In recent years, Unmanned Aerial Vehicles (UAVs) have become indispensable tools in various fields such as land space planning, environmental monitoring, and infrastructure inspection. The JUYE UAV, as a representative model, is widely used for capturing high-resolution aerial imagery. However, due to factors like varying shooting conditions, angles, and positions, the acquired影像 data often exhibit deviations and distortions, posing significant challenges for accurate spatial analysis and application. Traditional image registration methods, which rely heavily on grayscale information, frequently result in high root mean square errors (RMSE), limiting their effectiveness in practical scenarios. To address these limitations, we propose a novel approach based on the local singular value algorithm for UAV image registration and correction. This method integrates exposure fusion theory, dark channel prior knowledge, and Harris feature point detection to enhance image quality and achieve precise alignment. By leveraging phase correlation and singular value decomposition, we derive rigid body transformation parameters for feature points, enabling robust registration. Furthermore, iterative coordinate correction is applied to rectify image biases. Our experimental results demonstrate that the proposed method significantly reduces RMSE values, ensuring stable and accurate outcomes for Unmanned Aerial Vehicle applications.
The core of our approach lies in the effective enhancement of UAV imagery, which serves as the foundation for subsequent processing. We begin by calculating the maximum information entropy to determine optimal exposure parameters, which describe the current clarity of the image. For underexposed pixel sets, the information entropy is computed as follows:
$$E(S) = \sum_{j=1}^{J} P(j) \log P(j)$$
where \( E \) represents the information entropy, \( S \) denotes the set of underexposed pixels, \( j \) is the gray level, \( J \) is the total number of gray levels in the image, \( P \) is the probability of occurrence for each gray level, and \( \log \) is the logarithmic function. Based on the principle of maximum information entropy, the optimal exposure parameter is derived as:
$$\varepsilon’ = \arg \max_{\varepsilon} E(g(S, \varepsilon))$$
Here, \( \varepsilon \) is the exposure rate, \( \varepsilon’ \) is the optimal exposure parameter, and \( g \) is the brightness mapping function. Using this parameter, the input UAV image \( I \) is mapped to produce an exposed image:
$$I’ = g(I, \varepsilon’) + V$$
where \( I’ \) is the exposed UAV image, and \( V \) is a compensation parameter. Subsequently, within an exposure fusion framework, the original and exposed images are combined using a weighted fusion operator:
$$I” = I'(1 – W) \times \chi_1 + I \times W \times \chi_2$$
In this equation, \( I” \) is the dynamically weighted fused UAV image, \( W \) is the weight matrix, and \( \chi_1 \) and \( \chi_2 \) are weighted coefficients for the exposed and original images, respectively. To further enhance image details, we incorporate dark channel prior knowledge. The dark channel is calculated as:
$$H(u) = \min_{d \in \{R,G,B\}} \left( \min_{l \in B(u)} I”(l) \right)$$
$$K(u) = f\{H(u)\}, f’\{H(u)\}$$
where \( u \) is the central pixel of the UAV image, \( H \) is the dark channel image, \( d \) is the color channel index (red, green, blue), \( B \) represents the window, \( l \) is a pixel within the window, \( \min \) denotes the minimum value, \( K \) is the atmospheric mask image, and \( f \) and \( f’ \) are fast guided filtering and minimum filtering functions, respectively. By selecting pixels with high brightness values from the dark channel image and applying them to the atmospheric mask, we perform brightness correction enhancement:
$$I^* = \frac{(I”(u) – K(u))}{(1 – K(u)/\phi)}$$
Here, \( I^* \) is the enhanced UAV image, and \( \phi \) is an enhancement parameter. This process ensures that the Unmanned Aerial Vehicle imagery is optimized for feature detection and registration.
