Shallow sea shell image detection method based on target-background coupled tensor decomposition

Abstract

The shallow sea shell image detection method based on target-background coupling tensor decomposition belongs to the technical fields of computer vision, image processing and tensor analysis. The present application proposes a radial-angular tensor representation method for shell margin structure, constructs a five-order radial-angular coupling tensor containing kernel, shell margin candidate and peripheral background area, reflects the spatial variation of shell from the inside to the background, converts target rotation into angular cyclic shift, and weakens the interference of complex underwater background. With the help of multi-component coupling tensor decomposition, the background, shell margin target, internal and external difference and sparse interference components are separated, and the underwater color deviation and target size variation are adapted. The angular closure and radial concentration constraints are introduced, and the cross-scale consistency is combined to generate a detection response tensor, so as to suppress false responses caused by local factors and reduce false detection and missed detection. The category prototype tensor subspace is constructed, and the shell positioning, boundary generation and classification counting are realized by relying on the reconstruction error matching.

Description

Technical Field

[0001] This invention belongs to the fields of computer vision, image processing and tensor analysis technology, and specifically relates to a method for detecting shallow sea shellfish images based on target-background coupled tensor decomposition. Background Technology

[0002] Shallow-sea shellfish aquaculture is an important component of the marine economy. The spatial location, type, and quantity of shellfish are crucial for assessing aquaculture density, growth status, and resource distribution. Traditional methods of manual underwater observation and sampling suffer from high operating costs, limited coverage, strong subjectivity, and difficulty in continuous monitoring. With the development of underwater cameras, unmanned vessels, and underwater robots, the use of underwater images for automatic detection, classification, and counting of shellfish has become an important technological direction for intelligent monitoring of shallow-sea aquaculture.

[0003] However, shallow sea imaging environments are susceptible to light absorption, scattering, suspended particles, and localized reflections, which can easily lead to color shifts, reduced contrast, blurred textures, and localized noise in acquired images. Shellfish targets also exhibit significant scale variations, inconsistent orientation, dense distribution, and localized occlusion; their shell colors blend well with backgrounds such as mud, rocks, and seaweed, and their shell edges can easily mix with background textures under low-contrast conditions, making it difficult to consistently distinguish target boundaries.

[0004] Current methods for detecting shallow-sea organisms mainly employ sliding windows, manual feature classification, and end-to-end methods based on convolutional neural networks, Transformers, or general object detection frameworks. Traditional methods typically rely on preset color, texture, or edge thresholds, exhibiting limited adaptability to underwater color variations, lighting changes, and complex seabed backgrounds. Deep learning methods can learn target features from labeled data, but usually require a large number of labeled samples and primarily rely on implicit discrimination through rectangular feature maps or candidate box features, failing to explicitly characterize the radial structural relationships between the mollusks' kernel, shell margin, and surrounding background. When training samples are limited, target scale varies significantly, or background textures are similar to the shell, false positives, false negatives, and class confusion are still prone to occur.

[0005] Tensor decomposition can preserve the multidimensional organization of image data and describe the correlation between space, color, and scale from multiple modalities. Existing tensor detection methods mostly construct tensors from the entire image, local rectangular image patches, or spatiotemporal image sequences, and use low-rank and sparse decomposition to separate the target, background, and noise. These methods usually do not set specific tensor modalities for the radial organization and angular closure characteristics of shellfish, and also lack a joint representation of the relationship between the intima region, shell edge candidate region, and peripheral background region; at the same time, ordinary low-rank-sparse decomposition is difficult to distinguish between high-contrast but unclosed reef edges, seaweed textures, and real shell edges of shellfish.

[0006] In summary, existing technologies lack a method for detecting shallow-sea shellfish images that can simultaneously represent the radial organization, angular closure, cross-scale variations, and target-background relationships of shellfish targets at the tensor structure level, and directly utilize the decomposition results to complete target localization, classification, and counting. Summary of the Invention

[0007] This invention addresses the problems of shallow-sea mollusks being similar to their background, exhibiting significant variations in scale and orientation, and having their shell margins susceptible to underwater degradation and local disturbances. It proposes a shallow-sea mollusk image detection method based on target-background coupled tensor decomposition.

[0008] The technical solution adopted in this invention is: a shallow-sea shellfish image detection method based on target-background coupled tensor decomposition, which includes, but is not limited to, the following steps:

[0009] Step 1: Perform multi-scale sampling on the input shallow sea image, rearrange each sampling region according to radial and angular partitions, and determine the kernel region, shell edge candidate region and peripheral background region respectively.

[0010] Step 2: Arrange the kernel region, shell edge candidate region and peripheral background region according to radial, angular, color, scale and region relationship to construct a fifth-order radial-angular coupled tensor with three types of region relationship slices.

[0011] Step 3: Construct the common relation direction, shell edge concentration relation direction and internal-external difference relation direction along the regional relation mode of the fifth-order radial-angular coupling tensor, and obtain the three-domain common component, shell edge target component and internal-external difference component respectively.

[0012] Step 4: By decomposing the coupled block term tensor with shared color-scale factor, angular cyclic continuity constraint, radial shell edge concentrated constraint and group sparse constraint, the fifth-order radial-angular coupled tensor is separated into background common component, shell edge target component, inner and outer difference component and sparse interference component.

[0013] Step 5: Generate a spatial-scale mollusk detection response tensor based on the radial energy concentration, angular closure, cross-scale consistency, and energy ratio of the background common component and sparse interference component of the target component at the shell edge.

[0014] Step 6: Search for a continuous high-response region in the detection response tensor that satisfies the conditions of radial concentration and angular closure, and determine the location and bounding box of the mollusk target based on its spatial center, optimal scale and angular coverage.

[0015] Step 7: Perform cyclic alignment and reconstruction error matching between the radial and angular target components corresponding to each shellfish target and the shellfish category prototype tensor. Determine the shellfish category and complete the classification and counting based on the matching results.

[0016] Step 1 involves multi-scale sampling of the input shallow sea image, rearranging the sampled regions according to radial and angular partitions, and determining the kernel region, shell edge candidate region, and peripheral background region, as detailed below:

[0017] This step involves uniformly sampling different spatial locations and target scales in the input image before constructing the fifth-order radial-angular coupled tensor. By converting ordinary planar image patches into radial-angular representations, the internal structure, shell edge structure, and external background of the mollusk target are made to form an ordered relationship along the radial direction, and the target rotation is mainly manifested as cyclic displacement in the angular mode.

[0018] Suppose the input shallow sea color image is:

[0019] ;

[0020] in, and These represent the height and width of the image, respectively. Indicates the number of color channels; for RGB images, Settings are provided by A set of scales consisting of sampling scales:

[0021] ;

[0022] in, Indicates the first The reference radius corresponding to each scale This represents the total number of scales. The scale set can be set according to the image resolution and the imaging size of the shellfish to be detected, for example, taking... for Each pixel is sampled by sliding the image along a preset step size to obtain the sampling center. ,in Indicates the sampling location number.

[0023] For sampling center and scale Establish polar coordinate sampling directions. Divide the angular direction into... The number of equally spaced partitions, the first The angular positions are:

[0024] ;

[0025] Three continuous regions are set radially, serving as the core region, shell edge candidate region, and peripheral background region, respectively. Let... The radial ranges corresponding to the three regions are respectively , and .in, , and This is the regional boundary scaling factor; for example, it can be taken as... , , However, the specific value can be adjusted according to the appearance and size of the shellfish.

