ε is the tuning parameter.
The enhancement module 61 is further configured to enhance the image to be processed by using the adaptive first fractional order V (x, y) and the omnidirectional image enhancement template, so as to obtain final image enhancement.
Specifically, the final image enhancement acquisition mode is:
Any pixel (x 0, y 0) of the image F (x, y) to be processed is taken, the corresponding values of a1, a2, a3, a4 and b4 are calculated by adopting the first fractional order v=V (x 0, y 0), and then the values are substituted into the omnibearing image enhancement template In the specific formula of (2), a corresponding second image enhancement template is calculated and is recorded as/>Then, the pixel (x 0, y 0) is enhanced to obtain a new pixel value P3 (x 0, y 0), which has the following specific formula: /(I)Wherein/>Representing convolution operation, wherein F Ω5 (x, y) represents a sub-image formed by a 5X 5 region section of a pixel point (x 0, y 0) on the image F (x, y) to be processed; and after all pixels of the image to be processed are enhanced according to a specific formula of a new pixel value P3 (x 0, y 0), obtaining final image enhancement, wherein the image enhancement result is P3 (x, y).
According to the image enhancement method and system based on the self-adaptive fractional order differentiation, the self-adaptive first fractional order V (x, y) and the omnibearing image enhancement template are adopted to enhance the image to be processed, so that the final image enhancement is obtained, the texture detail can be effectively enhanced, the image quality is improved, the algorithm complexity is low, and the real-time processing requirement can be well met.
In this document, the terms "upper", "lower", "front", "rear", "left", "right", "top", "bottom", "inner", "outer", "vertical", "horizontal", etc. refer to the directions or positional relationships based on those shown in the drawings, and are merely for clarity and convenience of description of the expression technical solution, and thus should not be construed as limiting the present invention.
In this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a list of elements is included, and may include other elements not expressly listed.
The foregoing is merely illustrative of the present invention, and the present invention is not limited thereto, and any person skilled in the art will readily recognize that variations or substitutions are within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (2)
1. An image enhancement method based on self-adaptive fractional order differentiation is characterized by comprising the following steps: step S1: calculating and improving an image to be processed to obtain an image enhancement template based on R-L fractional differentiation, wherein the image to be processed is marked as F (x, y), and the image enhancement template comprises an image enhancement template with horizontal information removed, an image enhancement template with vertical information removed and an omnibearing image enhancement template; step S2: locally enhancing the image to be processed under the condition of fixed order by using the image enhancement template with the horizontal information removed to obtain a first locally enhanced image P1 (x, y); step S3: locally enhancing the image to be processed under the condition of fixed order by using the image enhancement template with the vertical information removed, so as to obtain a second locally enhanced image P2 (x, y); step S4: calculating a different first fractional order, denoted V (x, y), for each pixel of said image to be processed using said P1 (x, y) and said P2 (x, y); step S5: the image to be processed is enhanced by adopting the self-adaptive first fractional order V (x, y) and the omnibearing image enhancement template to obtain final image enhancement, wherein the image enhancement template further comprises a first image enhancement template and a second image enhancement template;