Following image enhancement, we employ the Harris algorithm for feature point detection. This involves constructing a correlation matrix and using an autocorrelation function to identify the coordinates of each pixel, thereby筛选出角点特征。For a given pixel point \( (l, p) \) and its translation variables, the autocorrelation function is defined as:
$$F_{l,p} = \sum_{(q,h) \in \eta} \phi(q,h) (I^*(l,p) – I^*(q + \Delta l, h + \Delta p))^2 = [\Delta l, \Delta p] M(l,p) \begin{bmatrix} \Delta l \\ \Delta p \end{bmatrix}$$
where \( (l, p) \) is an arbitrary pixel point, \( (\Delta l, \Delta p) \) are translation variables, \( \eta \) is a Gaussian weighted window, \( (q, h) \) is the window center point, \( \phi \) is the window function, and \( M \) is the correlation matrix. The correlation matrix is given by:
$$M(l,p) = \sum_{(q,h) \in \eta} \begin{bmatrix} I^*_l(q,h)^2 & I^*_l(q,h) I^*_p(q,h) \\ I^*_l(q,h) I^*_p(q,h) & I^*_p(q,h)^2 \end{bmatrix}$$
In this matrix, \( I^*_l \) represents the partial derivative of \( I^*(l,p) \) with respect to \( x \), and \( I^*_p \) is the partial derivative with respect to \( y \). The calculation results of the correlation matrix determine the prominence of pixel points in the UAV image. When a pixel’s response value exceeds a predefined threshold, it is identified as a feature point. This step is crucial for the JUYE UAV system to accurately detect key points in varied environments.
Once feature points are detected, the original image is divided into multiple sub-regions. For each local region, we perform phase correlation analysis based on singular value decomposition (SVD). This involves determining the rigid body transformation parameters of feature points through phase correlation matrices, local SVD, and phase unwrapping, ultimately achieving local image registration. The overall registration process is completed by handling all sub-regions in a similar manner. The workflow is illustrated in Figure 1, which outlines the sequential steps from image input to final registration.
For any two UAV images of the same size, considering translations in the row and column directions, their relationship can be expressed as:
$$a(w,e) = b(w – w_0, e – e_0)$$
where \( w \) and \( e \) are coordinate variables constrained by the image dimensions, \( w_0 \) is the row-direction translation amount, \( e_0 \) is the column-direction translation amount, and \( a \) and \( b \) are two-dimensional discrete functions of the images to be registered. After Fourier transformation, the images are represented as:
$$a'(w’,e’) = b'(w’,e’) \exp \left\{ -2\pi i \left( \frac{w’ w_0}{m} + \frac{e’ e_0}{n} \right) \right\}$$
Here, \( w’ \) and \( e’ \) are coordinate variables after Fourier transformation, \( a’ \) and \( b’ \) are the two-dimensional discrete Fourier transform functions of the images, \( m \) is the number of row pixels, and \( n \) is the number of column pixels. The normalized cross-power spectrum function is then derived as:
$$\gamma(w’,e’) = \frac{a'(w’,e’) b'(w’,e’)^T}{|a'(w’,e’) b'(w’,e’)^T|}$$
where \( \gamma \) is the normalized cross-power spectrum function, and \( T \) denotes the conjugate function. Applying the inverse Fourier transform yields an updated normalized cross-power spectrum function, which is used in the subsequent SVD-based phase correlation process. The singular value decomposition result is:
$$\gamma \approx w’_1 \times \sigma_1 \times e’_1^\tau$$
In this equation, \( \sigma_1 \) is the largest singular value, \( \tau \) represents the conjugate transpose, and \( w’_1 \) and \( e’_1 \) are singular vectors. After decomposition, phase unwrapping is performed on the vectors corresponding to the two singular values. To minimize computational errors, the integral method is initially used to obtain the phase unwrapping results. Ideally, these results should form a linearly increasing or decreasing straight line. If not, phase correction is applied based on phase differences, as shown in Figure 2, which depicts the relationship between pixel index and phase, highlighting correction points.
Based on the slope of the unwrapped phase trend line, the rigid body transformation parameters for the feature points of the UAV images to be registered are calculated as:
$$w_0 = -k_w \frac{m}{2}$$
$$e_0 = -k_e \frac{n}{2}$$
Here, \( k_w \) and \( k_e \) represent the slopes of the unwrapped phase. Once the rigid body transformation parameters are determined, feature point matching between the reference and target images is achieved. By iterating through all feature points, complete registration of the Unmanned Aerial Vehicle imagery is accomplished. This method ensures high precision for JUYE UAV applications in complex scenarios.