[0026] To ensure that the three regions have a consistent tensor size, each region is sampled at equal intervals along the radial direction. The position. For the first position. Each region , its first The radial sampling distance is denoted as ,in Therefore, the radial-angular region tensor is obtained:

[0027] ,

[0028] in, Indicates the color channel index; and Represent the radial-angular tensors of the kernel region, the shell edge candidate region, and the peripheral background region, respectively, with dimensions of [missing information]. For non-integer coordinates, bilinear interpolation can be used to obtain the corresponding pixel values; for positions that exceed the image boundaries, mirror filling or edge copying can be used to complete the image.

[0029] This step does not predetermine whether a sampling location contains a molluskaloid target. The shell edge candidate region only represents the intermediate ring zone between the core region and the outer background region; whether it corresponds to the actual shell edge is determined jointly by subsequent coupled tensor decomposition and detection response. This yields three types of radial-angular region tensors at each sampling location and scale, which serve as input for step 2.

[0030] Step 2 arranges the kernel region, shell edge candidate region, and peripheral background region according to radial, angular, color, scale, and region relationship to construct a fifth-order radial-angular coupled tensor with three types of region relationship slices, as follows:

[0031] This step combines the three types of region tensors obtained in step 1 into the same high-order data structure, so that the radial relationship between regions is no longer represented by three independent image patches, but is explicitly represented by a dedicated region relationship mode.

[0032] For any sampling center ,Will The region tensors at each scale are stacked according to the scale mode and the region relation mode to construct a fifth-order radial-angular coupled tensor:

[0033] ;

[0034] The five modalities represent radial position, angular partitioning, color channels, sampling scale, and region relationships, respectively. Their elements are defined as follows:

[0035] ;

[0036] Among them, the regional relationship index , and These correspond to the kernel region, shell edge candidate region, and peripheral background region, respectively; the symbol ":" indicates that all elements of the corresponding mode are taken. Since the three regions use the same radial sampling number... Angular partition number and number of color channels Therefore, it is possible to form a one-to-one correspondence of three types of relation slices on the fifth mode.

[0037] In one implementation, to reduce the impact of different acquisition devices and local lighting intensities on subsequent decomposition, normalization can be performed on each scale and region slice:

[0038] ,

[0039] in, and These represent the mean and standard deviation of the corresponding slices, respectively. To prevent positive numbers with a denominator of zero, a normalized tensor can be used in subsequent processing. For the sake of simplicity, it will be referred to as ; .

[0040] Therefore, each sampling center corresponds to a fifth-order coupling tensor. This tensor simultaneously preserves the radial organization, angular closure, color information, scale variation, and three-domain relationship of the kernel-shell edge-background of the mollusk candidate region, serving as the input for constructing the region relationship direction in step 3.

[0041] Step 3 involves constructing the shared relation direction, the shell edge concentration relation direction, and the inside-outside difference relation direction along the regional relation modes of the fifth-order radial-angular coupling tensor, thereby obtaining the three-domain shared relation tensor, the shell edge concentration tensor, and the inside-outside difference tensor, as detailed below:

[0042] This step constructs mutually orthogonal regional relation directions for the three types of slices in the fifth mode: kernel, shell edge candidate, and peripheral background. This maps the common changes of the three domains, the relative enhancement of the shell edge, and the differences between the inside and outside to different relation subspaces.

[0043] The directions of shared relations, shell edge concentration relations, and internal-external difference relations are defined as follows:

[0044] ,

[0045] ,

[0046] ;

[0047] in, Used to represent the underwater lighting, substrate color, and slowly changing texture that coexist in the three areas; Used to represent the concentrated enhancement of shell edge candidate regions relative to the core region and the peripheral background region; Used to represent the color or texture difference between the kernel region and the surrounding background region. The superscript T indicates vector transpose. The three directions are pairwise orthogonal, forming a region relationship transformation matrix. .

[0048] Projecting the fifth-order coupling tensor along the fifth mode onto the three region relation directions, we obtain:

[0049] ;

[0050] in, This indicates that the tensor and vector are modally multiplied along the fifth mode; , and All The fourth-order tensors are called the three-domain common relation tensor, the shell edge concentration relation tensor, and the inside-outside difference relation tensor, respectively.

[0051] The relation tensor described above only represents the initial projection result obtained based on the region structure. The actual background shared structure, shell edge target structure, and sparse disturbance may still be mixed together. Therefore, in step 4, the structure separation is further completed through coupled block term tensor decomposition with special constraints.

[0052] Step 4 involves decomposing the fifth-order radial-angular coupled tensor into background common components, shell edge target components, internal-external difference components, and sparse interference components using coupled block term tensor decomposition with shared color-scale factor, angular cyclic continuity constraints, radial shell edge concentrated constraints, and group sparse constraints, as detailed below:

[0053] This step, based on the three regional relationship directions constructed in step 3, performs joint decomposition on the fifth-order coupling tensor of the same sampling center. Let the background common component, the shell edge target component, and the internal / external difference component be respectively... , and All three are the same size Let the sparse interference component be... Its size and The same. The following decomposition model is established:

[0054] ,

[0055] The symbol “∘” indicates that the fourth-order tensor and the region relation vector are expanded by the outer product along the fifth mode. Used to describe the background structures such as underwater lighting, silt, reefs and aquatic plants that coexist in the three types of areas; Used to describe closed or nearly closed structures that are mainly concentrated in candidate regions of the shell margin; Used to describe the overall color and texture differences between the kernel region and the surrounding background; Used to absorb bubbles, suspended particles, localized reflections, and abnormal pixels.

[0056] To maintain consistency in color and scale among different components, for any structural component Block terms with shared color and scale factors are used for representation:

[0057] ;

[0058] in, Representing components The number of block items contained; Represents the kernel tensor of the k-th block term; and These represent the factor matrices of the component in the radial and angular modes, respectively; and These represent the color factor matrix and scale factor matrix shared by the background common component, the shell edge target component, and the internal and external difference component, respectively; Represents the product of the nth modality. Shared. and This allows for a unified interpretation of underwater color distortion and scale variations across all structural components, while different radial and angular factors are used to preserve the spatial differences between the components.

[0059] To ensure that the target component of the shell edge has angular closure, an angular cyclic continuity constraint is defined:

[0060] ;

[0061] in, ;when season This cyclically connects the first and last angular slices. This constraint ensures continuous variation between adjacent angular partitions and explicitly maintains the shell edge structure. and The closure relationship at the direction.

[0062] To concentrate the target energy at the shell edge within the candidate region of the shell edge, a radial concentration weight is defined. It takes a smaller value near the center radial position and gradually increases as it moves away from the center, and is set as follows:

[0063] ;

[0064] in, Desirable , This indicates the central radial location of the candidate region at the shell edge. This constraint suppresses excessively dispersed responses within the candidate region at the shell edge.

[0065] Sparse constraints are applied to the sparse interference components using color channel groups:

[0066] ;

[0067] Considering the above constraints, the coupled tensor decomposition can be expressed as the following optimization problem:

[0068] ;

[0069] in, Denotes the Frobenius norm; This indicates the smoothing constraints of the background component in the angular and scale directions; , , , and These are non-negative weighting coefficients. An alternating minimization method can be used to sequentially update the structural components, block term kernel tensor, radial factor, angular factor, shared color factor, shared scale factor, and sparse disturbance components until the reconstruction error change is less than a preset threshold or the maximum number of iterations is reached.

[0070] Through the above decomposition, the background common component corresponding to each sampling center is obtained. Shell edge target components Internal and external difference components and sparse interference components This serves as the input for calculating the detection response in step 5.

