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CN118168514B - Underwater section mapping system and method based on intelligent algorithm imaging - Google Patents

Underwater section mapping system and method based on intelligent algorithm imaging Download PDF

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CN118168514B
CN118168514B CN202410596305.7A CN202410596305A CN118168514B CN 118168514 B CN118168514 B CN 118168514B CN 202410596305 A CN202410596305 A CN 202410596305A CN 118168514 B CN118168514 B CN 118168514B
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CN118168514A (en
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顾长春
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Nanjing Suce Measuring Mapping Technology Co
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Nanjing Suce Measuring Mapping Technology Co
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Abstract

The invention relates to the technical field of underwater topography mapping, and discloses an intelligent algorithm imaging underwater section mapping system and method. The method comprises the following steps: collecting underwater topography data; generating an underwater geological image and an underwater magnetic image; extracting features of the underwater topography data, the underwater geological image and the underwater magnetic image; performing feature matching and preliminary alignment of the underwater geological image and the underwater magnetic force image; performing image registration of the underwater geological image and the underwater magnetic force image; and performing image fusion on the underwater geological image and the underwater magnetic force image after image registration to generate an underwater section map. The method realizes the acquisition of diversified underwater topography data through the combination of various sensor technologies; and the intelligent algorithm is adopted to register and fuse the images, so that the accuracy and reliability of the underwater section mapping are improved.

Description

Underwater section mapping system and method based on intelligent algorithm imaging
Technical Field
The invention relates to the technical field of underwater topography mapping, in particular to an intelligent algorithm imaging underwater section mapping system and method.
Background
With the development of marine science and technology, the underwater section mapping technology plays an important role in the fields of marine resource development, submarine topography survey, underwater engineering construction and the like. Traditional underwater section mapping methods mainly depend on sonar technology and optical imaging technology, however, the methods have various limitations in complex underwater environments, such as the sonar technology is greatly interfered by noise of the underwater environment, and the optical imaging technology is limited by water quality and illumination conditions. The acquisition of the underwater geological image is difficult, and the problems of low resolution, incomplete information acquisition and the like exist. The resolution of the underwater topography image obtained by the traditional method is limited, the imaging effect with high quality is difficult to provide, various data of the underwater topography are difficult to be completely obtained, and the characteristics and the structure of the underwater environment are difficult to be accurately depicted. With the development of technology, there is an increasing demand for underwater topography mapping, and thus there is an increasing demand for acquiring more diversified underwater topography data and images.
The existing underwater section mapping method generally needs comprehensive analysis of various sensor data so as to improve the accuracy of mapping results. However, data fusion and registration between different sensors remains a challenge. Secondly, when the existing method processes data in a complex underwater environment, accuracy and instantaneity are difficult to achieve. In addition, the existing method has larger calculated amount and lower efficiency when facing the underwater section mapping task with large range and high resolution. In addition, some underwater topography data fusion technologies are also available, underwater topography data with different dimensions acquired by various sensors are fused to obtain underwater topography mapping images with more information, but the multi-source data fusion is difficult, a large amount of data cleaning, feature extraction and analysis work are required, and the automation degree of the work needs to be improved.
As disclosed in the publication CN111880185A, a method for processing a survey of an underwater target, the method comprising: the array transmits a narrow-band pulse signal, and scans an underwater target; the array receives echo signals in response to the transmit beams of the transmit array; based on the obtained echo signals, azimuth direction information is obtained by utilizing a beam forming algorithm, and a three-dimensional data result of the target image is obtained by utilizing an improved CAATI algorithm. According to the invention, the high-resolution three-dimensional imaging result of the underwater target is obtained by setting the height difference multi-array element array to be combined with the frequency domain beam forming algorithm and the improved CAATI algorithm to carry out mapping-level three-dimensional imaging of the underwater target, the submarine topography survey is carried out, the underwater target is three-dimensional explored, and the task of better completing underwater operation is further achieved.
