Moving target detection method based on low-rank full-connection tensor network decomposition and total variation model

Abstract

The invention discloses a moving target detection method based on low-rank full-connection tensor network decomposition and a total variation model, and belongs to the technical field of computer vision and real-time video analysis. Aiming at the problems of poor real-time performance, dynamic background misjudgment, serious noise interference and the like caused by neglect of space-time relevance, fixed rank constraint and high calculation complexity of a traditional method in a complex dynamic scene, the following technical scheme is provided: through full-connection tensor network (FCTN) decomposition, a common rank is utilized to realize accurate modeling of a dynamic background; interference from background leakage to foreground is reduced; incremental updating of time core parameters is carried out in combination with a sliding window strategy, and a historical space core is fixed to reduce calculation complexity; total variation (TV) regularization is combined to optimize a low-rank-sparse separation process, the continuity of a space gradient and a time gradient is restrained, the contour integrity of a moving target is enhanced, and noise is suppressed.

Description

Technical Field

[0001] The present invention belongs to the field of computer vision and real-time video analysis, and its specific design is a motion target detection method based on low-rank fully connected tensor network decomposition and total variation model. Background Art

[0002] The core task of moving target detection is to separate sparse moving targets from dynamic backgrounds. Traditional methods are mainly based on two types of technologies: (1) Low-rank sparse decomposition: The video frame matrix is ​​decomposed into a low-rank background and a sparse foreground, but the spatiotemporal correlation of the video data is ignored, resulting in dynamic background (such as swaying trees, ripples on the water surface) being misjudged as targets. (2) Tensor decomposition method: The spatiotemporal information is modeled by high-order tensors, but existing methods (such as Tucker decomposition) use fixed rank constraints, which makes it difficult to adapt to sudden changes in the scene. In addition, the computational complexity of the global decomposition is high and cannot meet real-time requirements.

[0003] In recent years, total variation (TV) models have been used to enhance contour continuity. However, direct application to frame-by-frame processing ignores temporal consistency, and joint optimization with tensor decomposition remains unresolved. Therefore, a collaborative optimization approach combining incremental tensor modeling and total variation models is needed to achieve high-precision, real-time detection in complex dynamic scenes. Summary of the Invention

[0004] To address these issues, the fully connected tensor network (FCTN) decomposition was proposed as a core innovation, and then optimized collaboratively with the total variation (TV) model:

[0005] (1) Fully connected interaction modeling:

[0006] FCTN achieves fully connected interactions through shared rank, allowing each core tensor to directly share multi-dimensional correlation information with other core tensors. Compared to the chain or centralized structures of traditional tensor decomposition, FCTN can fully capture the complex spatiotemporal coupling characteristics of dynamic backgrounds and significantly reduce interference from background leakage into the foreground.

[0007] (2) Incremental optimization mechanism:

[0008] Through the sliding window strategy, only the time core parameters related to the new frame are optimized, and the historical core tensor is fixed, which reduces the computational complexity and supports real-time processing.

[0009] (3) TV regularization collaborative optimization:

[0010] The total variation (TV) regularization term is jointly optimized in the low-rank-sparse separation to constrain the spatial and temporal gradients, suppress isolated noise and enhance the contour continuity of moving objects.

[0011] To address the problems of poor real-time performance and severe noise interference in moving target detection in complex dynamic scenes, this paper proposes a moving target detection method based on low-rank fully connected tensor network decomposition and total variation model. Through the joint optimization of incremental tensor modeling and low-rank-sparse separation, efficient and robust detection is achieved. The specific implementation steps are as follows:

[0012] Step 1: Video tensor construction and sliding window initialization

[0013] The input video stream is divided into consecutive frames in time order to construct the initial three-dimensional tensor: (0) ∈R Tw×H×W

[0014] Where T w is the window size (15 frames), H and W are the spatial dimensions.

[0015] Sliding window update formula:

[0016] Assume that the total window length is T w , each time the window is updated, it contains the latest T w frame.

[0017] When the new frame X t When it arrives, the window changes from X t -T w+1 Start intercepting to X t , automatically discarding old frames.

[0018] Step 1 preserves the spatiotemporal correlation of the video by dividing the video stream into sequential frames in chronological order and constructing a three-dimensional tensor (time × height × width), providing a structured data foundation for subsequent processing. A sliding window mechanism (default 15 frames) retains only the most recent frame and automatically discards older frames, significantly reducing memory usage and computational complexity while ensuring the algorithm can quickly respond to dynamic scene changes (such as sudden lighting changes or moving objects).

[0019] Step 2: Fully Connected Tensor Network (FCTN) Modeling

[0020] Define the FCTN decomposition form of the window tensor, and each core tensor Gk is fully connected through the common rank:

[0021]

[0022] where r pq To connect to the core G p With G qThe common rank of R pq .

[0023] FCTN decomposition achieves fully connected interactions through multi-dimensional common rank, accurately capturing the complexity of dynamic backgrounds. Compared to traditional chain tensor decompositions (such as Tucker or CP decomposition), FCTN's fully connected structure reduces the interference of background information leaking into the foreground.