[0071] Step 5 generates a spatial-scale mollusk detection response tensor based on the radial energy concentration, angular closure, cross-scale consistency, and energy ratio of background common components and sparse interference components of the target component at the shell margin, as detailed below:

[0072] This step converts the structural components obtained in step 4 into detection responses that can be used for target localization. For the sampling center... and the At each scale, target slices of the crustal edge were taken. Shared slices with background And calculate its energy:

[0073] ;

[0074] Using non-negative weights with a peak value at the central radial position Calculate the radial energy concentration factor:

[0075] ;

[0076] in, ,and It is advisable Gaussian weights centered on the center; To prevent positive numbers with a denominator of zero. The larger the value, the more concentrated the target energy is at the central radial position of the candidate region at the edge of the shell.

[0077] Calculate the angular closure coefficient based on the difference between the first and last angular slices:

[0078] ;

[0079] in, This represents an exponential function. The closer it is to 1, the more continuous the target component of the shell edge is at the beginning and end positions in the angular direction.

[0080] To suppress texture responses that occur only occasionally at a single scale, the calculation of the... The normalized tensor inner product between each scale and its adjacent scales yields the cross-scale consistency coefficient:

[0081] ;

[0082] in, Representing scale The set of adjacent scale indices, Indicates the number of scales in the set. This represents the tensor inner product. Since step 1 has already uniformly resampled all scales... Therefore, slices of different scales can be directly compared.

[0083] set up Indicates the first Sparse interference slices at various scales, defining the interference ratio:

[0084] ;

[0085] The detection response is defined by considering the target-to-background energy ratio, radial concentration, angular closure, cross-scale consistency, and interference ratio.

[0086] ;

[0087] Arrange all the response values ​​corresponding to the sampling centers and scales according to their original spatial locations to obtain the space-scale detection response tensor. ,in:

[0088] ;

[0089] For spatial locations not directly sampled, the response can be completed using nearest neighbor interpolation. The detection response achieves a larger value when the target energy at the shell edge is high, the radial distribution is concentrated, the angular structure is closed, adjacent scales are consistent, and there is little sparse interference. This value serves as the basis for determining the location and bounding box of the mollusk target in step 6.

[0090] Step 6 involves searching the detection response tensor for a continuous high-response region that satisfies both radial concentration and angular closure conditions. The location and bounding box of the mollusk target are then determined based on its spatial center, optimal scale, and angular coverage, as detailed below:

[0091] This step first sets the detection response threshold. Select a response of not less than [a certain value] within the spatial-scale domain. And it is greater than the local extremum of its neighborhood response. The candidate extremum set is represented as:

[0092] ,and It is the local maximum value within its spatial-scale neighborhood.

[0093] For candidate extrema According to its shell edge target component Calculate the effective set of angular directions. Let the first... The target energy for each angular partition is:

[0094] ;

[0095] when Not less than the preset ratio of maximum angular energy When this happens, the corner partition is recorded as a valid partition. The number of valid corner partitions is related to... The ratio of angular coverage to angular coverage is called the angular coverage ratio. When the angular coverage ratio of a response is lower than a preset threshold, the response is considered to lack closed shell edge support and is discarded.

[0096] For the retained candidate extrema, the high-energy support set is determined on the radial-angular plane:

[0097] ;

[0098] in, This represents the shell edge energy threshold ratio. The radial-angular coordinates in the support set are mapped back to the original coordinates according to the sampling relationship from step 1:

[0099] ;

[0100] in, Indicates the first The first candidate region of the crustal margin at the scale A radial sampling distance. The minimum and maximum values ​​of the mapped coordinates are taken to obtain the target bounding box:

[0101] ;

[0102] in, This indicates the target number. The target's spatial center can be the center of the bounding box, or it can be calculated using a weighted average of the response value and shell edge energy; the optimal target scale is the scale that produces local extrema. .

[0103] When multiple candidate bounding boxes highly overlap, compare their detection response with the optimal scale: for boxes with spatial centers close together and an overlap ratio exceeding a threshold. Candidate boxes are selected, and those with higher responses are retained. Adjacent high-response regions with significantly different spatial centers are also retained separately to adapt to scenarios with dense mollusks. The final output is a set of mollusk targets.

[0104] ;

[0105] in, Indicates the number of targets detected. , and They represent the first The bounding box, optimal scale, and detection response of each target.

[0106] Step 7 involves performing cyclic alignment and reconstruction error matching between the radial and angular target components corresponding to each shellfish target and the shellfish category prototype tensor. Based on the matching results, the shellfish category is determined and classification counting is completed, as detailed below:

[0107] This step includes the pre-construction of a category prototype tensor library and online matching of the targets to be detected. The category prototype tensor library is built based on shellfish samples with category labels, and does not require training convolutional networks or object detection networks.

[0108] For the Each shellfish category, collected Each labeled sample is used to obtain the corresponding shell edge target component according to steps 1 to 4. ,in To eliminate angular cyclic shift caused by different target orientations, a reference tensor of the same type is selected, and the position of maximum correlation is found through angular cyclic translation to align the samples. The aligned target components of the same type are then stacked along the sample modalities to construct a class sample tensor:

[0109] ;

[0110] For class sample tensor P k Perform higher-order singular value decomposition to obtain the class basis matrices on the four modes of radial, angular, color, and scale. , , and And construct the corresponding projection matrix:

[0111] ;

[0112] in, Indicates the first Class in The prototype subspace projection matrix on the modality. The four projection matrices together constitute the . The class prototype of mollusks is the quantum space.

[0113] For the output of step 6, the first For each target, take the fourth-order shell edge target component corresponding to its sampling center. .set up Indicates cyclic movement along the angular direction. One partition, For each category and cyclic displacement Projecting the moved target component onto the corresponding class prototype subspace yields the reconstructed tensor:

[0114] .

[0115] Calculate the first The first goal and the first Minimum normalized refactoring error between class prototypes:

[0116] ;

[0117] The class with the smallest reconstruction error is used as the predicted class of the target:

[0118] ;

[0119] in, This represents the category index that minimizes the reconstruction error. When the minimum reconstruction error for all categories is greater than a preset rejection threshold... In such cases, the target can be classified as an unknown target or a non-shellfish target, thereby reducing misclassification caused by reefs, seaweed, and other marine organisms.

[0120] After completing the category determination of all targets, the first... The counting results for mollusks are as follows:

[0121] ;

[0122] in, This is an indicator function; it takes the value 1 when the condition within the parentheses is true, and 0 otherwise. The final output includes the location, bounding box, optimal scale, detection response, category, and number of each category for each target, thus completing the detection, classification, and counting of shallow-sea mollusks.

[0123] Without altering the core technical concept of this invention, the number of sampling scales, radial sampling numbers, angular partition numbers, region boundary ratios, number of block items, constraint weights, and various judgment thresholds can all be adjusted according to image resolution, acquisition environment, and shellfish species. The specific parameters and solution methods described above are merely illustrative of the implementation process of this invention and do not constitute a limitation on the scope of protection of this invention.

[0124] This invention uses a radial-angular three-domain relation tensor as a unified data representation and employs coupled block term tensor decomposition with structural constraints as a target-background separation method, without relying on convolutional target detection networks or Transformer detection networks. By simultaneously utilizing the energy concentration of the shell margin in the radial direction, the cyclic continuity in the angular direction, and the structural consistency between adjacent scales, it can reduce false responses caused by mud, reefs, aquatic plants, suspended particles, and local reflections, thereby improving the stability of shellfish target detection, classification, and counting in complex shallow sea backgrounds.