The patent with the publication number of CN115641277A discloses an underwater sonar mapping image noise reduction device and a noise reduction method thereof, the device comprises a communication module, a storage module, a noise sampling module, a filtering module and a deep learning module, wherein the communication module is used for establishing communication connection with a cloud server, communicating and transmitting picture data between the communication module and the cloud server, the storage module is used for storing the picture data and intermediate data in the running process of the device, the noise sampling module is externally connected with a central control computer, the noise sampling module is connected with the filtering module, the filtering module is externally connected with a sonar device, the sonar device is used for underwater detection and transmitting signals to the central control computer for imaging, the deep learning module is respectively connected with the central control computer, the filtering module, the noise sampling module and the storage module, and the deep learning module is used for receiving the underwater noise data acquired by the noise sampling module and carrying out noise reduction treatment on the picture imaged by the sonar according to the underwater noise data.
The problems presented in the background art exist in the above patents: the resolution of the obtained underwater topography image is limited, and the imaging effect with high quality is difficult to provide; and it is difficult to completely acquire various data of underwater topography and accurately describe features and structures of underwater environment.
The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person of ordinary skill in the art.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides an intelligent algorithm imaging underwater section mapping system and an intelligent algorithm imaging underwater section mapping method, and adopts an intelligent algorithm to register and fuse images through the combination of various sensor technologies, so that the accuracy and reliability of underwater section mapping are improved.
In order to solve the technical problems, the invention provides the following technical scheme:
In one aspect, the invention provides an intelligent algorithm imaging underwater section mapping method, which comprises the following steps: s1: collecting underwater topography data through a sensor;
s2: imaging based on the underwater topography data, including an underwater geological image and an underwater magnetic image;
S3: extracting the characteristics of the underwater topography data, the underwater geological image and the underwater magnetic force image;
S4: performing feature matching and preliminary alignment of the underwater geological image and the underwater magnetic force image based on the feature extraction result;
S5: performing image registration of the underwater geological image and the underwater magnetic force image based on the preliminary alignment result;
S6: and performing image fusion on the underwater geological image and the underwater magnetic force image after image registration to generate an underwater section map.
As a preferable scheme of the intelligent algorithm imaging underwater section mapping method, the invention comprises the following steps: the underwater topography data comprises geological data, acoustic data and magnetic data.
As a preferable scheme of the intelligent algorithm imaging underwater section mapping method, the invention comprises the following steps: the imaging method of the underwater geological image is to carry out offset imaging based on the geological data; the imaging method of the underwater magnetic force image is to carry out magnetic anomaly inversion imaging based on the magnetic force data.
As a preferable scheme of the intelligent algorithm imaging underwater section mapping method, the invention comprises the following steps: the feature extraction method comprises the following steps:
S301: carrying out noise reduction treatment on the sound wave data, the underwater geological image and the underwater magnetic image;
s302: extracting the position and form information of underwater topography based on the acoustic wave data after noise reduction to obtain the position of an underwater target point;
s303: and extracting the characteristics of the noise-reduced underwater geological image and the noise-reduced underwater magnetic force image to obtain characteristic points of the underwater geological image and characteristic points of the underwater magnetic force image.
As a preferable scheme of the intelligent algorithm imaging underwater section mapping method, the invention comprises the following steps: the feature matching and preliminary alignment method of the underwater geological image and the underwater magnetic force image comprises the following steps:
s401: performing feature point matching to obtain corresponding feature points in the underwater geological image and the underwater magnetic image;
s402: positioning the underwater target point in an underwater geological image and an underwater magnetic image;
S403: estimating geometric transformation parameters between the underwater geological image and the underwater magnetic force image based on the result of feature matching and the positioning of the underwater target point in the underwater geological image and the underwater magnetic force image;
s404: and carrying out translation and rotation operation on the underwater magnetic force image according to the geometric transformation parameters, and aligning the underwater magnetic force image with the underwater geological image.