Wherein, the step S1 includes: step S11: based on the R-L fractional differentiation, a classical 5X 5 first image enhancement basic template of the R-L fractional differentiation is obtained: Wherein, V is the second fractional order, Γ (2-v) represents the gamma function operation, and then the RL1 is normalized with b1=8× (a1+a2+a3), resulting in the first image enhancement template/>Step S12: the first image enhancement basic template RL1 is improved, information in the horizontal direction is removed, values of the other 4 points except the center point of the 3 rd line of the RL1 are all 0, and then the center point is adjusted to be 6a1 from 8a1, so that a second image enhancement basic template RL2 is obtained: /(I)Then the RL2 is normalized by b2=6× (a1+a2+a3), and finally the graph enhancement template/>, of which the level information is removed, is obtainedStep S13: the first image basic template RL1 is improved, information in the vertical direction is removed, values of the other 4 points except the center point of the 3 rd column of the RL1 are all 0, and then the center point is adjusted to be 6a1 from 8a1, so that a third image enhancement basic template RL3 is obtained: /(I)Then, the RL3 is normalized by b3=6× (a1+a2+a3), and finally the image enhancement template/>, with the vertical information removed, is obtainedStep S14: the first image basic template RL1 is improved, and firstly, a point with a value of 0 in the RL1 is adjusted to be/>Then, the center point is adjusted from 8a1 to 12a1, and a fourth image enhancement basic template RL4 is obtained, wherein the specific formula is as follows: /(I)Then, the RL4 is normalized by b4=12× (a1+a2+a3), and finally the omnibearing image enhancement template is obtained
The step S2 specifically comprises the following steps: using the saidAnd carrying out convolution processing on the F (x, y) to obtain the first local enhanced image P1 (x, y), wherein the specific formula is as follows: /(I)Wherein/>Representing a convolution operation, said/>The second fractional order v used in (c) is a fixed value,
The step S3 specifically comprises the following steps: using the saidAnd carrying out convolution processing on the F (x, y) to obtain the second local enhanced image P2 (x, y), wherein the specific formula is as follows: /(I)Wherein/>Representing a convolution operation, said/>The second fractional order v used in (c) is a fixed value,
The step S4 includes: step S41: extracting the horizontal gradient information of the P1 (x, y) by using a sobel operator, and marking the horizontal gradient information as G1 (x, y), wherein the specific formula is as follows: wherein/> Representing a convolution operation; step S42: extracting vertical gradient information of the P2 (x, y) by using a sobel operator, and marking the vertical gradient information as G2 (x, y), wherein the specific formula is as follows: /(I)Wherein S' is the transposed matrix of S in step S41,/>Representing a convolution operation; step S43: calculating gradient information of the image F (x, y) to be processed by using the G1 (x, y) and the G2 (x, y), and marking the gradient information as G (x, y), wherein the specific formula is as follows: /(I)Step S44: counting the maximum value of G (x, y), and marking as G max; step S45: calculating a first fractional order V (x, y) corresponding to each pixel according to gradient information G (x, y) of each pixel of the image to be processed, wherein the specific formula is as follows: Where epsilon is the adjustment parameter and,
The step S5 includes: step S51: taking one pixel (x 0, y 0) of the image F (x, y) to be processed, calculating the corresponding values of a1, a2, a3, a4 and b4 by adopting the second fractional order v=V (x 0, y 0), and substituting the values into the omnibearing image enhancement template in the step S14In the specific formula of (2), a corresponding second image enhancement template is calculated and is recorded as/>Then, the pixel (x 0, y 0) is enhanced to obtain a new pixel value P3 (x 0, y 0), and the specific formula is as follows: /(I)Wherein/>Representing convolution operation, wherein F Ω5 (x, y) represents a sub-image formed by a 5X 5 field interval of pixel points (x 0, y 0) on the image F (x, y) to be processed; step S52: and (3) enhancing all pixels of the image to be processed according to the specific formula of the new pixel value P3 (x 0, y 0) in the step S51 to obtain final image enhancement, wherein the image enhancement result is P3 (x, y).