[0125] Existing shallow-sea target detection methods are mostly based on rectangular image patches, general target detection networks, or ordinary low-rank sparse tensor decomposition, without simultaneously utilizing the radial organization, angular closure, and three-domain relationship of the inner core, shell edge, and surrounding background of mollusks. This invention differs from existing technologies in the following substantial ways:

[0126] (1) Construct a fifth-order radial-angular coupled tensor with three types of regional relationship slices: kernel, shell edge, and peripheral background.

[0127] This invention does not process the central image block and the background image block separately, nor does it simply stack rectangular image blocks along the sample or scale direction. Instead, it rearranges the image region into a radial-angular structure based on the sampling center, and treats the kernel region, shell edge candidate region, and peripheral background region as the region relation mode of the same tensor. Therefore, target rotation is mainly manifested as a cyclic shift in the angular mode, while the shell edge structure is manifested as a concentrated response of the radially central region relative to the inner and outer sides, providing a structured input directly corresponding to the morphology of mollusks for subsequent decomposition.

[0128] (2) A coupled block term tensor decomposition is proposed, which is jointly limited by the regional relation direction and the special structural constraints.

[0129] This invention establishes shared relationship directions, shell edge concentration directions, and internal / external difference relationship directions along the regional relationship mode. During the decomposition process, the background shared components, shell edge target components, and internal / external difference components share color and scale factors. Simultaneously, angular cyclic continuity constraints and radial concentration constraints are applied to the shell edge target components, and group sparsity constraints are applied to anomalous interferences. This structure does not solely rely on low rank and sparsity to separate the target from the background; rather, it incorporates the radial concentration, angular closure, and underwater color and scale variations of the shell edge into the same coupled decomposition model.

[0130] (3) Construct the detection response using the decomposed components, and complete the classification and counting using the cyclically aligned class prototype tensor;

[0131] This invention determines the space-scale detection response by combining the target energy at the shell edge, the shared background energy, the radial concentration, the angular closure, the cross-scale consistency, and the sparse interference ratio, rather than solely based on a single energy or local contrast. For the detected target, further cyclic alignment along the angular modes is performed, and the category is determined based on its reconstruction error in the tensor quantum space of each category's prototype. This allows target localization, orientation adaptation, category determination, and quantity statistics to form a continuous tensor processing flow.

[0132] The beneficial effects of this invention are: (1) It establishes a radial-angular tensor representation of the shell edge structure of mollusks, improving the separability of the target from the complex background. This invention arranges the multi-scale sampling regions according to radial position, angular partition, color channel, sampling scale, and regional relationship, and constructs a fifth-order radial-angular coupling tensor containing the core region, shell edge candidate region, and peripheral background region. This representation can explicitly characterize the spatial variation relationship of the mollusk target from the interior, shell edge to the peripheral background, and transforms the target rotation into cyclic displacement on the angular mode, which is beneficial to reduce the interference caused by similar backgrounds such as mud, reefs, and aquatic plants.

[0133] (2) Through multi-component coupled tensor decomposition, the background structure, shell edge structure, and local disturbances are separated collaboratively. This invention constructs common relationship directions, shell edge concentration relationship directions, and internal-external difference relationship directions along the regional relationship mode. Through coupled block term tensor decomposition with shared color-scale factors, the fifth-order coupled tensor is separated into background common components, shell edge target components, internal-external difference components, and sparse disturbance components. Shared color factors and scale factors can uniformly describe underwater color cast and target scale changes, while different radial and angular factors preserve the spatial differences of each structural component, thereby improving the accuracy of shellfish target structure separation.

[0134] (3) Combining angular closure and radial concentrated constraints improves the structural reliability of shellfish detection response.

[0135] This invention addresses the closed or near-closed shell edge characteristics of mollusks by introducing angular cyclic continuous constraints, cyclically connecting the first and last angular partitions. Simultaneously, radial shell edge concentration constraints concentrate the target response at the main radial position of the candidate shell edge region. Furthermore, by combining cross-scale consistency, background energy ratio, and sparse interference ratio to generate a spatial-scale detection response tensor, it can suppress accidental high responses caused solely by local textures, reflections, bubbles, or suspended particles, reducing false positives and false negatives in complex underwater backgrounds.

[0136] (4) Class prototype tensor matching is used to achieve classification and counting without relying on target detection networks. This invention constructs a class prototype tensor quantum space based on shellfish samples with class labels, and determines the target class through angular cyclic alignment and multimodal reconstruction error matching. This method can complete the location determination, bounding box generation, class identification and quantity statistics of shellfish targets without training convolutional networks or existing target detection networks; by setting an unknown target rejection threshold, it can also reduce misclassification caused by reefs, seaweed and other marine organisms, and improve the reliability of shallow sea shellfish image detection and counting results. Attached Figure Description

[0137] Figure 1 This is a general flowchart of an embodiment of the present invention.

[0138] Figure 2 This is a flowchart of multi-scale radial-angular sampling and three-domain partitioning in an embodiment of the present invention.

[0139] Figure 3 This is a flowchart of the fifth-order radial-angular coupling tensor and the direction of the region relationship in an embodiment of the present invention.

[0140] Figure 4 This is a flowchart illustrating the coupled tensor decomposition, detection response generation, and classification counting processes according to an embodiment of the present invention.

[0141] Figure 5This is a diagram showing the qualitative detection results of shallow-sea shellfish targets in an embodiment of the present invention. Detailed Implementation

[0142] To enable those skilled in the art to better understand the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them; other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort should all fall within the protection scope of the present invention.

[0143] A method for detecting shallow-sea mollusks based on target-background coupled tensor decomposition is proposed. This method first performs multi-scale spatial sampling on the input shallow-sea image, and then converts the sampling region into a radial-angular representation based on each sampling center. The region is then divided into an inner core region, a shell edge candidate region, and a peripheral background region according to radial range. Subsequently, these three types of regions are arranged according to radial position, angular partitioning, color channels, sampling scale, and regional relationships to construct a fifth-order radial-angular coupled tensor. This allows the internal structure of the mollusks, the shell edge structure, and the peripheral background to form a one-to-one corresponding slice within the same high-order data structure.

[0144] Based on the regional relational mode of the fifth-order radial-angular coupled tensor, three-domain common relational directions, shell edge concentration relational directions, and inner-outer difference relational directions are constructed to describe the common background changes in the three regions, the concentrated enhancement of the shell edge candidate region relative to the inner and outer regions, and the comprehensive color and texture differences between the core region and the peripheral background, respectively. On this basis, coupled block term tensor decomposition with shared color-scale factor, angular cyclic continuity constraint, radial shell edge concentration constraint, and group sparsity constraint is employed to separate the fifth-order coupled tensor into background common components, shell edge target components, inner-outer difference components, and sparse interference components.

[0145] Based on the energy ratio of the shell edge target component relative to the background common component, the radial energy concentration, the angular closure, cross-scale consistency, and the sparse interference ratio, a spatial-scale shellfish detection response tensor is generated. The spatial location, optimal scale, and bounding box of the shellfish target are then determined from continuous high-response regions. For each detected target, its radial-angular shell edge target component is angularly cyclically aligned and reconstructed with the pre-established shellfish category prototype tensor quantum space to obtain the target category and complete the classification and counting.

