CN109615590B - Sonar image enhancement method based on fuzzy algorithm and fractional differential algorithm - Google Patents
Sonar image enhancement method based on fuzzy algorithm and fractional differential algorithm Download PDFInfo
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Abstract
The invention discloses a sonar image enhancement method based on a fuzzy algorithm and a fractional differential algorithm, which realizes enhancement of multi-beam forward-looking sonar images. The invention provides a novel fuzzy image enhancement algorithm based on a classical fuzzy enhancement algorithm, so that the calculation difficulty is greatly reduced when the fuzzy enhancement operation is carried out. And the information contained in the multi-beam forward-looking sonar image after enhancement is not reduced by reserving part of information with low gray values. And on the basis, the sonar image obtained by the fuzzy enhancement algorithm is sharpened by applying a fractional differential algorithm. The sharpened sonar image is not only clear, but also the contrast between the information is enhanced.
Description
Technical Field
The invention relates to a multi-beam sonar carried by an underwater remote control robot, in particular to a sonar image enhancement method based on a fuzzy algorithm and a fractional differential algorithm, and belongs to the field of sonar image processing.
Background
With the rapid development of automatic control, electronic computer and power electronics technologies, underwater robots are increasingly used. Compared with other detection means such as optical vision, radar, infrared and the like, underwater sound detection is the most effective mode at present. The sonar can sense and process the underwater environment in real time and judge the position, type and other information of surrounding objects. In contrast, light waves and electromagnetic waves propagate in water at a high attenuation speed, the propagation distance is very limited, short-distance detection can be performed only under the condition of good hydrologic conditions, and the effect is limited in a complex underwater environment, so that the practical requirements of underwater cannot be met. The acoustic wave has a long propagation distance under water, and the acoustic wave has the best propagation performance, and is suitable for the condition of complex and changeable hydrologic conditions. Therefore, the sound wave is the first choice carrier for underwater long-distance propagation, and the underwater sound detection technology has the characteristics of strong electromagnetic interference resistance, good concealment and high target positioning precision.
Along with the rapid development of the modern photoelectric technology, the imaging precision of the sonar is greatly improved, and the target detection distance is also greatly improved. Therefore, a large-scale underwater target detection system can be established by taking the sonar as a core sensor and combining an image information processing technology.
However, due to the complex and changeable characteristics of the underwater acoustic channel of the acoustic information transmission channel and the transmission characteristics of the acoustic wave, the forward-looking sonar image has obvious self characteristics. Due to acoustic shadows and side lobe effects, a single target may split into multiple bright spots on a forward looking sonar image, and areas such as other objects in the water and uneven underwater may form a linear bright area in the acoustic image. For a stationary target, imaging of the target on the sonar may exhibit positional differences due to the different scan directions. The target portion of the forward looking sonar image is typically relatively low in gray level, while the background portion is typically rich in gray level. Because of these limitations, it is necessary to develop an image processing technology study for forward-looking sonar, and select features that can effectively distinguish each target, so as to perform effective target recognition on the sonar image.
The sonar image can be said to be the premise of all works, and the denoising and the characteristic enhancement of the sonar are particularly important due to the limitations of the image scanned and formed by the multi-beam forward-looking sonar and the complexity of the underwater environment. Patent document with application number of 201711036788.1 discloses a "sonar image target recognition method based on a deep learning technology", and the processing of a sonar image becomes complicated due to the fact that a large amount of data is required for supporting by adopting the deep learning method. Patent document with application number of 200810064436.1 discloses a "hierarchical MRF-based sonar image adaptive segmentation method", but the reliability of the algorithm needs a large number of tests, and the adaptivity of image processing needs to be further improved.
Disclosure of Invention
The invention aims to provide a sonar image enhancement method based on a fuzzy algorithm and a fractional differential algorithm, which is applied to the field of underwater robot sonar image processing, improves the processing speed of a sonar image by applying the fuzzy enhancement algorithm based on an ln function, enhances the sonar image enhancement effect, and sharpens the sonar image by applying the fractional differential algorithm on the basis.