2. The image enhancement system based on the self-adaptive fractional order differential is characterized by comprising a calculation module and an enhancement module, wherein the calculation module is used for calculating and improving an image to be processed to obtain an image enhancement template based on R-L fractional order differential, the image to be processed is marked as F (x, y), and the image enhancement template comprises an image enhancement template for removing horizontal information, an image enhancement template for removing vertical information and an omnibearing image enhancement template; the enhancement module is used for locally enhancing the image to be processed under the condition of fixed order by using the image enhancement template with the horizontal information removed to obtain a first local enhancement image P1 (x, y), and locally enhancing the image to be processed under the condition of fixed order by using the image enhancement template with the vertical information removed to obtain a second local enhancement image P2 (x, y); the calculation module is further configured to calculate a different first fractional order, denoted as V (x, y), for each pixel of the image to be processed using the P1 (x, y) and the P2 (x, y); the enhancement module is further configured to perform enhancement processing on the image to be processed by using the adaptive first fractional order V (x, y) and the omnidirectional image enhancement template, so as to obtain final image enhancement, where the image enhancement template further includes a first image enhancement template, and the first image enhancement template, the image enhancement template for removing horizontal information, the image enhancement template for removing vertical information, and the omnidirectional image enhancement template are specifically obtained in the following manner: based on the R-L fractional differentiation, a classical 5X 5 first image enhancement basic template of the R-L fractional differentiation is obtained: Wherein/> V is the second fractional order, Γ (2-v) represents the gamma function operation, and then the RL1 is normalized with b1=8× (a1+a2+a3), resulting in the first image enhancement template/>The first image enhancement basic template RL1 is improved, information in the horizontal direction is removed, values of the other 4 points except the center point of the 3 rd line of the RL1 are all 0, and then the center point is adjusted to be 6a1 from 8a1, so that a second image enhancement basic template RL2 is obtained: /(I)Then the RL2 is normalized by b2=6× (a1+a2+a3), and finally the graph enhancement template/>, of which the level information is removed, is obtainedThe first image basic template RL1 is improved, information in the vertical direction is removed, values of the other 4 points except the center point of the 3 rd column of the RL1 are all 0, and then the center point is adjusted to be 6a1 from 8a1, so that a third image enhancement basic template RL3 is obtained: /(I)Then, the RL3 is normalized by b3=6× (a1+a2+a3), and finally the image enhancement template/>, with the vertical information removed, is obtainedThe first image basic template RL1 is improved, and firstly, a point with a value of 0 in the RL1 is adjusted to be/>Then, the center point is adjusted from 8a1 to 12a1, and a fourth image enhancement basic template RL4 is obtained, wherein the specific formula is as follows: /(I)Then, the RL4 is normalized by b4=12× (a1+a2+a3), and finally the omnibearing image enhancement template is obtainedThe first locally enhanced image P1 (x, y) is obtained by: using the/>And carrying out convolution processing on the F (x, y) to obtain the first local enhanced image P1 (x, y), wherein the specific formula is as follows: /(I)Wherein/>Representing a convolution operation, said/>The second fractional order v used in (a) is a fixed value; the second locally enhanced image P2 (x, y) is obtained by: using the/>And carrying out convolution processing on the F (x, y) to obtain the second local enhanced image P2 (x, y), wherein the specific formula is as follows: /(I)Wherein/>Representing a convolution operation, said/>The second fractional order v used in (a) is a fixed value; the first fractional order is obtained by the following steps: extracting the horizontal gradient information of the P1 (x, y) by using a sobel operator, and marking the horizontal gradient information as G1 (x, y), wherein the specific formula is as follows: /(I)Wherein/> Representing a convolution operation; extracting vertical gradient information of the P2 (x, y) by using a sobel operator, and marking the vertical gradient information as G2 (x, y), wherein the specific formula is as follows: /(I)Wherein S' is the transposed matrix of S,/>Representing a convolution operation; calculating gradient information of the image F (x, y) to be processed by using the G1 (x, y) and the G2 (x, y), and marking the gradient information as G (x, y), wherein the specific formula is as follows: /(I)Counting the maximum value of G (x, y), and marking as G max; calculating a first fractional order V (x, y) corresponding to each pixel according to gradient information G (x, y) of each pixel of the image to be processed, wherein the specific formula is as follows: /(I)Wherein ε is the tuning parameter; the image enhancement template further comprises a second image enhancement template, and the final image enhancement acquisition mode is as follows: taking one pixel (x 0, y 0) of the image F (x, y) to be processed, calculating corresponding values of a1, a2, a3, a4 and b4 by adopting the second fractional order v=V (x 0, y 0), and substituting the values into the omnibearing image enhancement template/>In the specific formula of (2), a corresponding second image enhancement template is calculated and is recorded as/>Then, the pixel (x 0, y 0) is enhanced to obtain a new pixel value P3 (x 0, y 0), and the specific formula is as follows: /(I)Wherein/>Representing convolution operation, wherein F Ω5 (x, y) represents a sub-image formed by a 5X 5 field interval of pixel points (x 0, y 0) on the image F (x, y) to be processed; and after all pixels of the image to be processed are enhanced according to a specific formula of the new pixel value P3 (x 0, y 0), obtaining final image enhancement, wherein the image enhancement result is P3 (x, y).
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