[0146] like Figure 1 As shown in the figure, this embodiment provides a method for detecting shallow sea shellfish images based on target-background coupled tensor decomposition. Figure 2 The process of multi-scale radial-angular sampling and the division of the core region, shell edge candidate region and peripheral background region is shown. Figure 3The construction process of the fifth-order radial-angular coupling tensor and the three types of region relation directions is shown; Figure 4 The process of coupled block term tensor decomposition, detection response generation, target localization, and category prototype tensor matching and counting is illustrated.

[0147] The specific implementation process of this embodiment includes the following seven steps:

[0148] Step 1 involves multi-scale sampling of the input shallow sea image, rearranging the sampled regions according to radial and angular partitions, and determining the kernel region, shell edge candidate region, and peripheral background region, as detailed below:

[0149] This step involves uniformly sampling different spatial locations and target scales in the input image before constructing the fifth-order radial-angular coupled tensor. By converting ordinary planar image patches into radial-angular representations, the internal structure, shell edge structure, and external background of the mollusk target are made to form an ordered relationship along the radial direction, and the target rotation is mainly manifested as cyclic displacement in the angular mode.

[0150] Suppose the input shallow sea color image is:

[0151] ;

[0152] in, and These represent the height and width of the image, respectively. Indicates the number of color channels; for RGB images, Settings are provided by A set of scales consisting of sampling scales:

[0153] ;

[0154] in, Indicates the first The reference radius corresponding to each scale This represents the total number of scales. The scale set can be set according to the image resolution and the imaging size of the shellfish to be detected, for example, taking... for Each pixel is sampled by sliding the image along a preset step size to obtain the sampling center. ,in Indicates the sampling location number.

[0155] For sampling center and scale Establish polar coordinate sampling directions. Divide the angular direction into... The number of equally spaced partitions, the first The angular positions are:

[0156] ;

[0157] Three continuous regions are set radially, serving as the core region, shell edge candidate region, and peripheral background region, respectively. Let... The radial ranges corresponding to the three regions are respectively , and .in, , and This is the regional boundary scaling factor; for example, it can be taken as... , , However, the specific value can be adjusted according to the appearance and size of the shellfish.

[0158] To ensure that the three regions have a consistent tensor size, each region is sampled at equal intervals along the radial direction. The position. For the first position. Each region , its first The radial sampling distance is denoted as ,in Therefore, the radial-angular region tensor is obtained:

[0159] ,

[0160] in, Indicates the color channel index; and Represent the radial-angular tensors of the kernel region, the shell edge candidate region, and the peripheral background region, respectively, with dimensions of [missing information]. For non-integer coordinates, bilinear interpolation can be used to obtain the corresponding pixel values; for positions that exceed the image boundaries, mirror filling or edge copying can be used to complete the image.

[0161] This step does not predetermine whether a sampling location contains a molluskaloid target. The shell edge candidate region only represents the intermediate ring zone between the core region and the outer background region; whether it corresponds to the actual shell edge is determined jointly by subsequent coupled tensor decomposition and detection response. This yields three types of radial-angular region tensors at each sampling location and scale, which serve as input for step 2.

[0162] Step 2 arranges the kernel region, shell edge candidate region, and peripheral background region according to radial, angular, color, scale, and region relationship to construct a fifth-order radial-angular coupled tensor with three types of region relationship slices, as follows:

[0163] This step combines the three types of region tensors obtained in step 1 into the same high-order data structure, so that the radial relationship between regions is no longer represented by three independent image patches, but is explicitly represented by a dedicated region relationship mode.

[0164] For any sampling center ,Will The region tensors at each scale are stacked according to the scale mode and the region relation mode to construct a fifth-order radial-angular coupled tensor:

[0165] ;

[0166] The five modalities represent radial position, angular partitioning, color channels, sampling scale, and region relationships, respectively. Their elements are defined as follows:

[0167] ;

[0168] Among them, the regional relationship index , and These correspond to the kernel region, shell edge candidate region, and peripheral background region, respectively; the symbol ":" indicates that all elements of the corresponding mode are taken. Since the three regions use the same radial sampling number... Angular partition number and number of color channels Therefore, it is possible to form a one-to-one correspondence of three types of relation slices on the fifth mode.

[0169] In one implementation, to reduce the impact of different acquisition devices and local lighting intensities on subsequent decomposition, normalization can be performed on each scale and region slice:

[0170] ,

[0171] in, and These represent the mean and standard deviation of the corresponding slices, respectively. To prevent positive numbers with a denominator of zero, a normalized tensor can be used in subsequent processing. For the sake of simplicity, it will be referred to as ; .

[0172] Therefore, each sampling center corresponds to a fifth-order coupling tensor. This tensor simultaneously preserves the radial organization, angular closure, color information, scale variation, and three-domain relationship of the kernel-shell edge-background of the mollusk candidate region, serving as the input for constructing the region relationship direction in step 3.

[0173] Step 3 involves constructing the shared relation direction, the shell edge concentration relation direction, and the inside-outside difference relation direction along the regional relation modes of the fifth-order radial-angular coupling tensor, thereby obtaining the three-domain shared relation tensor, the shell edge concentration tensor, and the inside-outside difference tensor, as detailed below:

[0174] This step constructs mutually orthogonal regional relation directions for the three types of slices in the fifth mode: kernel, shell edge candidate, and peripheral background. This maps the common changes of the three domains, the relative enhancement of the shell edge, and the differences between the inside and outside to different relation subspaces.

[0175] The directions of shared relations, shell edge concentration relations, and internal-external difference relations are defined as follows:

[0176] ,

[0177] ,

[0178] ;

[0179] in, Used to represent the underwater lighting, substrate color, and slowly changing texture that coexist in the three areas; Used to represent the concentrated enhancement of shell edge candidate regions relative to the core region and the peripheral background region; Used to represent the color or texture difference between the kernel region and the surrounding background region. The superscript T indicates vector transpose. The three directions are pairwise orthogonal, forming a region relationship transformation matrix. .

[0180] Projecting the fifth-order coupling tensor along the fifth mode onto the three region relation directions, we obtain:

[0181] ;

[0182] in, This indicates that the tensor and vector are modally multiplied along the fifth mode; , and All The fourth-order tensors are called the three-domain common relation tensor, the shell edge concentration relation tensor, and the inside-outside difference relation tensor, respectively.

[0183] The relation tensor described above only represents the initial projection result obtained based on the region structure. The actual background shared structure, shell edge target structure, and sparse disturbance may still be mixed together. Therefore, in step 4, the structure separation is further completed through coupled block term tensor decomposition with special constraints.

[0184] Step 4 involves decomposing the fifth-order radial-angular coupled tensor into background common components, shell edge target components, internal-external difference components, and sparse interference components using coupled block term tensor decomposition with shared color-scale factor, angular cyclic continuity constraints, radial shell edge concentrated constraints, and group sparse constraints, as detailed below:

[0185] This step, based on the three regional relationship directions constructed in step 3, performs joint decomposition on the fifth-order coupling tensor of the same sampling center. Let the background common component, the shell edge target component, and the internal / external difference component be respectively... , and All three are the same size Let the sparse interference component be... Its size and The same. The following decomposition model is established:

[0186] ;

[0187] The symbol “∘” indicates that the fourth-order tensor and the region relation vector are expanded by the outer product along the fifth mode. Used to describe the background structures such as underwater lighting, silt, reefs and aquatic plants that coexist in the three types of areas; Used to describe closed or nearly closed structures that are mainly concentrated in candidate regions of the shell margin; Used to describe the overall color and texture differences between the kernel region and the surrounding background; Used to absorb bubbles, suspended particles, localized reflections, and abnormal pixels.