The aim of the invention is realized by the following technical scheme:
a sonar image enhancement method based on a fuzzy algorithm and a fractional differential algorithm comprises the following steps: firstly, blurring processing is carried out on a sonar image, then a fuzzy membership function based on an ln function is established, then a fuzzy enhancement operator is established, on the basis, fuzzy inverse transformation is carried out on the fuzzy membership function based on the ln function, and finally fractional differential operation is carried out.
The object of the invention can be further achieved by the following technical measures:
the sonar image enhancement method based on the fuzzy algorithm and the fractional differential algorithm comprises the following 2 steps:
step 1: firstly, inputting a sonar image, and calculating the highest value x of pixel gray in the sonar image max And a minimum value x min 。
Step 2: mapping the sonar image from the space gray domain to a fuzzy characteristic plane of the sonar image; the sonar image Y with the size of M rows and N columns is equivalent to a fuzzy set X:
wherein x is ij Representing the gray value of pixel (i, j), u ij /x ij Representing a pixel point x ij The degree of blurring characteristics that are present,representing the constituent element as +.>And there are fuzzy sets of M rows and N columns.
Fuzzy membership function u of all pixels in plane ij A fuzzy characteristic plane of the sonar image is formed; and 0.ltoreq.u is present ij ≤1，u ij Will soundThe sonar image Y is mapped from the fuzzy set X to (0, 1).
The sonar image enhancement method based on the fuzzy algorithm and the fractional differential algorithm comprises the following steps of:
the fuzzy membership function based on the ln function provided by the invention is shown as follows:
u ij ＝G(x ij )＝ln(1+(e-1)(x ij -x min )/(x max -x min )) (2)
where e=2.718281828459, g (x ij ) Is a fuzzy membership function based on an ln function.
According to the sonar image enhancement method based on the fuzzy algorithm and the fractional differential algorithm, the sonar image enhancement is a result obtained by operating a fuzzy enhancement operator in a fuzzy space, and the fuzzy enhancement operator is shown in the following formula:
u’ ij ＝T (m) (u ij )＝T(T (m-1) (u ij ))m＝1,2,3... (3)
wherein T is (m) Represents m calls to T, u' ij Is the value obtained after m calls for T, and its nonlinear transformation T is:
according to the sonar image enhancement method based on the fuzzy algorithm and the fractional differential algorithm, fuzzy inverse transformation is carried out on the fuzzy membership function based on the ln function:
wherein x' ij Represents the gray value of the pixel after the fuzzy inverse transformation of the fuzzy membership function based on the ln function,representation pair G (x ij ) And performing inverse transformation.
According to the sonar image enhancement method based on the fuzzy algorithm and the fractional differential algorithm, sharpening is carried out on a sonar image Y' subjected to fuzzy inverse transformation based on a fuzzy membership function of an ln function, a fractional differential equation of the sonar image is firstly established, then a mask filter is determined, and finally mask operation is carried out; the specific implementation comprises the following steps:
step 1: firstly constructing a fractional differential mask operator, wherein the fractional differential definition of G-L is derived from the definition of integer derivative of continuous function and is generalized to fractional, namely:
wherein Gamma function The v-order differential of the unitary signal f (t), t, a represent the upper and lower limits of the fractional-order differential, h is its differential step size, m is 0 to +.>Is an integer of (2); if the unary signal is in its duration [ a, t ]]In this case, the division is carried out in such a way that h=1, and +.>A differential expression of the fractional differentiation of the unitary continuous signal f (t) can thus be derived as shown in equation (7):
for arbitrary functions f (x, y) ∈L 2 (R 2 ) The differential expression of v-order partial differentiation on the x axis and the y axis is shown as the following formula:
step 2: since the sonar image Y' has M rows and N columns, it is necessary to construct M rows and N columns of filters ω (s, t) for linear filtering;
wherein s=0, 1,2, …, m-1 and t=0, 1,2, …, n-1, and the counter-clockwise isotropic filter is constructed in turn according to equation (10), using a fractional order differential of window size 5×5 into the mask, dividing each coefficient within the mask by 8-12v+4v 2 Carrying out normalization treatment;
the resulting output sonar image Y "(x, Y) can be expressed as discrete volume integral:
and a and b are radii of the fractional differential operator template in the directions of x and y coordinate axes respectively, and finally, the contrast of each part of the output sonar image is enhanced.