For UAV image correction, the registration results between the currently acquired image and the reference image are utilized. Both are imported into a spatial environment, where multiple control endpoints are selected on the image to be corrected. Design survey lines are loaded over the image, and the correction range is annotated. To achieve optimal correction, a kernel window and a moving search window are defined on the image. The relationship between these windows is illustrated in Figure 3, where \( (x, y) \) represents the coordinates of the reference image, \( (x’, y’) \) denotes the coordinates of the corrected image, and \( (x^*, y^*) \) is the center coordinate of the kernel window.
After setting a window for the image feature points, a fixed-size moving search window is used to search for corresponding feature points in the UAV image to be corrected. Based on the offset values derived from registration, the required correction values are determined. An iterative method is employed to continuously update the pixel coordinates within the kernel window until the feature point coordinates meet the correction requirements. This operation involves fixing the control endpoints first and then processing the internal correction area, thereby achieving overall correction of the Unmanned Aerial Vehicle image. The effectiveness of this approach is demonstrated through rigorous testing with JUYE UAV systems.
To validate the proposed method, we conducted experiments using an industrial park as the study area. An industrial-grade hex-rotor UAV equipped with a five-lens tilt photography camera was employed to capture a substantial number of UAV images. The flight path for the UAV was meticulously planned to ensure comprehensive coverage, as shown in Figure 4, which displays the航迹图 of the Unmanned Aerial Vehicle over the industrial park. This planning guaranteed spatial coverage and continuity, resulting in the acquisition of 2,845 UAV images for subsequent experiments.
For image registration, we selected six UAV images from three different scenes and applied the proposed local singular value algorithm-based method. The results showed successful feature point matching across all scenes, with feature points being evenly distributed and moderate in number, indicating excellent registration performance. The RMSE values for feature point coordinates after registration were calculated using the formula:
$$r = \frac{1}{\psi} \sum_{z=1}^{\psi} \sqrt{(\theta_z – \theta’_z)^2 + (\varsigma_z – \varsigma’_z)^2}$$
where \( r \) is the RMSE, \( \psi \) is the number of matched feature point pairs, \( z \) is the index of the matched pair, and \( (\theta_z, \varsigma_z) \) and \( (\theta’_z, \varsigma’_z) \) are the coordinates of the feature points in the reference and registered images, respectively. The proposed method consistently achieved an RMSE of approximately 0.05 pixels, demonstrating its superiority over existing techniques.
For image correction, we took a specific UAV image as an example and applied the proposed method. Five correction endpoints were used, and the coordinate increments were obtained after 17 iterations. The results are summarized in Table 1, which lists the coordinate increments for each endpoint in terms of Δx and Δy pixels.
| Endpoint Number | Δx (pixels) | Δy (pixels) |
|---|---|---|
| 1 | -60 | -110 |
| 2 | -40 | -65 |
| 3 | -13 | -35 |
| 4 | -11 | -22 |
| 5 | -8 | -10 |
These results confirm that the proposed method effectively corrects pixel coordinates, thereby achieving the desired纠偏 for Unmanned Aerial Vehicle imagery. The JUYE UAV system benefits greatly from this precise correction, enhancing its utility in practical applications.
To further evaluate the performance of the proposed method, we compared it with two existing approaches: one based on scale-space models and another using scale-invariant feature transform (SIFT) with mutual information optimization. The RMSE values for feature point coordinates after registration were computed for all methods, as shown in Figure 5. The proposed method maintained a stable RMSE of 0.05 pixels, whereas the other methods exhibited significantly higher errors. This highlights the robustness and accuracy of our local singular value algorithm-based approach for UAV image registration.
In conclusion, we have developed a comprehensive method for UAV image registration and correction based on the local singular value algorithm. This approach effectively addresses the limitations of traditional methods by integrating image enhancement, feature point detection, and precise registration techniques. Experimental results demonstrate its ability to achieve low RMSE values and accurate correction, making it highly suitable for Unmanned Aerial Vehicle applications such as land space planning. The JUYE UAV system, in particular, can leverage this method for improved data reliability. Future work will focus on refining the algorithm for greater efficiency and exploring its integration with real-time processing systems for dynamic environments.