[0188] To maintain consistency in color and scale among different components, for any structural component Block terms with shared color and scale factors are used for representation:

[0189] ;

[0190] in, Representing components The number of block items contained; Represents the kernel tensor of the k-th block term; and These represent the factor matrices of the component in the radial and angular modes, respectively; and These represent the color factor matrix and scale factor matrix shared by the background common component, the shell edge target component, and the internal and external difference component, respectively; Represents the product of the nth modality. Shared. and This allows for a unified interpretation of underwater color distortion and scale variations across all structural components, while different radial and angular factors are used to preserve the spatial differences between the components.

[0191] To ensure that the target component of the shell edge has angular closure, an angular cyclic continuity constraint is defined:

[0192] ;

[0193] in, ;when season This cyclically connects the first and last angular slices. This constraint ensures continuous variation between adjacent angular partitions and explicitly maintains the shell edge structure. and The closure relationship at the direction.

[0194] To concentrate the target energy at the shell edge within the candidate region of the shell edge, a radial concentration weight is defined. It takes a smaller value near the center radial position and gradually increases as it moves away from the center, and is set as follows:

[0195] ;

[0196] in, Desirable , This indicates the central radial location of the candidate region at the shell edge. This constraint suppresses excessively dispersed responses within the candidate region at the shell edge.

[0197] Sparse constraints are applied to the sparse interference components using color channel groups:

[0198] ;

[0199] Considering the above constraints, the coupled tensor decomposition can be expressed as the following optimization problem:

[0200] ;

[0201] in, Denotes the Frobenius norm; This indicates the smoothing constraints of the background component in the angular and scale directions; , , , and These are non-negative weighting coefficients. An alternating minimization method can be used to sequentially update the structural components, block term kernel tensor, radial factor, angular factor, shared color factor, shared scale factor, and sparse disturbance components until the reconstruction error change is less than a preset threshold or the maximum number of iterations is reached.

[0202] Through the above decomposition, the background common component corresponding to each sampling center is obtained. Shell edge target components Internal and external difference components and sparse interference components This serves as the input for calculating the detection response in step 5.

[0203] Step 5 generates a spatial-scale mollusk detection response tensor based on the radial energy concentration, angular closure, cross-scale consistency, and energy ratio of background common components and sparse interference components of the target component at the shell margin, as detailed below:

[0204] This step converts the structural components obtained in step 4 into detection responses that can be used for target localization. For the sampling center... and the At each scale, target slices of the crustal edge were taken. Shared slices with background And calculate its energy:

[0205] ;

[0206] Using non-negative weights with a peak value at the central radial position Calculate the radial energy concentration factor:

[0207] ;

[0208] in, ,and It is advisable Gaussian weights centered on the center; To prevent positive numbers with a denominator of zero. The larger the value, the more concentrated the target energy is at the central radial position of the candidate region at the edge of the shell.

[0209] Calculate the angular closure coefficient based on the difference between the first and last angular slices:

[0210] ;

[0211] in, This represents an exponential function. The closer it is to 1, the more continuous the target component of the shell edge is at the beginning and end positions in the angular direction.

[0212] To suppress texture responses that occur only occasionally at a single scale, the calculation of the... The normalized tensor inner product between each scale and its adjacent scales yields the cross-scale consistency coefficient:

[0213] ;

[0214] in, Representing scale The set of adjacent scale indices, Indicates the number of scales in the set. This represents the tensor inner product. Since step 1 has already uniformly resampled all scales... Therefore, slices of different scales can be directly compared.

[0215] set up Indicates the first Sparse interference slices at various scales, defining the interference ratio:

[0216] ;

[0217] The detection response is defined by considering the target-to-background energy ratio, radial concentration, angular closure, cross-scale consistency, and interference ratio.

[0218] ;

[0219] Arrange all the response values ​​corresponding to the sampling centers and scales according to their original spatial locations to obtain the space-scale detection response tensor. ,in:

[0220] ;

[0221] For spatial locations not directly sampled, the response can be completed using nearest neighbor interpolation. The detection response achieves a larger value when the target energy at the shell edge is high, the radial distribution is concentrated, the angular structure is closed, adjacent scales are consistent, and there is little sparse interference. This value serves as the basis for determining the location and bounding box of the mollusk target in step 6.

[0222] Step 6 involves searching the detection response tensor for a continuous high-response region that satisfies both radial concentration and angular closure conditions. The location and bounding box of the mollusk target are then determined based on its spatial center, optimal scale, and angular coverage, as detailed below:

[0223] This step first sets the detection response threshold. Select a response of not less than [value] within the spatial-scale domain. And it is greater than the local extremum of its neighborhood response. The candidate extremum set is represented as:

[0224] ,and It is the local maximum value within its spatial-scale neighborhood.

[0225] For candidate extrema According to its shell edge target component Calculate the effective set of angular directions. Let the first... The target energy for each angular partition is:

[0226] ;

[0227] when Not less than the preset ratio of maximum angular energy When this happens, the corner partition is recorded as a valid partition. The number of valid corner partitions is related to... The ratio of angular coverage to angular coverage is called the angular coverage ratio. When the angular coverage ratio of a response is lower than a preset threshold, the response is considered to lack closed shell edge support and is discarded.

[0228] For the retained candidate extrema, the high-energy support set is determined on the radial-angular plane:

[0229] ;

[0230] in, This represents the shell edge energy threshold ratio. The radial-angular coordinates in the support set are mapped back to the original coordinates according to the sampling relationship from step 1:

[0231] ;

[0232] in, Indicates the first The first candidate region of the crustal margin at the scale A radial sampling distance. The minimum and maximum values ​​of the mapped coordinates are taken to obtain the target bounding box:

[0233] ;

[0234] in, This indicates the target number. The target's spatial center can be the center of the bounding box, or it can be calculated using a weighted average of the response value and shell edge energy; the optimal target scale is the scale that produces local extrema. .

[0235] When multiple candidate bounding boxes highly overlap, compare their detection response with the optimal scale: for boxes with spatial centers close together and an overlap ratio exceeding a threshold. Candidate boxes are selected, and those with higher responses are retained. Adjacent high-response regions with significantly different spatial centers are also retained separately to adapt to scenarios with dense mollusks. The final output is a set of mollusk targets.

[0236] ;

[0237] in, Indicates the number of targets detected. , and They represent the first The bounding box, optimal scale, and detection response of each target.

[0238] Step 7 involves performing cyclic alignment and reconstruction error matching between the radial and angular target components corresponding to each shellfish target and the shellfish category prototype tensor. Based on the matching results, the shellfish category is determined and the classification and counting are completed, as follows:

[0239] This step includes the pre-construction of a category prototype tensor library and online matching of the targets to be detected. The category prototype tensor library is built based on shellfish samples with category labels, and does not require training convolutional networks or object detection networks.

[0240] For the Each shellfish category, collected Each labeled sample is used to obtain the corresponding shell edge target component according to steps 1 to 4. ,in To eliminate angular cyclic shift caused by different target orientations, a reference tensor of the same type is selected, and the position of maximum correlation is found through angular cyclic translation to align the samples. The aligned target components of the same type are then stacked along the sample modalities to construct a class sample tensor:

[0241] ;

[0242] For class sample tensor P k Perform higher-order singular value decomposition to obtain the class basis matrices on the four modes of radial, angular, color, and scale. , , and And construct the corresponding projection matrix:

[0243] ;

[0244] in, Indicates the first Class in The prototype subspace projection matrix on the modality. The four projection matrices together constitute the . The class prototype of mollusks is the quantum space.