Compared with the prior art, the invention has the beneficial effects that:
1. compared with the existing sonar image enhancement method, the method has the advantages that the enhancement calculation process of the sonar image is simplified, and the influence of inverse fuzzy factors and index fuzzy factors is removed.
2. When the fuzzy membership function is calculated, the fuzzy membership function based on the ln function is provided, and the variables contained in the formula of the fuzzy membership function based on the ln function are fewer, so that the fuzzy membership function based on the ln function is convenient to observe and calculate.
3. When the fuzzy membership function based on the ln function is calculated, the calculation process is simple, the image information with low gray value in the sonar image is reserved, and the enhancement effect is better.
4. The improved fuzzy enhancement algorithm is combined with the fractional differential algorithm, so that the enhancement processing of the sonar image is more accurate, and the enhancement effect is better.
Drawings
FIG. 1 is a block flow diagram of sonar image enhancement of the present invention;
FIG. 2 is a flow chart of the blur enhancement algorithm of the present invention;
FIG. 3 is a flow chart of the fractional differential algorithm of the present invention;
fig. 4 is 8 directions of fractional order differentiation of the present invention.
Detailed Description
The invention will be further described with reference to the drawings and the specific examples.
As shown in FIG. 1, the sonar image enhancement method based on the fuzzy algorithm and the fractional differential algorithm comprises the steps of inputting a sonar image, carrying out fuzzy processing on the sonar image, establishing a fuzzy membership function based on an ln function, establishing a fuzzy enhancement operator, carrying out fuzzy inverse transformation on the fuzzy membership function based on the ln function, carrying out fractional differential, and outputting the sonar image. The blurring processing of the sonar image mainly comprises the steps of blurring the sonar image and preparing for establishing a fuzzy membership function based on an ln function. Establishing a fuzzy membership function based on an ln function to process the sonar image in a frequency domain, and carrying out fuzzy enhancement on the sonar image through a fuzzy enhancement operator on the basis. And then performing fuzzy inverse transformation on a fuzzy membership function based on an ln function, and finally sharpening the sonar image through fractional differential operation.
As shown in fig. 2, the blurring process of the sonar image mainly includes: gray level calculation of sonar images, blurring mapping processing, establishment of a blur membership function based on an ln function, establishment of a blur enhancement operator and image defuzzification.
The blurring processing of the sonar image mainly comprises the following 2 steps:
step 1: firstly, inputting a sonar image, and calculating the highest value x of pixel gray in the sonar image by MATLAB max And a minimum value x min 。
Step 2: mapping the sonar image from the space gray domain to a fuzzy characteristic plane of the sonar image; the sonar image Y with the size of M rows and N columns is equivalent to a fuzzy set X:
wherein x is ij Representing the gray value of pixel (i, j), u ij /x ij Representing a pixel point x ij To the extent of a certain feature is present,representing the constituent element as +.>And there are fuzzy sets of M rows and N columns. Fuzzy membership function u of all pixels in plane ij A blurred feature plane of the sonar image is formed. And 0.ltoreq.u is present ij ≤1，u ij The sonar image Y is mapped from matrix X to (0, 1).
The establishment of the fuzzy membership function based on the ln function mainly comprises the following parts:
and establishing a fuzzy membership function based on the ln function. Aiming at the defects of classical fuzzy sonar image augmentation algorithm, the invention provides a fuzzy membership function based on an ln function, so that the fuzzy membership function u ij The value range of (1) is (0). Therefore, compared with the classical fuzzy membership function, the fuzzy membership function based on the ln function provided by the invention keeps the sonar image information of the low gray value part when calculation is performed, so that the enhancement effect of the sonar image is better.
The fuzzy membership function based on the ln function provided by the invention is shown as follows:
u ij ＝G(x ij )＝ln(1+(e-1)(x ij -x min )/(x max -x min )) (2)
where e=2.718281828459, g (x ij ) Is a fuzzy membership function based on an ln function.