As a preferable scheme of the intelligent algorithm imaging underwater section mapping method, the invention comprises the following steps: the method for registering the underwater geological image and the underwater magnetic force image comprises the following steps:
s501: dividing the images of the underwater geological image and the underwater magnetic force image into N corresponding windows respectively;
S502: calculating the similarity of each corresponding window;
S503: initializing a registration transformation model; the registration transformation model is used for describing the geometric relationship between the underwater geological image and the underwater magnetic force image;
S504: performing global optimization on the registration transformation model by using an optimization algorithm so as to maximize the sum of the similarity between all corresponding windows;
s505: performing image registration on the underwater geological image and the underwater magnetic image based on the globally optimized registration transformation model;
S506: and (3) checking the result of image registration, and if at least one of the underwater geological image and the underwater magnetic force image is empty or overlapped, interpolating the empty or overlapped area.
As a preferable scheme of the intelligent algorithm imaging underwater section mapping method, the invention comprises the following steps: the method for fusing the image registered underwater geological image and the underwater magnetic force image comprises the following steps:
S601: gradient information of the underwater geological image and the underwater magnetic force image is calculated respectively;
s602: calculating the weight of each pixel point on the underwater geological image and the underwater magnetic force image according to the gradient information;
S603: carrying out weighted average on gradient information of the underwater geological image and the underwater magnetic force image to obtain a fusion gradient image;
S604: and (3) carrying out gray level image reconstruction on the fused gradient image by adopting a gradient domain reconstruction algorithm to obtain a fused underwater section map.
In a second aspect, the invention provides an intelligent algorithm imaging underwater section mapping system, which comprises a data collection module, a preprocessing module, an imaging module, a data analysis module, a registration module, an image fusion module and an output display module; wherein:
the data collection module is used for collecting underwater topography data, including geological data, acoustic data and magnetic force data;
The preprocessing module is used for preprocessing the underwater topography data;
The imaging module is used for imaging the underwater topography data to obtain an underwater geological image and an underwater magnetic image;
the data analysis module is used for carrying out feature extraction and data comparison on the sound wave data, the underwater geological image and the underwater magnetic force image;
The registration module is used for registering the underwater geological image and the underwater magnetic force image;
the image fusion module is used for fusing the registered underwater geological image and the underwater magnetic force image to generate a final underwater section map;
And the output display module is used for visually displaying the underwater section map.
In a third aspect, the present invention provides an electronic device comprising: a memory for storing instructions; and the processor is used for executing the instructions to enable the equipment to execute the operation of the underwater section mapping method for realizing intelligent algorithm imaging.
In a fourth aspect, the present invention provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements an intelligent algorithmic imaging underwater cross-section mapping method of the present invention.
Compared with the prior art, the invention has the following beneficial effects:
By combining multiple sensor technologies, geological data, acoustic data and magnetic data are acquired, and diversified underwater topography data are acquired. The accuracy and the reliability of underwater section mapping are improved; the accuracy is guaranteed, meanwhile, the calculation complexity is reduced, and the mapping efficiency is improved. The real-time performance of underwater section mapping is improved.
The intelligent algorithm is adopted to carry out image registration and fusion, and the method for comparing and analyzing the images imaged by the sonar data, the geological radar and the magnetic force sensor is adopted, so that the intelligent level of data processing is improved, and the relevance and complementarity between the multi-source data are improved; the method for registering and fusing the underwater geological image and the underwater magnetic image effectively improves the accuracy and reliability of the underwater section survey and drawing.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art. Wherein:
FIG. 1 is a flow chart of an intelligent algorithm imaging underwater section mapping method;
Fig. 2 is a schematic structural diagram of an intelligent algorithm imaging underwater section mapping system.
Detailed Description
The following detailed description of the present invention is made with reference to the accompanying drawings and specific embodiments, and it is to be understood that the specific features of the embodiments and the embodiments of the present invention are detailed description of the technical solutions of the present invention, and not limited to the technical solutions of the present invention, and that the embodiments and the technical features of the embodiments of the present invention may be combined with each other without conflict.