[0245] For the output of step 6, the first For each target, take the fourth-order shell edge target component corresponding to its sampling center. .set up Indicates cyclic movement along the angular direction. One partition, For each category and cyclic displacement Projecting the moved target component onto the corresponding class prototype subspace yields the reconstructed tensor:

[0246] ;

[0247] Calculate the first The first goal and the first Minimum normalized refactoring error between class prototypes:

[0248] ;

[0249] The class with the smallest reconstruction error is used as the predicted class of the target:

[0250] ;

[0251] in, This represents the category index that minimizes the reconstruction error. When the minimum reconstruction error for all categories is greater than a preset rejection threshold... In such cases, the target can be classified as an unknown target or a non-shellfish target, thereby reducing misclassification caused by reefs, seaweed, and other marine organisms.

[0252] After completing the category determination of all targets, the first... The counting results for mollusks are as follows:

[0253] ;

[0254] in, This is an indicator function; it takes the value 1 when the condition within the parentheses is true, and 0 otherwise. The final output includes the location, bounding box, optimal scale, detection response, category, and number of each category for each target, thus completing the detection, classification, and counting of shallow-sea mollusks.

[0255] Table 1 shows a comparison of the detection performance of the embodiments of the present invention with that of existing detection methods;

[0256]

[0257] The above table shows the performance comparison results of the method of the present invention with existing detection methods such as Faster R-CNN, Deformable DETR, YOLOv5, YOLOv8 and Cascade R-CNN; Figure 5 The qualitative detection results of the method of the present invention on images of shellfish in shallow seas are shown.

[0258] Without altering the core technical concept of this invention, the number of sampling scales, radial sampling numbers, angular partition numbers, region boundary ratios, number of block items, constraint weights, and various judgment thresholds can all be adjusted according to image resolution, acquisition environment, and shellfish species. The specific parameters and solution methods described above are merely illustrative of the implementation process of this invention and do not constitute a limitation on the scope of protection of this invention.

[0259] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for detecting shallow-sea shellfish images based on target-background coupled tensor decomposition, characterized in that, Includes the following steps: Step 1: Perform multi-scale sampling on the input shallow sea image, rearrange the sampling regions according to radial and angular partitions, and determine the kernel region, shell edge candidate region and peripheral background region respectively; Step 2: Arrange the kernel region, shell edge candidate region and peripheral background region according to radial, angular, color, scale and region relationship to construct a fifth-order radial-angular coupling tensor with three types of region relationship slices; Step 3: Construct the common relation direction, shell edge concentration relation direction and internal-external difference relation direction along the regional relation mode of the fifth-order radial-angular coupling tensor, and obtain the three-domain common component, shell edge target component and internal-external difference component respectively; Step 4: By decomposing the coupled block term tensor with shared color-scale factor, angular cyclic continuity constraint, radial shell edge concentrated constraint and group sparse constraint, the fifth-order radial-angular coupled tensor is separated into background common component, shell edge target component, inner and outer difference component and sparse interference component. Step 5: Generate a spatial-scale mollusk detection response tensor based on the radial energy concentration, angular closure, cross-scale consistency, and energy ratio of the background common component and sparse interference component of the target component at the shell edge. Step 6: Search for a continuous high-response region in the detection response tensor that satisfies the conditions of radial concentration and angular closure, and determine the location and bounding box of the mollusk target based on its spatial center, optimal scale and angular coverage. Step 7: Perform cyclic alignment and reconstruction error matching between the radial and angular target components corresponding to each shellfish target and the shellfish category prototype tensor. Determine the shellfish category and complete the classification and counting based on the matching results.

2. The shallow-sea shellfish image detection method based on target-background coupled tensor decomposition according to claim 1, characterized in that, Step 1 is as follows: By converting ordinary planar image blocks into radial-angular representations, the internal structure, shell edge structure, and external background of the mollusk target are made to form an ordered relationship along the radial direction, and the target rotation is made to manifest as a cyclic shift in the angular mode. Suppose the input shallow sea color image is: ； in, and These represent the height and width of the image, respectively. Indicates the number of color channels; settings are determined by... A set of scales consisting of sampling scales: ； in, Indicates the first The reference radius corresponding to each scale The total number of scales is represented; the sampling center is obtained by sliding the image at a preset step size. ,in Indicates the sampling location number; For sampling center and scale Establish polar coordinate sampling direction; divide the angular direction into The number of equally spaced partitions, the first The angular positions are: ； Three continuous regions are set radially, serving as the core region, shell edge candidate region, and peripheral background region, respectively; The radial ranges corresponding to the three regions are respectively , and ; in, , and This refers to the regional boundary scaling factor. Sample each region at equal intervals along the radial direction. The position, for the first position Each region , its first The radial sampling distance is denoted as ,in Thus, the radial-angular region tensor is obtained: ； in, c represents the color channel index; and These represent the radial and angular tensors of the kernel region, the shell edge candidate region, and the peripheral background region, respectively.

3. The shallow-sea shellfish image detection method based on target-background coupled tensor decomposition according to claim 2, characterized in that, Step 2 is as follows: The radial-angular tensors of the kernel region, shell edge candidate region and peripheral background region are jointly arranged in the same high-order data structure and explicitly represented by the region relationship mode; For any sampling center ,Will The region tensors at each scale are stacked according to the scale mode and the region relation mode to construct a fifth-order radial-angular coupled tensor: ； The five modalities sequentially represent radial position, angular partitioning, color channel, sampling scale, and region relationship; their elements are defined as follows: ； Among them, the regional relationship index , and These correspond to the kernel region, shell edge candidate region, and peripheral background region, respectively; the symbol ":" indicates that all elements of the corresponding mode are taken; the three regions use the same radial sampling number. Angular partition number and number of color channels It can form a one-to-one correspondence of three types of relationship slices on the fifth mode.

4. The shallow-sea shellfish image detection method based on target-background coupled tensor decomposition according to claim 3, characterized in that, Normalization was performed on each scale and region slice to reduce the impact of different acquisition devices and local lighting intensities on subsequent decomposition: ； in, and These represent the mean and standard deviation of the corresponding slices, respectively. To prevent positive numbers with a denominator of zero, This is the normalized tensor.

5. The shallow-sea shellfish image detection method based on target-background coupled tensor decomposition according to claim 3, characterized in that, Step 3 is as follows: For the three types of slices in the fifth mode, namely kernel, shell edge candidate and peripheral background, construct mutually orthogonal regional relationship directions, and map the common changes of the three domains, the relative enhancement of the shell edge and the differences between the inside and outside to different relationship subspaces respectively. The directions of shared relations, shell edge concentration relations, and internal-external difference relations are defined as follows: ， ， ； in, Used to represent the underwater lighting, substrate color, and slowly changing texture that coexist in the three areas; Used to represent the concentrated enhancement of shell edge candidate regions relative to the core region and the peripheral background region; Used to represent the color or texture difference between the kernel region and the surrounding background region; the superscript T indicates vector transpose; the three directions are pairwise orthogonal, forming the region relationship transformation matrix. ; Projecting the fifth-order coupling tensor along the fifth mode onto the three region relation directions, we obtain: ； in, This indicates that the tensor and vector are modally multiplied along the fifth mode; , and These are respectively called the three-domain common relation tensor, the shell edge concentration relation tensor, and the internal-external difference relation tensor.