[0024] Step 3: Incremental Core Tensor Update

[0025] 3.1 Core Tensor Extensions

[0026] Time Core Extension: Time Core Tensor Expand to The newly added last slice is initialized by weighted average of adjacent frames (weight coefficient α=0.8).

[0027]

[0028] Space core initialization: Space core and Inherit the parameters of the previous moment

[0029] 3.2 Alternating Optimization Updates for All Core Tensors

[0030] 1) Fix G2 and G3 and use the soft threshold iteration method (ISTA) to update G1. The objective function is:

[0031]

[0032] 2) Similarly, update G2 and G3 in sequence to ensure that only a single core is optimized in each iteration to reduce the computational burden.

[0033] Updated low-rank background Input to step 4, with sparse foreground S (t) Joint optimization.

[0034] Through incremental core tensor updates, the algorithm achieves efficient and stable low-rank background modeling in dynamic scenes.

[0035] Step 4: Joint optimization objective function of low-rank-sparse separation

[0036] Joint objective function:

[0037] Decompose the tensor into a low-rank background B (t) and sparse target S (t) , and apply TV regularization:

[0038]

[0039] FCTN norm: spatial gradient : Calculate the horizontal and vertical differences for each pixel

[0040]

[0041] Time gradient : Calculate the difference between corresponding pixels in adjacent frames

[0042]

[0043] || || 2,1 Norm: First calculate the L2 norm of the gradient vector of each pixel, and then calculate the L1 norm of all pixels.

[0044] λ3||S (t) ||1: Sparse constraint, L1 norm filters out significant motion areas and reduces false detections caused by small disturbances (such as leaf shaking). The formula in step 4 is the joint optimization objective function of low-rank-sparse separation, which aims to decompose the video frame into low-rank background (stable part) and sparse foreground (moving target) and enhance the separation effect through regularization. Low-rank constraint ||B (t) || FCTN Force the background to obey the low-rank property, effectively modeling the stable pattern of the dynamic background. TV regularization Constrain the spatiotemporal gradient continuity of the foreground, suppress noise and retain the complete outline of the target. Sparse constraint||S (t) ||1Filter out significant motion areas to reduce false detections caused by small disturbances (such as leaf shaking).

[0045] Step 5: Motion target extraction and window adaptation

[0046] 5.1 Moving Target Positioning and Binarization

[0047] Time dimension aggregation:

[0048] The sparse component tensor is summed along the time axis (first dimension) to generate a spatial saliency map:

[0049] The space-time mapping formula is

[0050] Where: T w : Time window length H, W: Space height and width S (t) : 3D sparse tensor (time, height, width) adaptive threshold segmentation:

[0051] The saliency map M for each channel (t) (:,:), use Otsu algorithm to calculate the optimal threshold τ and generate a binary mask:

[0052]

[0053] 5.2 Window Adjustment:

[0054] The degree of scene change is quantified by calculating the residual norm between the new frame and the updated background model.

[0055] Residual=||X new -B new || F

[0056] X new : Newly added frame (T w frame).

[0057] B new : Updated background model.

[0058] When the residual exceeds the historical background stability threshold, it is determined to be a scene mutation:

[0059] If Residual>η·median(||X old -B old || F ), then T′ w =T w +ΔT(ΔT=5)

[0060] η: threshold coefficient (default value η=2.0)

[0061] median(·): median of the residual norm within the historical window (statistics of the past Tw frames)

[0062] T w : Current window length (initial value T w =15)

[0063] 5.3 Maximum window length limit:

[0064] If the window is expanded after T w ′>50, then force the window to be reset to the initial size T w = 15 and reinitialize the FCTN core tensor. Targets are located through spatiotemporal saliency maps and adaptive threshold segmentation. Residual detection dynamically adjusts the window size to cope with sudden scene changes, and window length restrictions ensure long-term operational stability.

[0065] Optimize the process:

[0066] Initialization: Set the initial window T w =15, initialize FCTN core tensors G1, G2, G3.

[0067] Sliding window update: Every time a new frame is received, an incremental FCTN decomposition update B is performed ( t) .

[0068] Joint optimization: Alternately update B( t) and S( t) Until convergence (such as relative error < 1e-4).

[0069] Target extraction: For S( t) Sum along the time dimension and binarize.

[0070] Window adaptation: Dynamically adjust the window size T according to the residual detection results w . BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 This is a structural framework diagram of a moving target detection method based on low-rank fully connected tensor network decomposition and total variation model;

[0072] Figure 2 This is a flow chart of a moving target detection method based on low-rank fully connected tensor network decomposition and total variation model;

[0073] Figure 3 Schematic diagram of the fully connected tensor network (FCTN) structure. DETAILED DESCRIPTION

[0074] 1. Video tensor construction and sliding window initialization

[0075] Input processing: Split the video stream into consecutive frames in time sequence and store them in grayscale form.