Example 1
This embodiment describes an intelligent algorithm imaging underwater section mapping method, referring to fig. 1, the method includes the following steps:
s1: collecting underwater topography data through a sensor;
the underwater topography data comprises geological data, acoustic data and magnetic data;
S2: imaging is carried out based on the underwater topography data, and underwater topography images with different dimensions are constructed, wherein the underwater topography images comprise underwater geology images and underwater magnetic force images;
The imaging method of the underwater geological image is to carry out offset imaging based on the geological data; the imaging method of the underwater magnetic force image is to carry out magnetic anomaly inversion imaging based on the magnetic force data;
S3: extracting features of the underwater topography data, the underwater geological image and the underwater magnetic image; the method comprises the following steps:
S301: carrying out noise reduction treatment on the sound wave data, the underwater geological image and the underwater magnetic image;
s302: extracting the position and form information of underwater topography based on the acoustic wave data after noise reduction to obtain the position of an underwater target point;
S303: extracting features of the noise-reduced underwater geological image and the noise-reduced underwater magnetic image to obtain feature points; feature descriptors (e.g., SIFT, SURF, etc.) may be selected to describe key feature points in the image.
S4: performing feature matching and preliminary alignment of the underwater geological image and the underwater magnetic force image based on the results of the feature extraction and the correlation analysis; the method comprises the following steps:
S401: performing feature point matching to obtain corresponding feature points in the underwater geological image and the underwater magnetic image; feature point matching is achieved using feature distance based matching methods (e.g., nearest neighbor matching, nearest neighbor distance ratio matching, etc.).
S402: and positioning the underwater target point in the underwater geological image and the underwater magnetic force image. This step may help determine the approximate translational and rotational relationship of the underwater target point between the underwater geologic image and the underwater magnetometric image.
S403: based on the result of feature matching and the positioning of the underwater target point in the underwater geological image and the underwater magnetic force image, the geometric transformation parameters between the underwater geological image and the underwater magnetic force image are estimated by utilizing a rigid transformation model (translation and rotation).
S404: and carrying out translation and rotation operation on the underwater magnetic force image according to the geometric transformation parameters, and aligning the underwater magnetic force image with the underwater geological image.
S5: performing image registration of the underwater geological image and the underwater magnetic force image based on the preliminary alignment result; the method comprises the following steps:
s501: dividing the images of the underwater geological image and the underwater magnetic force image into N corresponding windows respectively; and ensures that each window contains enough information for registration.
S502: calculating the similarity of each corresponding window; a Mean Square Error (MSE), a Structural Similarity Index (SSIM), etc. may be selected to measure the degree of similarity between overlapping regions.
S503: initializing a registration transformation model; the registration transformation model is used for describing the geometric relationship between the underwater geological image and the underwater magnetic force image; one of affine transformation and polynomial transformation can be selected for initialization.
S504: global optimization is carried out on the registration transformation model by utilizing an optimization algorithm, such as a gradient descent method, a genetic algorithm and the like, so that the sum of the similarity between all corresponding windows is maximized; the step integrates the registration results of all corresponding windows to ensure that the registration effect of the whole image is more accurate and consistent.
S505: performing image registration on the underwater geological image and the underwater magnetic image based on the globally optimized registration transformation model;
S506: checking the result of image registration, if at least one of the underwater geological image and the underwater magnetic image is empty or overlapped, interpolating the empty or overlapped area; the purpose of interpolation is to make the image smoother and more complete in space by estimating or deducing missing pixels, so as to ensure the integrity and continuity of the whole image.
In this step, based on the results of the preliminary alignment, further image registration is performed, and the position and orientation of the images are adjusted using intelligent algorithms to ensure that they are spatially fully aligned for better overlapping and fusion of the different sensor data.
S6: and performing image fusion on the underwater geological image and the underwater magnetic force image after image registration to generate an underwater section map. The method comprises the following steps:
S601: gradient information of the underwater geological image and the underwater magnetic force image is calculated respectively; and calculating the gradient value of the image by using a Sobel operator to obtain gradient information of each pixel point in the horizontal and vertical directions.
S602: calculating the weight of each pixel point on the underwater geological image and the underwater magnetic force image according to the gradient information; and assigning a weight according to the gradient value, wherein the pixel point with a larger gradient value has a higher weight so as to retain more edge and detail information.
S603: carrying out weighted average on gradient information of the underwater geological image and the underwater magnetic force image to obtain a fusion gradient image;
s604: and (3) carrying out gray level image reconstruction on the fused gradient image by adopting a gradient domain reconstruction algorithm, such as a total variation reconstruction algorithm, so as to obtain a fused underwater section map.