The sonar image enhancement is a result obtained by carrying out operation on a fuzzy space through a fuzzy enhancement operator, and the fuzzy enhancement operator is shown in the following formula:
u’ ij ＝T (m) (u ij )＝T(T (m-1) (u ij ))m＝1,2,3... (3)
wherein T is (m) Represents m calls to T, u' ij Is the value obtained after m calls for T, and its nonlinear transformation T is:
from the above equation, when the value of the fuzzy membership function of the original pixel is less than 0.5, the membership will become large when it is T-transformed. In contrast, when the value of the fuzzy membership function of the original pixel is greater than 0.5, the membership will be smaller by performing T transformation on the fuzzy membership function. Therefore, the contrast of the sonar image is enhanced, the ambiguity of the sonar image is reduced, and the contrast of the sonar image is reduced for u ij The gray value corresponding to=0.5 is referred to as a transition point.
Inverse fuzzy transformation of ln-function-based fuzzy membership function
Wherein x' ij Represents the gray value of the pixel after the fuzzy inverse transformation of the fuzzy membership function based on the ln function,representation pair G (x ij ) And performing inverse transformation.
As shown in fig. 3, the sharpness processing is performed on the sonar image after the blurring enhancement, first, a fractional differential equation of the sonar image is established, then, a mask filter is determined, and finally, a mask operation is performed. The specific implementation comprises the following steps:
step 1: first, constructing a fractional order differential mask operator: the fractional differential definition of G-L is derived from the definition of the integer derivative of the continuous function and extends to the fractional order, namely:
wherein Gamma function The v-order differential of the unitary signal f (t), t, a represent the upper and lower limits of the fractional-order differential, h is its differential step size, m is 0 to +.>Is an integer of (2); if the unary signal is in its duration [ a, t ]]In this case, the division is carried out in such a way that h=1, and +.>A differential expression of the fractional differentiation of the unitary continuous signal f (t) can thus be derived as shown in equation (7):
for arbitrary functions f (x, y) ∈L 2 (R 2 ) The differential expression of v-order partial differentiation on the x axis and the y axis is shown as the following formula:
step 2: since the sonar image Y' has M rows and N columns, it is necessary to construct M rows and N columns of filters ω (s, t) for linear filtering;
as shown in FIG. 4, and constructing a counter-clockwise isotropic filter according to equation (10), masking the fractional differentiation with a window size of 5×5, dividing each coefficient in the mask by 8-12v+4v 2 Carrying out normalization treatment; the solution by filling 0 out of the 8 directions in the table, the resulting final differential mask is shown in the table below:
| a 2 | 0 | a 2 | 0 | a 2 |
| 0 | a 1 | a 1 | a 1 | 0 |
| a 2 | a 1 | 8×a 0 | a 1 | a 2 |
| 0 | a 1 | a 1 | a 1 | 0 |
| a 2 | 0 | a 2 | 0 | a 2 |
table 1 5 ×5 eight-direction fractional order differential operator
The resulting output sonar image X "(X, y) can be expressed as discrete volume integral:
and a and b are radii of the fractional differential operator template in the directions of x and y coordinate axes respectively, and finally, the contrast of each part of the output sonar image is enhanced.
In addition to the above embodiments, other embodiments of the present invention are possible, and all technical solutions formed by equivalent substitution or equivalent transformation are within the scope of the present invention.
Claims (5)
1. A sonar image enhancement method based on a fuzzy algorithm and a fractional differential algorithm is characterized by mainly comprising the following steps: firstly, blurring processing of a sonar image, then establishing a fuzzy membership function based on an ln function, then establishing a fuzzy enhancement operator, carrying out fuzzy inverse transformation on the fuzzy membership function based on the ln function on the basis, and finally sharpening the sonar image through fractional differential operation;
the blurring processing of the sonar image mainly comprises the following 2 steps:
step 1: firstly, inputting a sonar image, and calculating the highest value x of pixel gray in the sonar image max And a minimum value x min ；
Step 2: mapping the sonar image from the space gray domain to a fuzzy characteristic plane of the sonar image; the sonar image Y with the size of M rows and N columns is equivalent to a fuzzy set X:
wherein x is ij Representing the gray value of pixel (i, j), u ij /x ij Representing a pixel point x ij The degree of blurring characteristics that are present,representing the constituent element as +.>And there are fuzzy sets of M rows and N columns;
fuzzy membership function u of all pixels in plane ij A fuzzy characteristic plane of the sonar image is formed; and 0.ltoreq.u is present ij ≤1，u ij The sonar image Y is mapped from the fuzzy set X to (0, 1).