[0076] 3D tensor construction: initial window size is set to T w = 15 frames, construct tensor χ (0) ∈R Tw×H×W , where H and W are the spatial resolutions of the frame (e.g. H=240, W=320).

[0077] Sliding window update: every time a new frame is received X t When, according to the formula Update the window, discard the oldest frame, and keep the window length fixed at T w .

[0078] 2. Fully connected tensor network modeling

[0079] FCTN decomposition form: decompose the window tensor into three core tensors G1 (time dimension), G2 (spatial height), and G3 (spatial width), and its interactive form is:

[0080]

[0081] The common rank r 12 =r 13 =r 23 =R (default R=10).

[0082] 3. Incremental Core Tensor Updates

[0083] Core Tensor Dynamic Scaling:

[0084] The dimension of the time core G1 is from T w-1 Expand to T w ,The newly added last slice is initialized by the weighted average of adjacent frames.

[0085] The spatial cores G2 and G3 inherit the parameters of the previous moment to avoid destroying the existing spatial structure.

[0086] Alternately optimize all cores:

[0087] Fix G2 and G3, optimize the last slice of the temporal core G1, and minimize the reconstruction error of the new frame.

[0088] Fixed G1 and G3, optimized the spatial core G2 to capture the background spatial correlation.

[0089] Fixed G1 and G2, optimized the spatial core G3, and enhanced the model's expressiveness.

[0090] 4. Low rank-sparse separation

[0091] Joint optimization objective: Solve iteratively using the alternating direction method of multipliers (ADMM):

[0092]

[0093] Where λ1 = 0.1, λ2 = 0.5, and λ3 = 0.3 (default value).

[0094] 5. Motion target extraction and window adaptation

[0095] Saliency map generation: Sparse tensor S (t) Sum along the time dimension to get the spatial mapping

[0096]

[0097] Adaptive threshold segmentation: Use the Otsu algorithm to calculate the optimal threshold τ for M(t) and generate a binary mask Mask (t) (h,w).

[0098] Window dynamic adjustment:

[0099] 1. Calculate the new frame residual Residual = || X new -B new|| F ;

[0100] 2. If Residual>2.0·median(||X old -B old || F ), expand the window to T w ′=T w +5;

[0101] 3. If T w ′>50, reset the window to T w = 15 and reinitialize the core tensor.

Claims

1. A moving target detection method based on low-rank fully connected tensor network decomposition and total variation model, characterized in that: include: (1) Video tensor construction and sliding window initialization: Divide the input video stream into consecutive frames in chronological order and construct the initial three-dimensional tensor χ (0) ∈R Tw×H×W , where T w is the window size, H and W are the spatial dimensions; the tensor χ(t) is updated by a sliding window strategy, adding a new frame each time and discarding the oldest frame; (2) Fully Connected Tensor Network (FCTN) modeling: The window tensor is decomposed into three core tensors G1, G2, and G3, and fully connected interactions are achieved through common rank. The decomposition form is: where r pq To connect the core tensor G p With G q The common rank of (3) Incremental core tensor update: By extending the last slice of the temporal core G1 and performing weighted initialization, inheriting the historical parameters of the spatial cores G2 and G3, and alternately optimizing and updating all core tensors, a low-rank background B is generated. (t) ; (4) Low-rank-sparse separation joint optimization: Construct an objective function to decompose the video tensor into a low-rank background B( t) and sparse foreground S( t) , and jointly optimize the total variation (TV) regularization term to constrain the continuity of spatial gradient and temporal gradient; (5) Motion target extraction and window adaptation: Sparse foreground is aggregated along the time dimension to generate a saliency map, a binary mask is generated through adaptive threshold segmentation, and the window size is dynamically adjusted according to residual detection.

2. The method according to claim 1, characterized in that The decomposition form of the fully connected tensor network (FCTN) described in step 2 is further defined as: The core tensors G1, G2, and G3 achieve full connectivity in time and space dimensions through a common rank, and the FCTN norm is defined as 3. The method according to claim 1, characterized in that The specific method of the incremental core tensor update in step 3 is to use the soft threshold iteration method (ISTA) to alternately optimize all core tensors.

4. The method according to claim 1, wherein The spatial gradient of TV regularization described in step 4 Defined as: Time gradient Defined as:

5. The method according to claim 1, characterized in that The window adaptation condition in step 5 is further defined as follows: when the residual satisfies Residual>η·median(||X old -B old || F ) The window length is increased by ΔT=5, where the default value of η is 2.

0.

6. The method according to claim 1, characterized in that The initial window size T w If set to 15 and the window is expanded for more than 50 frames, reset the window to the initial value and reinitialize the core tensor.

7. The method according to claim 1, characterized in that The adaptive threshold segmentation adopts Otsu algorithm, according to the saliency map M (t) (h,w) generates a binary mask Mask (t) (h,w).

8. The method according to claim 1, characterized in that The optimization process of the low-rank-sparse separation includes: Alternately update the low-rank background B( t) and sparse target S( t) Until the relative error is less than 1×10 -4 .

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