The gradient domain fusion method can better retain the structure and detail information of the image, and is suitable for geological exploration data fusion scenes in which the image quality and characteristics are required to be maintained. Through the steps, gradient domain fusion can be realized, the fused image can be obtained, and more accurate and comprehensive data support is provided for subsequent underwater geological analysis and application.
Example 2
This embodiment is a second embodiment of the present invention; based on the same inventive concept as that of embodiment 1, referring to fig. 2, this embodiment introduces an intelligent algorithm imaging underwater section mapping system, which includes a data collection module, a preprocessing module, an imaging module, a data analysis module, a registration module, an image fusion module, and an output display module; wherein:
The data collection module is used for collecting underwater topography data, including geological data, acoustic data and magnetic force data; the geological radar is integrated and used for collecting geological data; the multi-frequency side scan sonar is used for acquiring sound wave data; the magnetic force sensor is used for acquiring magnetic force data;
the preprocessing module is used for preprocessing the underwater topography data and comprises filtering noise reduction and data smoothing operation;
The imaging module is used for imaging the underwater topography data to obtain an underwater geological image and an underwater magnetic image;
The data analysis module is used for carrying out feature extraction and data comparison on the acoustic wave data, the underwater geologic image and the underwater magnetic force image, and determining the association between the acoustic wave data and the underwater geologic image and between the acoustic wave data and the underwater magnetic force image;
the registration module is used for registering the underwater geological image and the underwater magnetic force image; the method comprises the steps of performing preliminary alignment according to sound wave data provided by a sonar sensor, accurately registering an underwater geological image and an underwater magnetic image by utilizing an intelligent algorithm, and adjusting the position and the direction of the images to ensure that the images are completely aligned in space;
the image fusion module is used for fusing the registered underwater geological image and the underwater magnetic force image to generate a final underwater section map;
The output display module is used for visually displaying the underwater section map for related personnel to check and analyze; the interactive functions of zooming, translation, rotation and the like are provided, so that a user can conveniently check a specific area in detail; allowing the user to export the final underwater section map in a common image format (e.g., JPEG, PNG) or vector graphics format (e.g., SVG, DXF) facilitates report composition and further analysis.
The specific functions of the above modules are related to the underwater section mapping method of the intelligent algorithm imaging in reference to embodiment 1, and will not be described in detail.
Example 3
Based on the same inventive concept as the other embodiments, this embodiment introduces an electronic device, including a memory and a processor, where the memory is configured to store instructions, and the processor is configured to execute the instructions, so that the computer device executes an underwater cross-section mapping method for implementing the intelligent algorithm imaging provided in the foregoing embodiment.
Since the electronic device described in this embodiment is an electronic device used for implementing the underwater section mapping method for intelligent algorithm imaging in this embodiment, based on the underwater section mapping method for intelligent algorithm imaging described in this embodiment, those skilled in the art can understand the specific implementation of the electronic device and various modifications thereof, so how to implement the method in this embodiment of the application in this electronic device will not be described in detail herein. As long as the person skilled in the art implements the electronic equipment adopted by the underwater section mapping method of intelligent algorithm imaging in the embodiment of the application, the electronic equipment belongs to the scope of protection of the application.
Example 4
Based on the same inventive concept as the other embodiments, this embodiment introduces a computer-readable storage medium, on which a computer program is stored, which when executed by a processor, implements the underwater cross-section mapping method for intelligent algorithm imaging provided by the above embodiments.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The embodiments of the present invention have been described above with reference to the accompanying drawings, but the present invention is not limited to the above-described embodiments, which are merely illustrative and not restrictive, and many forms may be made by those having ordinary skill in the art without departing from the spirit of the present invention and the scope of the claims, which are all within the protection of the present invention.