2. The sonar image enhancement method based on a fuzzy algorithm and a fractional differential algorithm as defined in claim 1, wherein the establishment of the fuzzy membership function based on the ln function mainly comprises the following parts:
the fuzzy membership function based on ln function is shown as follows:
u ij ＝G(x ij )＝ln(1+(e-1)(x ij -x min )/(x max -x min )) (2)
where e=2.718281828459, g (x ij ) Is a fuzzy membership function based on an ln function.
3. The sonar image enhancement method based on a fuzzy algorithm and a fractional differential algorithm as defined in claim 1, wherein the sonar image enhancement is a result obtained by performing an operation on a fuzzy space by a fuzzy enhancement operator, and the fuzzy enhancement operator is represented by the following formula:
u′ ij ＝T (m) (u ij )＝T(T (m-1) (u ij )) m＝1,2,3... (3)
wherein T is (m) Represents m calls to T, u' ij Is the value obtained after m calls for T, and its nonlinear transformation T is:
4. a sonar image enhancement method based on a fuzzy algorithm and a fractional order derivative algorithm as claimed in claim 1, wherein the inverse transformation is performed for the new fuzzy membership function:
wherein x' ij Represents the gray value of the pixel after the fuzzy inverse transformation of the fuzzy membership function based on the ln function,representation pairG(x ij ) And performing inverse transformation.
5. The sonar image enhancement method based on the fuzzy algorithm and the fractional differential algorithm as defined in claim 1, wherein the sonar image Y' after the fuzzy inverse transformation is performed on the fuzzy membership function based on the ln function is sharpened, the fractional differential equation of the sonar image is established first, then a mask filter is determined, and finally a mask operation is performed; the specific implementation comprises the following steps:
step 1: firstly constructing a fractional differential mask operator, wherein the fractional differential definition of G-L is derived from the definition of integer derivative of continuous function and is generalized to fractional, namely:
wherein Gamma function The v-order differential of the unitary signal f (t), t, a represent the upper and lower limits of the fractional-order differential, h is its differential step size, m is 0 to +.>Is an integer of (2); if the unary signal is in its duration [ a, t ]]In this case, the division is carried out in such a way that h=1, and +.>A differential expression of the fractional differentiation of the unitary continuous signal f (t) can thus be derived as shown in equation (7):
for arbitrary functions f (x, y) ∈L 2 (R 2 ) The differential expression of v-order partial differentiation on the x axis and the y axis is shown as the following formula:
step 2: since the sonar image Y' has M rows and N columns, it is necessary to construct M rows and N columns of filters ω (s, t) for linear filtering;
wherein s=0, 1,2, …, m-1 and t=0, 1,2, …, n-1, and the counter-clockwise isotropic filter is constructed in turn according to equation (10), using a fractional order differential of window size 5×5 into the mask, dividing each coefficient within the mask by 8-12v+4v 2 Carrying out normalization treatment;
the resulting output sonar image Y "(x, Y) can be expressed as discrete volume integral:
and a and b are radii of the fractional differential operator template in the directions of x and y coordinate axes respectively, and finally, the contrast of each part of the output sonar image is enhanced.
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| CN106204470A (en) * | 2016-07-01 | 2016-12-07 | 湖南源信光电科技有限公司 | Low-light-level imaging method based on fuzzy theory |
| CN106846257A (en) * | 2016-11-14 | 2017-06-13 | 山东理工大学 | A kind of Infrared DIM-small Target Image edge enhancement algorithm based on fuzzy technology |
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