6. The shallow-sea shellfish image detection method based on target-background coupled tensor decomposition according to claim 5, characterized in that, Step 4 is as follows: Based on the three constructed regional relationship directions, the fifth-order coupled tensor of the same sampling center is jointly decomposed; Let the background common component, the shell edge target component, and the internal-external difference component be respectively... , and All three are the same size ; set up Sparse interference components are Its size and Same; establish the following decomposition model: ； Among them, the symbol "∘" represents the outer product expansion of the fourth-order tensor and the region relation vector along the fifth mode; Used to describe the background structure that exists in all three types of regions; Used to describe closed or nearly closed structures that are mainly concentrated in candidate regions of the shell margin; Used to describe the overall color and texture differences between the kernel region and the surrounding background; Used to absorb bubbles, suspended particles, localized reflections, and abnormal pixels; For any structural component Block terms with shared color and scale factors are used for representation: ； in, Representing components The number of block items contained; Represents the kernel tensor of the k-th block term; and These represent the factor matrices of the component in the radial and angular modes, respectively; and These represent the color factor matrix and scale factor matrix shared by the background common component, the shell edge target component, and the internal and external difference component, respectively; Represents the product of the nth mode; shared and This allows for a unified interpretation of underwater color cast and scale variations across all structural components, while different radial and angular factors are used to preserve the spatial differences between the components. Define angular cyclic continuity constraints to ensure that the target component of the shell edge has angular closure: ； in, ;when season This cyclically connects the first and last angular slices; this constraint causes adjacent angular partitions to change continuously and explicitly maintains the shell edge structure at 0 and Closure relationship at the direction; Define radial lumped weights And set: ； in, Pick , This indicates the radial position of the center of the candidate region of the shell edge; it takes a smaller value near the center radial position and gradually increases as it moves away from the center. Sparse constraints are applied to the sparse interference components using color channel groups: ； Considering the above constraints, the coupled tensor decomposition can be represented as the following optimization problem: ； in, Denotes the Frobenius norm; This indicates the smoothing constraints of the background component in the angular and scale directions; , , , and The non-negative weight coefficients are used; an alternating minimization method is adopted to update the structural components, block term kernel tensor, radial factor, angular factor, shared color factor, shared scale factor and sparse disturbance components in sequence until the reconstruction error change is less than the preset threshold or the maximum number of iterations is reached.

7. The shallow-sea mollusk image detection method based on target-background coupled tensor decomposition according to claim 6, characterized in that, Step 5 is specifically as follows: The background common components are... Shell edge target components Internal and external difference components and sparse interference components Converted into a detection response that can be used for target localization; For sampling center and the At each scale, target slices of the crustal edge were taken. Shared slices with background And calculate its energy: ； Using non-negative weights with a peak value at the central radial position Calculate the radial energy concentration factor: ； in, ,and It is advisable Gaussian weights centered on the center; To prevent positive numbers with a denominator of zero; The larger the value, the more concentrated the target energy is at the central radial position of the candidate region at the shell edge; Calculate the angular closure coefficient based on the difference between the first and last angular slices: ； in, Represents an exponential function; The closer it is to 1, the more continuous the target component of the shell edge is at the beginning and end positions in the angular direction; Calculate the first The normalized tensor inner product between each scale and its adjacent scales suppresses texture responses that occur only occasionally at a single scale, yielding a cross-scale consistency coefficient: ； in, Representing scale The set of adjacent scale indices, Indicates the number of scales in the set. Represents the tensor inner product; set up Indicates the first Sparse interference slices at various scales, defining the interference ratio: ； The detection response is defined by considering the target-to-background energy ratio, radial concentration, angular closure, cross-scale consistency, and interference ratio. ； Arrange all the response values ​​corresponding to the sampling centers and scales according to their original spatial locations to obtain the space-scale detection response tensor. ,in: ； For spatial locations that were not directly sampled, the response was completed using nearest neighbor interpolation.

8. The shallow-sea shellfish image detection method based on target-background coupled tensor decomposition according to claim 7, characterized in that, Step 6 is as follows: First, set the detection response threshold. Select a response of not less than [value] within the spatial-scale domain. And the local extrema of its neighborhood response are greater than the local extrema of its neighborhood response; the candidate extrema set is represented as: ,and It is the local maximum value within its spatial-scale neighborhood. For candidate extrema According to its shell edge target component Calculate the effective set of angular directions; let the first... The target energy for each angular partition is: ； when Not less than the preset ratio of maximum angular energy When this happens, the angular partition is recorded as a valid partition; the number of valid angular partitions is related to... The ratio is called the angular coverage; when the angular coverage of a response is lower than a preset threshold, the response is considered to lack closed shell edge support and is discarded. For the retained candidate extrema, the high-energy support set is determined on the radial-angular plane: ； in, The shell edge energy threshold ratio is used; the radial-angular coordinates in the support set are mapped back to the original coordinates according to the sampling relationship in step 1: ； in, Indicates the first The first candidate region of the crustal margin at the scale A radial sampling distance; the minimum and maximum values ​​of the mapped coordinates are taken respectively to obtain the target bounding box: ； in, The target number is indicated; the target spatial center is taken as the center of the bounding box, or calculated by weighting the response value and shell edge energy; the optimal target scale is the scale that produces local extrema. ; The final output is the set of shellfish targets: ； in, Indicates the number of targets detected. , and They represent the first The bounding box, optimal scale, and detection response of each target.

9. The shallow-sea shellfish image detection method based on target-background coupled tensor decomposition according to claim 8, characterized in that, When multiple candidate bounding boxes highly overlap, compare their detection response with the optimal scale: for boxes with spatial centers close together and an overlap ratio exceeding a threshold. Candidate boxes with higher responses are retained; adjacent high-response regions with significantly different spatial centers are retained separately to adapt to scenarios with dense shellfish distribution.

10. The shallow-sea shellfish image detection method based on target-background coupled tensor decomposition according to claim 8, characterized in that, Step 7 includes the pre-construction of the category prototype tensor library and online matching of the target to be detected; The category prototype tensor library is built based on category-labeled shellfish samples: For the Each shellfish category, collected Each labeled sample is used to obtain the corresponding shell edge target component according to steps 1 to 4. ,in ; Select similar reference tensors and find the position of maximum correlation by cyclic translation in the angular direction to align the samples; stack the aligned similar target components along the sample modalities to construct a class sample tensor: ； For class sample tensor P k Perform higher-order singular value decomposition to obtain the class basis matrices on the four modes of radial, angular, color, and scale. , , and And construct the corresponding projection matrix: ； in, Indicates the first Class in The prototype subspace projection matrix on the modality; the four projection matrices together constitute the _th ... The prototypical quantum space of mollusks; For the output of step 6, the first For each target, take the fourth-order shell edge target component corresponding to its sampling center. ;set up Indicates cyclic movement along the angular direction. One partition, For each category and cyclic displacement Projecting the moved target component onto the corresponding class prototype subspace yields the reconstructed tensor: ； Calculate the first The first goal and the first Minimum normalized refactoring error between class prototypes: ； The class with the smallest reconstruction error is used as the predicted class of the target: ； in, This represents the category index that minimizes the reconstruction error; when the minimum reconstruction error for all categories is greater than the preset rejection threshold... At that time, the target is classified as an unknown target or a non-shellfish target; After completing the category determination of all targets, the first... The counting results for mollusks are as follows: ； in, This is an indicator function that takes the value 1 when the condition in parentheses is true, and 0 otherwise. The final output includes the position, bounding box, optimal scale, detection response, category, and number of each category for each target, thus completing the detection, classification, and counting of shallow-sea shellfish.

Images