Claims (5)

1. An intelligent algorithm imaging underwater section mapping method is characterized in that: the method comprises the following steps:
s1: collecting underwater topography data through a sensor;
s2: imaging based on the underwater topography data, including an underwater geological image and an underwater magnetic image;
The imaging method of the underwater geological image is to carry out offset imaging based on geological data; the imaging method of the underwater magnetic force image is to carry out magnetic anomaly inversion imaging based on magnetic force data;
S3: extracting the characteristics of the underwater topography data, the underwater geological image and the underwater magnetic force image; the method comprises the following steps:
S301: noise reduction processing is carried out on the sound wave data, the underwater geological image and the underwater magnetic image;
s302: extracting the position and form information of underwater topography based on the acoustic wave data after noise reduction to obtain the position of an underwater target point;
S303: extracting features of the noise-reduced underwater geological image and the noise-reduced underwater magnetic force image to obtain feature points of the underwater geological image and feature points of the underwater magnetic force image;
s4: performing feature matching and preliminary alignment of the underwater geological image and the underwater magnetic force image based on the feature extraction result; the method comprises the following steps:
s401: performing feature point matching to obtain corresponding feature points in the underwater geological image and the underwater magnetic image;
s402: positioning the underwater target point in an underwater geological image and an underwater magnetic image;
S403: estimating geometric transformation parameters between the underwater geological image and the underwater magnetic force image based on the result of feature matching and the positioning of the underwater target point in the underwater geological image and the underwater magnetic force image;
S404: performing translation and rotation operations on the underwater magnetic force image according to the geometric transformation parameters, and aligning the underwater magnetic force image with the underwater geological image;
S5: performing image registration of the underwater geological image and the underwater magnetic force image based on the preliminary alignment result; the method comprises the following steps:
s501: dividing the images of the underwater geological image and the underwater magnetic force image into N corresponding windows respectively;
S502: calculating the similarity of each corresponding window;
S503: initializing a registration transformation model; the registration transformation model is used for describing the geometric relationship between the underwater geological image and the underwater magnetic force image;
S504: performing global optimization on the registration transformation model by using an optimization algorithm so as to maximize the sum of the similarity between all corresponding windows;
s505: performing image registration on the underwater geological image and the underwater magnetic image based on the globally optimized registration transformation model;
s506: checking the result of image registration, if at least one of the underwater geological image and the underwater magnetic image is empty or overlapped, interpolating the empty or overlapped area;
S6: performing image fusion on the underwater geological image and the underwater magnetic force image after image registration to generate an underwater section map; the method comprises the following steps:
S601: gradient information of the underwater geological image and the underwater magnetic force image is calculated respectively;
s602: calculating the weight of each pixel point on the underwater geological image and the underwater magnetic force image according to the gradient information;
S603: carrying out weighted average on gradient information of the underwater geological image and the underwater magnetic force image to obtain a fusion gradient image;
S604: and (3) carrying out gray level image reconstruction on the fused gradient image by adopting a gradient domain reconstruction algorithm to obtain a fused underwater section map.
2. An intelligent algorithmic imaging underwater cross-section mapping method as claimed in claim 1, wherein: the underwater topography data comprises geological data, acoustic data and magnetic data.
3. An intelligent algorithm imaging underwater section mapping system, which is realized based on the intelligent algorithm imaging underwater section mapping method as set forth in any one of claims 1-2, and is characterized in that: the system comprises a data collection module, a preprocessing module, an imaging module, a data analysis module, a registration module, an image fusion module and an output display module; wherein:
the data collection module is used for collecting underwater topography data, including geological data, acoustic data and magnetic force data;
The preprocessing module is used for preprocessing the underwater topography data;
The imaging module is used for imaging the underwater topography data to obtain an underwater geological image and an underwater magnetic image;
the data analysis module is used for carrying out feature extraction and data comparison on the sound wave data, the underwater geological image and the underwater magnetic force image;
The registration module is used for registering the underwater geological image and the underwater magnetic force image;
the image fusion module is used for fusing the registered underwater geological image and the underwater magnetic force image to generate a final underwater section map;
And the output display module is used for visually displaying the underwater section map.
4. An electronic device, comprising: a memory for storing instructions; a processor for executing the instructions to cause the apparatus to perform operations implementing an underwater cross-section mapping method of intelligent algorithmic imaging as claimed in any of claims 1-2.
5. A computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements an underwater mapping method of intelligent algorithmic imaging as claimed in any of claims 1-2.
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